Universite Blaise

Pascal Clermont-Ferrand

Tiensin, T Anuwat Wiratsudakul

Thèse Dirigée Par

Professeur Mme Karine Chalvet-Monfray

Vetagro Sup

Dr David Biron

Dr Benoit Durand

MATHEMATICAL MODELLING OF THE INFECTIOUS SPREAD OF AVIAN INFLUENZA ON A BACKYARD CHICKEN PRODUCTION CHAIN IN THAILAND

Keywords: avian influenza, backyard chicken, epidemiology, mathematical model, Thailand

Highly pathogenic avian influenza H5N1 (HPAI H5N1) was recognized in Thailand by multiple epidemic waves and some sporadic cases between 2004 and 2008 but the risk of disease remerging in Thailand still remains up to present. Most of HPAI H5N1 confirmed outbreaks in Thailand occurred in backyard chicken populations. Backyard chickens are reared for many purposes including for additional cash income. Backyard chicken trade is informally managed by poultry traders which can be categorized into trader-slaughterhouse (TS), household trader (HT) and trader of trader (TT). These traders roam around different villages with the same unclean vehicle and facilities. Thus, their trade patterns in space and time are necessary to be elaborately studied. In our study, we developed a spatial compartmental stochastic dynamic model of backyard chicken trade network in a province of Thailand. Our model results indicated that the structure of poultry networks may contribute to HPAI H5N1 spread through overlapped catchment areas and long distance trades. Also, temporal variations of live poultry movements were observed during some major ritual festivals especially Chinese New Year. Subsequently, we developed an SIR model upon the dynamic model of backyard chicken trade network. It was assumed in this study that the disease can spread by two means: local spread to neighboring uninfected villages and spread by poultry traders. Then, we used this baseline infectious model to test multiple related control measures. Our ultimate results suggested that a complete ban of all poultry traders should be promptly implemented with poultry area disinfection campaign once the outbreak occurs.

La plupart des cas confirmé d'IAHP à H5N1 en Thaïlande ont eu lieu parmi les populations de volaille de basse-cour. Les poulets de basse-cour sont élevés sans biosécurité et libres de se promener dans la journée dans l'ensemble du village sans aucune clôture afin de s'alimenter. Ils sont gardés pendant la nuit auprès des maisons. Ainsi, la maladie peut facilement se propager au sein de ces populations.

Cependant, il n'est pas possible d'interdire aux villageois d'élever des poulets de basse-cour, parce que ces poulets font partie de leur mode de vie depuis la nuit des temps. Les poulets de basse-cour sont élevés pour de nombreuses raisons, y compris l'autoconsommation, le revenu supplémentaire, les combats de coqs et aussi pour certaines cérémonies religieuses ou traditionnelles.

Pour le commerce des poulets de basse-cour, le système est encore traditionnel.

La négociation entre les agriculteurs et les commerçants est géré par voie orale sans contacts écrits officiels. Les commerçants de volailles visitent de nombreux villages, collectent les poulets de basse-cour et fournissent les marchés traditionnels, en particulier, ceux des zones urbaines avec des exigences et un pouvoir d'achat élevés.

Dans notre étude, nous avons classé les commerçants de volailles en trois types selon leurs comportements commerciaux :

 en collecteur-abatteur (TS) qui recueille des poulets dans les villages et les abat lui-même, et ;  en sous-collecteur (HT), qui recueille les poulets dans les villages et vend à un autre type de collecteur (collecteur de collecteurs) ;

 collecteur de collecteurs (TT), qui regroupe les poulets recueillis par les sous-collecteurs (HT) et les abat.

Les activités de ces commerçants sont à risque pour la propagation de l'Influenza Aviaire Hautement Pathogène à H5N1, car ils se déplacent de villages en villages avec les mêmes véhicules et matériel non nettoyés. Ainsi, mieux connaitre les activités commerciales des collecteurs dans l'espace et le temps est nécessaire pour mieux quantifier le risque lié à ces activités.

A partir de nos questionnaires, d'observations que nous avons réalisé sur le terrain et de données officielles du recensement des poulets d'arrière-cour, nous avons développé un modèle spatial dynamique compartimental et stochastique de la filière de poulet de basse-cour dans la province Thaïlandaise de Phisanulok. Notre modèle prend, en particulier, en compte des variations temporelles de poulet de jardin commerce en raison de la demande considérable de poulets pendant quelques fêtes rituelles importantes en Thaïlande. Nous avons identifié cinq festivals importants qui influent directement sur la demande de poulets, y compris le Nouvel An Chinois en février, Festival de Qingming et Nouvel An Thaïlandais en Avril, festival de Hungry Ghost en août et le Nouvel An internationale en décembre.

La variation temporelle des populations de poulets de basse-cour dans les compartiments de village sont centrés sur le compartiment des poulets prêt-àvendre. Ce nombre chute fortement durant la période du Nouvel An chinois et diminue légèrement au cours des autres festivals avant d'être compensé et revenir au niveau initial en fin de l'année. Tandis que le nombre de poulets culmine dans les compartiments de collecteurs durant la période du Nouvel An chinois et de manière plus modérée pour les autres fêtes.

Les collecteurs de volailles ont visité environs trois quart des villages situés dans la zone modélisée. En outre, les zones des différents collecteurs se superposent comme nous avons pu l'observer sur le terrain. En moyenne, sur le village a été visité par deux commerçants. Le chevauchement des zones est susceptible de faciliter la propagation de l'IAHP à H5N1. En ce qui concerne les distances parcourues par les collecteurs TS et HT, nous avons observé sur le terrain qu'elles seulement à distance moyenne de 4,4 km de rayon autour de leurs domiciles en raison de leurs budgets limité et des types de véhicules utilisés (moto et motocyclette à trois roues). Tandis que les collecteurs TT, qui normalement utilisent des camions pick-up comme véhicule, peuvent se déplacer sur de plus grandes distances (25 km environ autour de leur domicile) et transporter beaucoup plus de poulets comparativement aux collecteurs HT et TS. En raison de la distance parcourue par les collecteurs, nous avons classé les collecteurs TS et HT en tant que « collecteurs de courtes distances » et TT en tant que « collecteurs de longues distances ».

Dans le chapitre 2, nous avons développé un modèle SIR couplé au modèle de dynamique de population de poulets dans la filière basse-cour du chapitre 1. Tous les compartiments au chapitre 1 ont ensuite été subdivisés selon leur statut vis-à-vis de l'IAHP à H5N1 : Sensible, Infectieux et Retirés. Dans les simulations, nous avons supposé qu'initialement l'IAHP était présente dans un village situé dans le district Muang (district contenant la capitale de la province et ses environs). Il a été supposé que la maladie se propageait par deux moyens :

 la propagation locale (déterminé par un kernel de transmission obtenu dans la littérature) à ses villages voisins non infectés et par ;  les collecteurs de poulets au travers de leurs activités commerciales.

Une analyse de sensibilité a été réalisée pour différents paramètres du modèle SIR à partir des valeurs obtenues dans la littérature. Avec les paramètres obtenus par l'étude de sensibilité qui maximise la probabilité d'avoir une propagation de l'IAHP àH5N1 et dans le cas où initialement qu'un seul village du district « Muang » est atteint, nous obtenons en moyenne une propagation de la maladie dans 44 % des cas avec 57 % des villages de la province Phisanulok atteints. A l'échelle de la province, lorsqu'il y a propagation de la maladie, elle dure en moyenne 65 jours et chaque village est resté infecté au maximum à 46 jours. Ensuite, différents scénarios de mesure de contrôle connexes ont été simulés à partir du modèle de référence. Nous avons constaté que l'interdiction seuls des « collecteurs de longues distances » ne réduisait en moyenne que de 4,4 % le nombre total de villages atteints tandis que l'interdiction de tous les collecteurs, quel que soit les distances parcourues diminuait le même indicateur de 30,5 % et que la probabilité de propagation de la maladie également était divisée par 3 fois par rapport au modèle de référence. D'autres mesures de contrôle complémentaires ont également été étudiées par simulation. Nos résultats indiquent que la combinaison de la désinfection des zones d'élevage des volailles dans les maisons et la désinfection des véhicules et du matériel des colleteurs était le moyen le plus efficace pour réduire la propagation d'un village à l'autre village quand les collecteurs continuent leur activité. Avec l'interdiction totale des activités des collecteurs et la désinfection des zones d'élevage des volailles dans les maisons, environ la moitié seulement des villages est touchée par la maladie. C'était la mesure la plus efficace parmi les mesures portant sur la restriction de l'activité des collecteurs et la désinfections des lieux. Nous n'avons pas pris en compte l'abattage des volailles qui nécessiterait de nombreuses autres hypothèses tel que le moment de l'alerte. Sur l'ensemble, la mesure de contrôle la plus efficace obtenue à partir de nos simulations était d'interdire tous les activités commerciales des collecteurs de volaille indépendamment les distances parcourues en collaboration avec une campagne de désinfection des zones d'élevage des volailles dans les villages. Cette mesure réduit la probabilité de propagation de maladie ainsi que nombre moyen de villages infectés par plus de 60 % par rapport au modèle de référence et ce n'est que cette mesure de contrôle qui a diminué le temps moyen où un village est infecté à moins d'une semaine.

Une des limites de cette étude est que le modèle dynamique stochastique de commerce de poulet de basse-cour a été simulé pendant la période non -épidémique.

Ainsi, les simulations des mesures de contrôle ont été élaborées sur le modèle de base applicables pour le début de l'épidémie lorsque les comportements des commerçants sont toujours les mêmes. Une fois informé de la présence d'un foyer confirmé, nos propositions de mesure de contrôle devraient être mises en oeuvre rapidement.

Nous nous souhaitons donc que les autorités vétérinaires thaïlandaises étudient nos suggestions comme une recommandation complémentaire dans le contrôle de la grippe aviaire H5N1 et d'autres maladies infectieuses dans les populations de volailles.

Dans la présente étude, nous recommandons d'interdire les activités commerciales des collecteurs indépendamment des distances parcourues.

Cependant, nous n'avons pas encore mis au point un modèle pour savoir combien de temps et dans quelles zones ils devraient être interdits. La période interdite ne doit pas être ni trop court (risque de reprise de la propagation de la IAHP à H5N1 avec la contamination résiduelle) ni trop long (risque d'activité illégale de la part des collecteurs). La période interdite approprié doit être examiné et modélisé dans une étude plus approfondie.

Dans les études futures, les mesures de contrôle qui sont actuellement mises en oeuvre par les autorités vétérinaires telles que l'abattage sanitaire pourraient prendre en compte sur la base du modèle actuel. Comparaison ou combinaison de notre mesure de contrôle proposée et les politiques actuelles de contrôle devraient être menées pour démontrer l'efficacité de chaque mesure et trouver la meilleure solution qui peut être directement appliqué une fois l'épidémie se produit. Many thanks to my beloved mother, father and friends for their encouragement which helps me surpass many difficulties in my life. Last but not least, I would like to gratefully thank ones whose names are not mentioned above who directly and indirectly supported me and my works.

To my beloved parents who always support me to this very far point.

To my French mother, Karine, who makes me a veterinarian who can also do mathematics.

Introduction

Since the emerging of highly pathogenic avian influenza (HPAI) subtype H5N1 in poultry in Hong Kong in 1997 followed by the wide spread of the disease in many countries in 2003, HPAI H5N1 has caused serious economic consequences and public health implications [START_REF] Coker | Emerging infectious diseases in southeast Asia: regional challenges to control[END_REF][START_REF] Neumann | H5N1 influenza viruses: outbreaks and biological properties[END_REF]. In Thailand, the virus was officially recognized in January 2004 and the last outbreak was announced in late 2008 [START_REF] Chantong | Poultry raising systems and highly pathogenic avian influenza outbreaks in Thailand: the situation, associations, and impacts[END_REF]. However, up present, the virus still presents in Thai neighboring countries i.e. Cambodia and Vietnam (OIE, 2014). The risk of remerging of HPAI H5N1 is not yet eliminated in Thailand It has been widely recognized that live poultry trade potentially promotes the spread of HPAI H5N1 in many countries (van den [START_REF] Van Den Berg | The role of the legal and illegal trade of live birds and avian products in the spread of avian influenza[END_REF] including Thailand [START_REF] Paul | Risk factors for highly pathogenic avian influenza (HPAI) H5N1 infection in backyard chicken farms, Thailand[END_REF]. Unlike other Asian counties, live poultry markets are very rare in Thailand [START_REF] Tiensin | Ecologic risk factor investigation of clusters of avian influenza A (H5N1) virus infection in Thailand[END_REF]. The poultry are traded via the activities of poultry traders. Nonetheless, details on mechanisms govern this live poultry trade have not yet been thoroughly explored especially in the backyard sector which the biosecurity level is very low.

In this thesis, background on avian influenza outbreak situations as well as control measures and the application of mathematical modeling on infectious disease were firstly reviewed. Then, followed by 2 main chapters of our works: (i) mathematical modeling of trade networks of backyard chickens and (ii) mathematical modeling of infectious spread of HPAI H5N1 along the trade networks obtained from the previous chapter. At the end, all of our study results were discussed and concluded in chapter of conclusion and perspectives.

In the current chapter, there are 5 topics involved consisting of (i) introduction which mentions about the importance of the study and our interests as well as illustrates the flow of the whole thesis, (ii) outbreaks of highly pathogenic avian influenza (HPAI) H5N1 which reviews HPAI H5N1 outbreak situation in different geographic levels and control measures applied, (iii) problem statement states about the problems and research gaps that lead us to conduct this study, (iv) objectives that we aimed at understanding from the study and (v) infectious disease modeling which reviews the general concepts of mathematical modeling and its application in infectious disease studies and goes deeper into avian influenza modeling and its application.

Outbreaks of highly pathogenic avian influenza (HPAI) H5N1

Global and regional situations HPAI H5N1 was firstly isolated from a flock of sick geese in the Guangdong Province of China in 1996 [START_REF] Xu | Genetic characterization of the pathogenic influenza A/Goose/Guangdong/1/96 (H5N1) virus: similarity of its hemagglutinin gene to those of H5N1 viruses from the 1997 outbreaks in Hong Kong[END_REF]. Afterward, a 3-year-old boy resided in Hong Kong was infected with H5N1 and died from respiratory failure in May 1997 [START_REF] Yee | Epidemiology of H5N1 avian influenza[END_REF]. By the end of 1997, 17 additional cases were reported and 6 of which died. 1.5 million chickens were culled to contain the outbreaks [START_REF] De Jong | Avian influenza A (H5N1)[END_REF]. Since then, HPAI H5N1 has been continually isolated from domestic and wild birds in Hong Kong, China, and Southeast Asia.

The virus was identified again in human in Vietnam in late 2003 and another epidemic of HPAI H5N1 began in Southeast Asia with sporadic cases in Europe, Africa, and the Middle East. The current endemic countries for HPAI H5N1 in poultry in January 2014 are Bangladesh, China, Egypt, India, Indonesia, and Vietnam (CDC, 2014). As of 13 January 2014, the outbreaks of HPAI H5N1 in poultry were notified to World Organization for Animal Health (OIE) from 52 countries located in three different continents as shown in Figure 1. According to the report of World Health Organization (WHO) on 25 February 2014, a total of 658 laboratory-confirmed human cases of H5N1 infection were notified from 15 countries and of these cases, 388 (59.0%) were fatal (WHO, 2014).

The graph and the map of confirmed human cases distribution in space and time were shown in Figure 2 and Figure 3.

In Southeast Asian region, seven out of ten ASEAN countries have been affected with HPAI H5N1 since 2003 including Cambodia, Indonesia, Lao PDR, Malaysia (Peninsular), Myanmar, Thailand and Viet Nam while Brunei Darussalam, Philippines and Singapore remained HPAI-free (ASEAN Secretariat, 2010). This region was also identified as one of the hot spots of HPAI H5N1 outbreaks [START_REF] Zhang | Risk signals of an influenza pandemic caused by highly pathogenic avian influenza subtype H5N1: spatio-temporal perspectives[END_REF] and many new HPAI H5N1 genetic variants have been emerging in the region through strong selective pressure [START_REF] Wei | Evolutionary and Ecological Dynamics of Transboundary Disease Caused by H5N1 Virus in Southeast Asia[END_REF]. In response to the outbreaks, more than 175 million birds were culled in Southeast Asia during [START_REF] Haitook | Options for Native Chicken (Gallus domesticus) Production in Northeastern Thailand[END_REF]-2010(ASEAN Secretariat, 2010). In January-February 2014, human cases infected with HPAI H5N1 were still reported from Cambodia, China and Vietnam (WHO, 2014) and the outbreaks in poultry were also notified from the same countries (OIE, 2014).

Since Southeast Asia is the hot spot of HPAI H5N1 outbreaks and the epidemics have been still being notified in the region, the risk of reintroduction and reemerging of HPAI H5N1 in Thailand still remains and the related authorities in Thailand must always prepare and be prompt in confronting the possible upcoming outbreaks.

Situation in Thailand

On 23 January 2004, the presence of HPAI H5N1 virus was officially declared in Thailand by National Institute of Animal Health (NIAH), Department of livestock development (DLD), Ministry of agriculture and cooperatives. The virus was isolated from a layer chicken farm located in Suphanburi province [START_REF] Tiensin | Highly pathogenic avian influenza H5N1, Thailand, 2004[END_REF]. In the same day, Ministry of public health (MOPH) of Thailand also announced the first laboratory-confirmed human case infected with HPAI H5N1. The case was a 6-yearboy from Kanchanaburi provinces which was subsequently fatal [START_REF] Auewarakul | The past and present threat of avian influenza in Thailand[END_REF].

Between 2004 and 2006, 25 laboratory-confirmed HPAI H5N1 human cases were reported in Thailand. Of which, 17 cases were fatal and no cases have been notified since 2006. Most human cases had a history of contact with infected backyard chickens [START_REF] Chunsuttiwat | Response to avian influenza and preparedness for pandemic influenza: Thailand's experience[END_REF].

In poultry, four major epidemic waves of HPAI H5N1 were reported from 2004 to 2006 [START_REF] Chantong | Poultry raising systems and highly pathogenic avian influenza outbreaks in Thailand: the situation, associations, and impacts[END_REF]. The poultry species reported in each wave include:

1. Wave I (23 January -24 May 2004): 63.7% of the cases and deaths were reported in backyard chickens and others were notified from broilers, laying hens, ducks, quails and other species.

2. Wave II (3 July 2004-12 April 2005): 57.6% of infected poultry were backyard chickens and 28.8% was ducks.

3.

Wave III (1 July -9 November 2005): 76.3% of infected poultry were backyard chickens followed by quails and ducks at 7.9% and 6.6% respectively. Spatially, the outbreaks were mostly reported from central region and lower part of northern region of Thailand as shown in Figure 5. As widely known, Thailand is one of the leading poultry meat producers in the world [START_REF] Haitook | Study on Chicken Meat Production for Small-Scale Farmers in Northest Thailand[END_REF]. It was estimated that more than 65 million birds were destroyed to halt the outbreaks and Thai government spent more than a billion Thai Baht (more than 35 million USD) to compensate poultry's owners [START_REF] Ranong | Structural Changes in Thailand's poultry sector: avian influenza and its aftermath[END_REF].

Moreover, almost 100,000 million Thai Baht (around 3,330 million USD) was lost in the poultry sector during the outbreaks (FAO., 2006).

Hence, HPAI H5N1 is not only important in term of animal and human health but also economically important and it is vital to have effective control strategies in confronting with the disease.

Control measures applied by Thai government

In Thailand, department of livestock development (DLD), ministry of agriculture and cooperatives is the officially authorized office that directly responses to outbreaks of HPAI H5N1. According to [START_REF] Burgos | Poultry, HPAI and Livelihoods in Thailand -A Review[END_REF], the chronological evolution of HPAI H5N1 control measure implementation during the outbreaks were revised and adapted for 4 times as shown in Table 1. [START_REF] Auewarakul | The past and present threat of avian influenza in Thailand[END_REF]. This campaign consists of two components [START_REF] Goutard | Optimizing early detection of avian influenza H5N1 in backyard and free-range poultry production systems in Thailand[END_REF]):

1. Clinical x-ray surveys that Thai integrated health authorities trained and recruited more than 750,000 village health volunteers (VHVs) to perform door-to-door actively searching for illness in humans or clinical cases in poultry according to current DLD case definition. HPAI H5N1 is suspected in case of (i) mortality rate of at least 5% in two days, (ii) sudden death, (iii) symptoms of respiratory tract, such as difficulty breathing, swelling face, (iv) neurologic symptoms such as seizures, neck twisting, (v) depression, diarrhea, ruffled feathers, reduction of feed consumption and egg production. The surveys were firstly performed nationwide and later on scale down to focus only high risk areas [START_REF] Ranong | Structural changes in Thailand's poultry sector and its social implications[END_REF].

2. Laboratory X-ray surveys which is based on testing of virological samples actively collected by veterinary authorities. Four backyard farms are selected from each village located in high risk areas using convenience sampling, and one pooled sample obtained five cloacal swabs of chickens is collected per farm. Free-grazing duck farms are visited nationwide and 12pooled cloacal swabs are collected per farm (Tiensin et al., 2007a).

The previous and current control measures as explained in this topic focus on only backyard chickens raised in the households while traditional trade of backyard chickens is overlooked. More understanding on backyard chicken trade can help us evaluate its role in HPAI H5N1 spreading. Then, we can apply some appropriate control policies and ultimately strengthen overall prevention and control strategies.

Problem statement

Up to date, the outbreaks of HPAI H5N1 are still occurring in many countries locating in different continents. As of January 2014, the first human case in the continent of America was reported. Canadian health authorities revealed that the patient had a history of travelling to Beijing before showing symptoms and later on died from infection (WHO, 2014). Nonetheless, the outbreaks in poultry have been sill continually notified to OIE from many countries including Vietnam which is located in Southeast Asia as Thailand (OIE, 2014).

A recent study revealed that brown headed-gull (Larus brunnicephalus), a longrange migratory bird, can travel from China to Vietnam passing many countries on its migratory corridor including Thailand and it has potential in spread the virus along the way [START_REF] Ratanakorn | Satellite tracking on the flyways of brown-headed gulls and their potential role in the spread of highly pathogenic avian influenza H5N1 virus[END_REF]. Although HPAI H5N1 has never been reported in Thailand since 2009, reemerging of the disease can occur anytime through reintroduction of the virus by migratory birds or other routes such as transboundary poultry movements. Effective surveillance, prevention and control measures are necessary to prevent the reoccurrence of the disease.

As mentioned earlier, the current HPAI H5N1 control measures have overlooked the activities of poultry traders that silently move poultry from villages to villages without any control registrations. Some trading characteristics of these traders have already been previously studied in subdistrict level by [START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF] but details studies in the village level that traders directly contact with farm households have not yet been revealed. Deeper understanding in trading mechanism and behavior in space and time can help us focus more on the points that we can strengthen our current prevention and control programs by taking into account these backyard trading activities.

Objectives

The study aimed to

1.

Comprehensively understand the mechanisms that govern traditional backyard chicken trade chain starting from the traditional backyard chicken production in the farm households until the chickens are slaughtered by poultry traders. At this step, the spatiotemporal movements of live backyard chickens by poultry traders are revealed.

2.

Illustrate HPAI H5N1 spreading in village level via (i) activities of poultry traders and (ii) local spread from infected villages to their neighboring villages.

3.

Simulating different scenarios of HPAI H5N1 control measures related with poultry traders and local spread. Ultimately, we can assess the importance of poultry traders in HPAI H5N1spread and we can suggest veterinary authorities how to control their activities during the outbreaks.

Mathematical modeling is the main tool used in the present study. We firstly gathered data related with backyard chicken population and backyard chicken trade behavior from official authorities and field surveys. Subsequently, these data were put into the model and backyard chicken trade chain was dynamically simulated.

Given that the real situation in the field was mimicked by the dynamic model, we then put susceptible-infectious-removed (SIR) model upon the previous model to show the spread of the disease. In the last step, we simulated different control measures to test their effectiveness.

Mathematical modeling is a kind of infectious disease modeling which spreads into the epidemiology field due to its cost-effectiveness and its efficiency.

Mathematical modeling and its applications is reviewed in details in the next topic.

Mathematical modeling of infectious diseases

Mathematical modeling makes it possible to test some scenarios that real experiments cannot be performed, for examples, infecting chickens in the village with HPAI H5N1 virus and observing how disease spread. Therefore, it is an effective tool in predicting, assessing, and controlling potential outbreaks of infectious diseases [START_REF] Siettos | Mathematical modeling of infectious disease dynamics[END_REF].

This topic includes 4 main parts: (i) evolution of mathematical modeling applying in infectious disease studies which reviews general ideas and origin of mathematical modeling on infectious diseases as well as its applications, (ii) Stochastic approaches in mathematical modeling of infectious diseases which introduces how stochastic processes came into use in infectious disease modeling, (iii) mass action law and pseudo-mass action law that represent different ways of contamination (iv) mathematical modeling of avian influenza and its applications that focus on how mathematical modeling involves in epidemiological study of avian influenza.

Evolution of mathematical modeling applying in infectious disease studies

Mathematical modeling has been involved in epidemiological study of vector borne and infectious diseases and also acted as a tool in guiding and assessing empirical control measures for more than 40 years [START_REF] Reiner | A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010[END_REF][START_REF] Stegeman | Use of epidemiologic models in the control of highly pathogenic avian influenza[END_REF]. Mathematical modelling allowed researchers to assess the contribution of the complex network of livestock movements and trading patterns on the spread of diseases, estimate the risk of disease introduction in different scenarios and further develop contingency plans for possible outbreaks [START_REF] Thrush | Stochastic simulation of live salmonid movement in England and Wales to predict potential spread of exotic pathogens[END_REF][START_REF] Ciccolini | Disease transmission on fragmented contact networks: livestock-associated Methicillin-resistant Staphylococcus aureus in the Danish pig-industry[END_REF][START_REF] Napp | Assessment of the risk of a bluetongue outbreak in Europe caused by Culicoides midges introduced through intracontinental transport and trade networks[END_REF].

Mathematical modeling applied in infectious disease dynamics is a systemic way of transforming data and assumptions regarding disease transmission into an estimation quantitatively of how an epidemic develops in space and time [START_REF] Wu | The use of mathematical models to inform influenza pandemic preparedness and response[END_REF].

However, this quantitative approach is not recent. are homogeneously mixing in a closed system [START_REF] Siettos | Mathematical modeling of infectious disease dynamics[END_REF] and the expected number of secondary cases per primary case in an entirely susceptible population was determined by basic reproductive number ( 0 R ) [START_REF] Roberts | The pluses and minuses of R0[END_REF]. The disease can persist and spread in the population if 0 R > 1 and the disease disappears when 0 R < 1 (Capaldi, 2009). However, the fundamental concept of homogeneous mixing of total population is not always true in reality. The concept of metapopulation is thus used to divide total population into different subpopulations and these subpopulations connect each other by some means of mobility flows [START_REF] Apolloni | Metapopulation epidemic models with heterogeneous mixing and travel behaviour[END_REF]. For instance, all backyard chickens in the province are account together as total population and the chickens raised in each village are subpopulation. The chickens in a subpopulation of village are possible to contact with chickens in other villages through animal movements which are managed by poultry traders or by other means. The contacts of each individual or subpopulation can also be explained in term of social network. Social network is a term obtained from social science which is defined as a group of elements and the connections between or among them (Martınez-Lopez et al., 2009). In term of infectious disease modeling, social network can facilitate in contacting individuals or subpopulations as per considered assumptions or empirical evidences and make the model more realistic.

As mathematical models improve ability to describe the spreading of the disease, they have been used to guide control measures. It is particularly the case of many mosquito borne diseases such as malaria, dengue, West Nile Virus and filariasis since 1970s [START_REF] Reiner | A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010[END_REF]. At the same time, the disciplines of infectious disease modeling have expanded to other emerging infectious diseases.

Mathematical model was used in assessing the strategic plans in controlling the diseases and interventions as well as providing some guides to choose the appropriate ones as shown in case of bovine spongiform encephalopathy (BSE) in sheep in Great Britain [START_REF] Fryer | Quantifying the risk from ovine BSE and the impact of control strategies[END_REF][START_REF] Gubbins | Simulation of the options for a national control programme to eradicate scrapie from Great Britain[END_REF], epidemics of foot-and-mouth disease in Japan [START_REF] Hayama | Mathematical model of the 2010 foot-and-mouth disease epidemic in Japan and evaluation of control measures[END_REF] and the human immunodeficiency virus (HIV) epidemic in Newark, New Jersey, the US [START_REF] Birger | Modeling the impact of interventions along the HIV continuum of care in Newark, New Jersey[END_REF]. Also, many mathematical models were applied with different approaches in case of avian influenza [START_REF] De Jong | Modelling control of avian influenza in poultry: the link with data[END_REF].

However, before we study mathematical modeling for avian influenza, it is necessary to elaborately focus on which mathematical model are being used in this case. Deterministic models, we previously talked about, are based on hypothesis that the size of population in each compartment must be large enough to meet mean field theory. The same results are always obtained from the same deterministic model depending only on initial conditions given to the model [START_REF] Chalvet-Monfray | Contribution to the modeling of epidemic processes in its environment[END_REF]. As the number in the exchange is low, deterministic models based on the mean field theory are no more adapted. In this case, stochastic models are applicable.

Stochastic approaches in mathematical modeling of infectious diseases

Stochastic model is more applicable than deterministic one in case of small size population [START_REF] Chaharborj | The use of generation stochastic models to study an epidemic disease[END_REF] [START_REF] Andersson | Stochastic epidemic models and their statistical analysis[END_REF]. The Reed-Frost model was a chain-binomial model which simply explains how an epidemic behaves over time.

In 1931, Greenwood proposed another chain-binomial model which assumed a constant probability of infection. Then, [START_REF] Bartlett | Some evolutionary stochastic process[END_REF] found the stochastic general epidemic model which proposes the removal of infected individuals from closed population [START_REF] Billard | The stochastic general epidemic model revisited and a generalization[END_REF]. Subsequently, Markov chain methods were developed in chain-binomial model by Bailey (1968) and [START_REF] Gani | A chain binomial study of inoculation in epidemics[END_REF][START_REF] Gani | Markov chain methods in chain binomial epidemic models[END_REF]. In a series of papers proposed by [START_REF] Becker | Estimation for discrete time branching processes with applications to epidemics[END_REF][START_REF] Becker | An epidemic chain model[END_REF][START_REF] Becker | A general chain binomial model for infectious diseases[END_REF], Reed-Frost model and Greenwood model were combined into a general chain binomial model [START_REF] Cairoli | Chain binomial epidemic models[END_REF].

For the deterministic as for stochastic models, there is also the same distinction about the way the contamination is simulated according the hypothesis is made : law of mass action or the pseudo -law mass action.

Law of mass action and pseudo-law of mass action

Law of mass action was originated from chemical studies and it was firstly called fundamental law of chemical kinetics and, later on, it has been applied in many area of science including mathematical epidemiology. The law was proposed by Norwegian scientists Guldberg and Waag during 1864-1879. It was explained by the law that, for any homogeneous system, the rate of any simple chemical reaction is proportional to the probability that the reacting molecules will be found together in a small volume. Thus, for mathematical modeling, the law is applicable to rates of transition of individuals between two interacting compartments of the whole population, for example, the rate that susceptible population become infected after an adequate contact [START_REF] Bubniakova | The mathematics of infectious diseases[END_REF].

In the hypothesis of the law of mass [START_REF] Hethcoth | The mathematics of infectiuos diseases[END_REF].

Nonetheless, law of mass action has been applied in mathematical modeling more than pseudo-law of mass action. The parameter 0 R depends on the size of population ( N ) in pseudo-law of mass action but it is independent in case of law of mass action [START_REF] De Jong | How does transmission of infection depend on population size?[END_REF]. In contrary to law of mass action, a population threshold is obtained in case of pseudo-law of mass action which the value below this threshold makes the disease cannot spread anymore because 0 1 R  [START_REF] Anderson | Population biology of infectious diseases: part I[END_REF]. This idea seems intuitive but it is still not sufficient to prove the hypothesis of pseudo-law of mass action. Indeed, with stochastic models, we also have the threshold values that follow law of mass action [START_REF] Dietz | Some problems in the theory of infectious disease transmission and control[END_REF]. In stochastic models, the disease can disappear when the population is low.

In large population, either in case of wildlife or livestock, it was evident that 0 R is not a linear function of N and law of mass action is the best option in explaining how disease spread in populations [START_REF] De Jong | How does transmission of infection depend on population size?[END_REF]. Moreover, law of mass action is still effective even in case of low population as shown in the study of [START_REF] Eble | A metaanalysis quantifying transmission parameters of FMDV strain O Taiwan among non-vaccinated and vaccinated pigs[END_REF] which applied law of mass action on only 10 animals per group.

Among the direct transmission diseases studied by models drift from the Kermack and McKendrick models, the influenza has an important place due to its public health importance and the interest of dynamic models to simulate the outbreaks for this very contagious virus and its surveillance and control measures.

Mathematical modeling of Avian Influenza

Mathematical models have been more and more accepted, during the last decade, as a tool in designing surveillance programs and assessing control measures in many infectious diseases including HPAI H5N1 [START_REF] Stegeman | Use of epidemiologic models in the control of highly pathogenic avian influenza[END_REF].

In epidemiological study of HPAI H5N1, mathematical modeling has been applied in many steps including (i) quantifying transmission parameters [START_REF] Bett | Transmission Rate and Reproductive Number of the H5N1 Highly Pathogenic Avian Influenza Virus During the December 2005-July 2008 Epidemic in Nigeria[END_REF][START_REF] Bouma | Estimation of transmission parameters of H5N1 avian influenza virus in chickens[END_REF], (ii) modeling how disease spread in populations [START_REF] Ayyalasomayajula | A network model of H5N1 avian influenza transmission dynamics in domestic cats[END_REF][START_REF] Breban | The role of environmental transmission in recurrent avian influenza epidemics[END_REF][START_REF] Penny | Transmission dynamics of highly pathogenic avian influenza at Lake Constance (Europe) during the outbreak of winter 2005-2006[END_REF] and (iii) assessing current control strategic plans and providing some suggestions and guidelines [START_REF] De Jong | Modelling control of avian influenza in poultry: the link with data[END_REF][START_REF] El Masry | Modelling influenza A H5N1 vaccination strategy scenarios in the household poultry sector in Egypt[END_REF][START_REF] Elbakidze | Modeling of Avian Influenza Mitigation Policies within the Backyard Segment of the Poultry Sector[END_REF].

Among the tools used in studying how HPAI spread in population, spatial modelling is widely used so far. Spatial modeling applied in animal and public health has mainly 3 purposes: (i) explaining risk regarding existing spatial patterns, (ii) trying to study biological mechanisms related with disease occurrences and (iii) predicting the trends in medium and long-term future (temporal predictions) or in different geographic locations (spatial prediction) [START_REF] Stevens | Spatial modelling of disease using data-and knowledge-driven approaches[END_REF]. The methods of spatial modeling can be integrated with SIR model to form spatial SIR model as developed in the studies of Boender et al., 2007a[START_REF] Menach | Key strategies for reducing spread of avian influenza among commercial poultry holdings: lessons for transmission to humans[END_REF][START_REF] Truscott | Control of a highly pathogenic H5N1 avian influenza outbreak in the GB poultry flock[END_REF]. Boender et al., 2007 estimated transmission kernel of HPAI between poultry farms using outbreaks data in the Netherlands in 2003. [START_REF] Menach | Key strategies for reducing spread of avian influenza among commercial poultry holdings: lessons for transmission to humans[END_REF] stochastically modeled between farms transmission of avian influenza based on 2003 H7N7 outbreaks in the Netherlands. High-risk areas were mapped and control measures were also evaluated in this study. In the study of Truscott et al., 2007, transmission Nonetheless, there were not any mathematical models developed so far for HPAI H5N1 epidemics in Thailand in the steps of disease spread modeling and control measure evaluation. Only some statistical risk models on HPAI H5N1 spread in subdistrict level are present to dates [START_REF] Paul | Anthropogenic factors and the risk of highly pathogenic avian influenza H5N1: prospects from a spatial-based model[END_REF][START_REF] Vergne | Zero-inflated models for identifying disease risk factors when case detection is imperfect: application to highly pathogenic avian influenza H5N1 in Thailand[END_REF].

The present study thus fulfills the gaps by developing mathematical models in all three consecutive steps include: (i) finding out transmission parameters more delicately in village level, (ii) illustrating how disease spread based on obtained parameters and (iii) testing different control measures.

However, prior to taking into account the disease, the first mathematical model we must develop is one to quantify the flows of target population, backyard chickens in the traditional trade networks in our case, in space and time and later on use the obtained model as basis in developing disease model as discussed earlier. The present chapter is divided into 5 sections including (i) backyard chicken production chain that gives overviews on poultry production systems in Thailand, backyard chicken rearing system, backyard chicken trade system and effects of ritual festivals on backyard chicken trade, (ii) data source which describes our study area (Phitsanulok province), backyard chicken population data obtained from 'x-ray' campaign and our field survey description, (iii) mathematical modeling and social network analysis which explained concepts of our dynamic models, parameters used, mathematical equations and how we analyzed the models with social network tools.

(iv) results obtained from filed studies, model output and social network analysis and, finally, (v) discussion and conclusion based on analyzed data, information and outputs earlier explained within the chapter and comparison our results with other related publications.

Backyard chicken production chain 1.2.1. Poultry production systems in Thailand

The poultry production system in Thailand can be categorized into 4 sectors according to the level of biosecurity. These four sectors include (i) industrial integrated system with high biosecurity (poultry are always kept in closed houses),

(ii) commercial poultry production system with moderate biosecurity (poultry are kept in closed houses or houses with netting), (iii) commercial poultry production system with low biosecurity (poultry are kept in open houses) and (iv) backyard poultry production system with no biosecurity (backyard chicken or free-grazing duck) [START_REF] Haitook | Study on Chicken Meat Production for Small-Scale Farmers in Northest Thailand[END_REF]Tiensin et al., 2007a;[START_REF] Chantong | Poultry raising systems and highly pathogenic avian influenza outbreaks in Thailand: the situation, associations, and impacts[END_REF].

The latter two sectors can produce only around 10% of overall poultry production in the country but 98% of poultry producers are accounted into these sectors [START_REF] Heft-Neal | Supply Chain Auditing for Poultry Production in Thailand[END_REF].

Backyard chicken rearing system

Backyard chickens have long been a part of traditional Thai lifestyle.

Nowadays, around 80% of the households with backyard chickens are located in remote areas [START_REF] Haitook | Options for Native Chicken (Gallus domesticus) Production in Northeastern Thailand[END_REF][START_REF] Choprakarn | Village chicken production systems in Thailand[END_REF]. Each household can produce around 30-50 birds of marketable size annually. This represents 100-120 million birds for the whole country.

Traditionally, the chickens are mainly produced from the parent stocks kept in the households consisting of one cockerel and three to five hens. All ages and sexes of chickens are raised together. The chickens are allowed to freely scavenge during day time and they are confined in a simple farm house or shed at night [START_REF] Haitook | Study on Chicken Meat Production for Small-Scale Farmers in Northest Thailand[END_REF][START_REF] Choprakarn | Village chicken production systems in Thailand[END_REF][START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF]. Backyard chickens are well adapted to the local and harsh environment of rural areas. However, the survival rate of backyard chickens, from one-day old to marketable size, is only around 30-50 % due to lack of vaccinations, poor management and seasonal changing [START_REF] Choprakarn | Village chicken production systems in Thailand[END_REF].

Backyard chicken is an important protein source for Thais especially in the rural areas. These chickens are raised for many purposes including home consumption, cash income, cock fighting and also for some religious or traditional ceremonies.

Moreover, backyard chicken meat is classified as a premium product which has the reputation to be tastier and healthier than broiler meat [START_REF] Haitook | Study on Chicken Meat Production for Small-Scale Farmers in Northest Thailand[END_REF][START_REF] Duangjinda | Impacts of Avian Influenza outbreaks on indigenous chicken genetic resources in Thailand[END_REF][START_REF] Heft-Neal | Assessment of Smallholder Indigenous Poultry Producer Viability in Thailand[END_REF][START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF].

Backyard chickens were globally aggregated by poultry traders via the traditional trading network and supplied to the wet markets, especially, markets with high demands and purchasing power located in urban areas [START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF].

Backyard chicken trade system

Farmers who keep backyard chicken at home, normally, earn their lives by activities other than rearing chicken but they raise chickens for securing their protein source and as supplementary to their income [START_REF] Heft-Neal | Supply Chain Auditing for Poultry Production in Thailand[END_REF][START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF]. Backyard chickens are generally sold by head to the neighbors and sold by weight to the poultry traders and market vendors [START_REF] Haitook | Study on Chicken Meat Production for Small-Scale Farmers in Northest Thailand[END_REF].

Unlike many other Asian countries, live bird markets are rare in Thailand [START_REF] Tiensin | Ecologic risk factor investigation of clusters of avian influenza A (H5N1) virus infection in Thailand[END_REF]. Instead, backyard poultry trade is based on a network of poultry traders who roam around villages to catch poultry and gather them at home before slaughtering or selling them to slaughterers. In traditional trading networks of backyard chickens, four types of actors are involved: (i) farmer, (ii) poultry trader, (ii) market vendor and (iv) consumer.

Poultry traders play an important role in connecting poultry production areas (rural villages) to consumption centers (urban markets). These traders always use small pick-up truck or motorbike depending on distances for carrying collected chickens. The selling negotiation between farmers and poultry traders are generally informal and performed orally without any written contacts [START_REF] Heft-Neal | Supply Chain Auditing for Poultry Production in Thailand[END_REF][START_REF] Heft-Neal | Assessment of Smallholder Indigenous Poultry Producer Viability in Thailand[END_REF][START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF].

It was observed that trade pattern of backyard chickens is seasonal and is influenced by some ritual festivals such as Chinese New Year [START_REF] Choprakarn | Village chicken production systems in Thailand[END_REF][START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF].

Effects of ritual festivals on backyard chicken trade

A study in Southern China revealed that, around Chinese New Year, chicken markets were significantly connected with more chicken sources in expanded geographic coverage [START_REF] Soares Magalhães | Live poultry trade in Southern China provinces and HPAIV H5N1 infection in humans and poultry: the role of Chinese New Year festivities[END_REF]. In Thailand, it was also evident that volume of chickens sold in the market and the price of chickens increased significantly during Chinese New Year festival [START_REF] Choprakarn | Village chicken production systems in Thailand[END_REF][START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF]. Compared with broiler meat, the increase in both volume and price of chickens was higher in backyard chicken due to premium position in the market.

However, a previous study conducted in Cambodia suggested that the amount of chickens traded was also increased in other festivals besides Chinese New Year, for examples, Khmer New Year, Islamic New Year and Qingming Festival [START_REF] Van Kerkhove | Poultry movement networks in Cambodia: implications for surveillance and control of highly pathogenic avian influenza (HPAI/H5N1)[END_REF]. Thus, it is possible that the trade pattern of backyard chickens in Thailand behaves the same way during Thai major ritual festivals. This province was chosen for the study because it recorded the highest number of confirmed HPAI H5N1 outbreaks in chickens during the first and second waves of epidemics [START_REF] Paul | Risk factors for highly pathogenic avian influenza (HPAI) H5N1 infection in backyard chicken farms, Thailand[END_REF].

Backyard chicken population

In Thailand, 'x-ray' campaign designates an intensive Avian Influenza active surveillance program which used nationwide door-to-door surveys since October 2004 [START_REF] Tiensin | Highly pathogenic avian influenza H5N1, Thailand, 2004[END_REF]. This campaign was organized by Department of livestock development (DLD) of Thailand which holds official authorities in managing animal statistics and health cares. After the outbreaks faded down, the program was also scaled down to focus only in at-risk areas (Na [START_REF] Ranong | Structural changes in Thailand's poultry sector and its social implications[END_REF] including Phisanulok province.

In the present study, we used backyard chicken population in Phitsanulok According to database of DLD, 1,661,168 backyard chickens raised in the province were taken into account in our model construction. Nevertheless, data on age and sex of chickens were not available in this survey. We needed to do our own survey to gain this information and also information on behavior of chicken traders that we missed in order to construct the model realistically.

Field survey on backyard chicken trade

Between June and August 2012, we went to our study site, Phitsanulok province, and conducted a field survey on behavior of poultry traders and also on descriptive characteristics of backyard chicken flocks i.e. sex and age ratio of chickens in each flock. These key information reflected the situation in the area, gave us a comprehensive understanding on what was going on and we could thus build a realistic model.

We obtained addresses of 16 chicken traders located in urban and suburban area of Phitsanulok province from the study of [START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF] Then, during our survey, we visited 14 out of 16 traders identified by the previous study (one trader shut down the business and another was missing). With snowball sampling methods [START_REF] Hay | Qualitative Research Methods in Human Geography[END_REF], we identified 6 more traders in the same area and also expanded to some remote areas of the province. Totally 20 traders were involved in this study.

Our survey was divided into 2 steps: (i) traders interview with a questionnaire and (ii) intensive observation on trader activities. In the first step, all 20 traders were questioned about their poultry trade activities during normal period and festivals.

The questionnaire included (i) general data of traders regarding locations and chicken catching facilities, (ii) chicken catchment details (iii) biosecurity practice, (iv) festival effects and (v) practices during AI outbreaks. The questionnaire is shown in Annex 2: Original version of questionnaire for poultry traders (in Thai) and Annex 3:

Translated version of questionnaire for poultry traders (in English).

In the second step, four traders allowed us to intensively follow and observe their trading activities. Each trader was followed daily during a 2-week-period.

They were monitored twice a day in the morning and evening during their chicken catchments. The movement of traders was tracked with a GPS tracking device.

During our observation, the farmers who sold chickens to the traders were also In each village, the flow of chickens started with chickens in the compartment of young chicken that left the compartment after growing up. After 5 months of age, some grown-up chickens were moved into the compartment of stocked chicken and some to ready-to-sell chicken compartment. For example, a village with a population of 100 chickens and 55 of them are immature. After the model was run for 5 months, 25 chickens were sent to ready-to-sell compartment and another 30 were kept for producing new chicken generations. However, in order to maintain population size, newborn chickens produced from stocked chickens or imported from elsewhere were refilled to young chicken compartment whenever chickens in this compartment grow up and move to other compartments. Dead chickens from each village were consecutively removed from each compartment as time passed by.

Parameters used in developing the model are shown in Table 3. In the present study, we stochastically run the model on daily basis for oneyear period (365 days: start from January 1 to December 31). As the model is stochastic, in order to study behavior of the model, we run the model for 1,000 simulations. The mechanism driving the model was explained in term of mathematical equations as follows.

Initial Values

Firstly, the model was initialized by distributing chicken population in Phitsanulok province into different village compartments: young chicken (YC), grown-up chicken (GC), stocked chicken (SC) and ready-to-sell chicken (RC).

,1 ,1 n n YC nbc py   (1.1.1)
,1

,1 ( 1)

n n GC nbc py   (1.1.2) ,1 ,1 (1 ) nn SC nbc py pst    (1.1.3) ,1
,1 ( 1)( 1)

nn RS nbc py pst    (1.1.4)
Where ,1 n YC is the number of chickens in the young chicken compartment in village n on day 1; Then, the flow of chickens within village compartments in all 1,045 villages was modeled as shown in equations 1.2.1-1.4.4.

Young chicken compartment

Then, chickens in young chicken compartment were daily moved out of the compartment as time passed by and they grew up (outputYC). Whenever the chickens got out of the compartment, number of chickens was compensated by newborn chickens produced from the stocked chickens inside the village or imported chickens (inputYC). The input and output of chickens in the compartment were determined by binomial distribution with probability p . outputYCg is the number of grown-up chickens in village n on day t.

Stocked chicken compartment

In this compartment, about half of grown-up chickens from young chicken compartment daily moved in (inputSCg) following binomial distribution with probability pst . Then, chickens in the compartment have possibility to move out by two ways: mortality (outputSCm) and being too old to be stocked chickens (getting retired) and being moved to ready-to-sell compartment to be sold together with other chickens (outputSCr). The movement of chickens out of the compartment followed binomial distribution with probability mp  and sst respectively. , nt outputSCr is the number of retired chickens in village n on day t ; pst is the proportion of grown-up chickens that become stocked chickens and sst is the daily probability of retired stocked chickens that leave the compartment.

Ready-to-sell chicken compartment

The input chickens (inputRCg) in this compartment were obtained from another half of grown-up chickens in young chicken compartment. The chickens moved out of the compartment by two ways: mortality (outputRCm) following binomial distribution with probability mp  and selling to poultry traders (outputRCc). By selling, the chickens can be sold to either TS or HT with number of chickens these traders requested or as available in the compartment. HTV is the number of household traders visiting village n on day t. The minimum function is applied to prevent the traders from taking more chickens than what available.

Then, chicken catching activities of all traders in the traded area were modeled according to equations 1.5.1-1.6.1.

Trader Slaughterhouse (TS) and Household Trader (HT)

Number of chickens collected by TS and HT in each day was the accumulation of chickens collected from villages the trader visited on that day. HT on day t′.

Trader-of-trader (TT)

In the following day, each TT accumulated all chickens collected by HTs under his network that day.

, 1 , 1

NHT k t j t j TT HT     (1.6.1)
Where , kt TT is the total number of chickens collected by k TT on day t , and NHT is the number of HTs visited by k TT on day t.

Social network analysis of backyard chicken trade

Social network analysis was used in this study to illustrate the connectivity of village-trader networks. By constructing a sociogram, the network was well visualized and more understandable for ones who are not familiar with mathematical equations.

The social networks of village-trader connectivity in backyard chicken trade were simulated for 1,000 simulations. A node in these networks referred to a village and a tie referred to trading activities that occurred between a village and a trader.

Since trader was a part of the village, the trader was also counted as a node. Degree centrality which is the number of immediate ties that each node has [START_REF] Martinez-Lopez | Social network analysis. Review of general concepts and use in preventive veterinary medicine[END_REF] was measured in each network. In our study, degree centrality was defined as the number of connections between villages and traders. In this model, villages could not connect with one another without traders.

All statistical and geographical analyses were performed using statistical computing language R version 3.0.1 (R development Core Team, 2013). Package 'fitdistrplus' was used in fitting the distribution. Package 'sp' was used in creating spatial coordinates. Package 'igraph' was used in illustrating the sociogram and package 'spdep' was used in locating the villages within the defined range.

Results

Backyard chicken movement characteristics and model inputs

With the questionnaires, we totally interviewed 20 traders including 9 HTs, 8

STs, and 3 TTs. To mimic the actual satiation, we put 8 STs, and 3 TTs into the model but we could not directly put number of HTs accordingly because we got data from only 1 TTs. We thus simulated number of HTs for each TT to be 6, 8 and 12 respectively. Then, we followed 4 traders to intensively observe and record their trading activities. We tracked traders for 2 weeks each (9 days excluding weekends and holiday). The traders did the business in 2-8 days during the tracking period. Days of chicken catching for each trader were shown in 1 Trader went to catch chickens.

. With a GPS tracking device, we obtained Euclidian distances that traders traveled to catch chickens as shown in Annex 7: Euclidian distance traveled to catch chickens by traders. The mean distance traveled by TS and HT was 6.55 km and the maximum distance traveled by HT was 6.06 km. We thus assumed that TS and HT could travel to collect chickens at the limit of 7 km. TTs normally traveled longer with an average of 14 km. TTs were free to travel in any distances necessary in collecting chickens from HT. This assumption was supported by the fact that all TTs used pick-up trucks and were able to travel in a long distance.

Simulation output

Backyard chicken populations in village compartments

The median values of chicken number after 1,000 simulations were 874.30, 351.10 and 361.00 in compartment of young chicken, ready-to-sell chicken and stocked chicken respectively. The values of median, minimum and maximum numbers derived from 1 and 1,000 simulations in each compartment are almost identical. Details on number of chickens in each village compartment are shown in

Temporal pattern of traditional backyard chicken trade

On average, 500 villages were involved in traditional live poultry trade networks in Phitsanulok province during a one-year period (95% confidence interval [CI] = 452-547) as calculated from 1,000 simulations. Median values of number of chickens caught per day were similar for all types of traders with 1 and 1,000 simulations.

Statistical analysis of stochastic temporal simulation for trader part is shown in The temporal pattern of backyard chicken trade for a one-year period is depicted in the present study. Details of the pattern were illustrated in Figure 9, Figure 10 and Figure 11. When considering all STs, the sub-peaks were far lower than the main one. The temporal pattern of number of chickens caught by different types of HTs throughout the year is illustrated in Figure 10. It was noticeable that a similar temporal trend as STs was observed in chickens catching activities of HT in all types of traders (A, B, C and all). The similarity occurred in both number of chickens caught and time frame of the peak periods. Temporal pattern of number of chicken accumulated by TTs is shown in Figure 10. The same temporal pattern was also observed for TT1, TT2, TT3 and all TTs, but with different level of the peaks. The peaks were about 600, 650 and 280 chickens for TT1, TT2 and TT3 respectively. The average peak for all TTs was around 500 chickens.

Spatial pattern of traditional backyard chicken trade

The catchment area of each trader was mapped in Figure 12. It was noticeably that area each trader operated their chicken catchment activities was mostly overlapped with the catchment areas of other traders.

Spatiotemporal pattern of traditional backyard chicken trade

Number of distinct traders visiting villages in different period of the year is illustrated in Figure 14. Each individual village was visited by average of 1.3 traders 24.9 to 25.2 km (95% CI = 24.2-25.9).

Social network analysis of traditional backyard chicken trade

The sociogram shown in Figure 16 depicts a simulation of backyard chicken trade network over a one-year period. This network contains 469 nodes and 961 ties, representing 961 connections occurred among 469 villages. Within the network, 19

villages were connected to more than one sub-network of TTs. The mean number and its 95% CI of villages connected with a TS or a HT was 27.3 villages (95% CI = 24.8-29.7), with a maximum number of 34 villages. Mean and its 95% CI and maximum number of TSs and HTs connected to a village were 2.0 traders (95% CI = 1.9-2.2) and 7 traders respectively.

In 1,000 simulations, mean degree centrality between villages and traders was 2.0 (95% CI = 1.7-2.6), with a maximum degree centrality of 2.7.

Discussion and conclusion

In the current chapter, the structure of live backyard chicken trading network that involved many actors from villages until the chickens got slaughtered by traders was depicted. Three distinct types of traders were examined in this study:

slaughterhouse traders, household-traders, and traders-of-traders.

It was evidenced the temporal pattern of backyard chicken trade at the village part as well as at the trader part. At the village part, the stochastic model showed the temporal variations of the number of chickens in the ready-to-sell compartment.

This number sharply dropped down during the period of Chinese New Year (in February). It also slightly decreased during the other festivals (Qingming Festival and Thai New Year in April, Hungry Ghost festival in August and International New Year in December) before being compensated to the initial level at the end of the year. This demonstrated that these festivals influenced the availability of marketable poultry in villages. On contrary, the number of chickens in the young chicken and stocked chicken compartments was stable throughout the year because these two compartments were not connected to traders. This result showed that the average number of marketable chickens in villages was low during Chinese New Year, which is a period of high demands. Moreover, there was little difference in model outputs between 1 and 1,000 simulations for all compartments of the village part. This indicated that the model was stable over multiple simulations. The stability of the model also indicated its consistency as we firstly hypothesis the trends of chicken trade and our model makes it possible to meet our hypothesis.

At the trader part, the activities (quantified through the number of chickens collected per day) of all trader types were peaked during the period of Chinese New Year festival. Previous studies also pointed out the importance of Chinese New Year for poultry trading business [START_REF] Choprakarn | Village chicken production systems in Thailand[END_REF][START_REF] Soares Magalhães | Live poultry trade in Southern China provinces and HPAIV H5N1 infection in humans and poultry: the role of Chinese New Year festivities[END_REF][START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF], but the present study is the first to reveal the importance of other festivals which backyard chicken trading activities were also higher than regular period.

In this work, chicken traders were categorized into two levels including traders who collect chickens directly from the farm households (TS and HT) and the traders who collect chickens from other traders (TT) while Paul et al., 2013 classified poultry traders into trader, slaughterhouse trader and trader-slaughterhouse-retailer. This new classification made it possible to define TT which is important in terms of disease spread because these traders aggregate much higher number of chickens from different traders and put them together at their place before slaughtering.

It was found that TS and HT had similar overall median of average number of chickens caught during the year (TS: 13.01, HT: 11.46 in 1,000 simulations) and traders type C in both TS and HT which collected chickens in all festivals had the highest overall number of chickens caught as shown in 79

Table 7. This result is consistent with the temporal patterns in Figure 9 and Figure 10 which show that trader type C had the highest number of peaks.

It was mentioned in previous study that the traders catch at a minimum number of 25-30 chickens per round [START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF] while we found that each trader catches around 12-15 chickens per day. We got about half number of chickens caught because we calculated on a day-to-day basis but it was counted per round in the previous study. Moreover, we assumed that the traders do not catch chickens every day during regular period and the traders catch much more chickens during festivals. Thus, our results seem be compatible with the previous study if we calculate the same way.

For TTs, the average number of chickens caught during the year is likely to be accordance with number of HTs belonging to each TT. For example, TT2 had the highest number of chicken caught because this TT connected with the highest number of HTs at 12HTs while TT1 and TT3 had connected with 8 and 6 HTs respectively. This numeric calculation coincided with temporal pattern shown in Regarding distances traveled by traders to catch chickens, we found that TSs and HTs collect chickens within average distance of 4.4 km radius around their locations. This limited distance was determined by their limited budgets and their vehicles i.e. mostly motorcycle and three-wheeled motorcycle. Our finding is thus consistent with studies carried out in Thailand [START_REF] Poolkhet | Social Network Analysis for Assessment of Avian Influenza Spread and Trading Patterns of Backyard Chickens in Nakhon Pathom, Suphan Buri and Ratchaburi[END_REF], indicating that traders conducted business only in their vicinity.

In contrary to the previous study conducted in China (Soares Magalhaes et al., 2012), extension of trading areas was not found in our study during Chinese New Year although our parameter setting allowed the catchment radius to be vary in case of TT. This evidenced that even if traders need to collect more chickens during the Chinese New Year, a sufficient supply was available within an average radius of 4 to 25 km around their house.

The distance traders can travel and number of chickens caught was also determined by type of vehicles as TTs generally used pick-up trucks in their chicken transportation while TSs and HTs used motorcycle, three-wheeled motorcycle and only some of them used pick-up truck. STs and HTs thus traveled in shorter distances and transport less chickens per trip compared with TTs in all studied periods. This finding is agreeable with another study in Vietnam [START_REF] Soares Magalhães | Associations between attributes of live poultry trade and HPAI H5N1 outbreaks: a descriptive and network analysis study in northern Vietnam[END_REF], where it was found that traders using motorcycles transported chickens only in a short distance.

Moreover, in one year, traders visited approximately 75% of all villages in the modeled area. The spatial pattern of catchment areas of traders showed that they partially overlapped as shown in Figure 12. This situation was emphasized by the sociogram obtained from a social network analysis which showed that almost 20 villages connected with more than one sub-network of TTs and on average one village connected with 2 traders (degree centrality). These overlapped chicken catchment areas in Phitsanulok province were also previously reported at subdistrict level by [START_REF] Paul | Practices associated with Highly Pathogenic Avian Influenza spread in traditional poultry marketing chains: Social and economic perspectives[END_REF] In this chapter, the flows of backyard chickens were stochastically modeled and quantified within villages and along the trade network consisting of different types of traders in Phitsanulok province, Thailand during a one-year period. Number of chickens in compartment of ready-to-sell chicken in villages was directly affected by trader's activities and the temporal pattern of backyard chicken trade for each type of traders was analyzed in details. Dramatic increase of chicken trading activities during Chinese New Year was pointed out and the increasing of trading activities during four other festivals in Thailand was firstly highlighted.

It was evident in this chapter that despite being mainly organized on short distances, the structure of poultry networks in Thailand may contribute to HPAI H5N1 diffusion through overlaps between trade zones and long distance trading of TT. This study also highlighted the temporal variations of live poultry movements, which were intensified during the 15 days preceding the Chinese New Year and, to a lesser extent, during four other festivals.

In the next chapter, we aimed at developing a dynamic transmission model of HPAI H5N1 on the poultry trade network with various disease-related parameters based on the current quantified trade model. Moreover, different scenarios of control measures would be tested to find out appropriate control strategies which are practical and ready to be implemented once HPAI H5N1 re-emerges or other subtypes of influenza, for example H7N9, emerge in Thailand.

Introduction

To Among various types of models applied in the study of HPAI transmission, spatial transmission has been simulated in many studies so far (de [START_REF] De Jong | Modelling control of avian influenza in poultry: the link with data[END_REF]. One parameter that is directly related with spatial transmission and has been widely used is transmission kernel () hr . It is a parameter that determines spatial transmission of disease from infected villages to uninfected villages as a function of inter-village distance (Boender et al., 2007a). The application of this parameter was found, as an example, in the study of [START_REF] Dorigatti | Modelling the spatial spread of H7N1 avian influenza virus among poultry farms in Italy[END_REF] Transmission kernel was used in simulation of between-farm transmission of HPAI H7N1 in Italy. Thus, this parameter is useful to estimate how disease spread spatially between infectious and susceptible premises.

Based on our stochastic dynamic simulation of backyard chicken trade network in the last chapter, we intently put HPAI H5N1 related parameter upon the previous model. Thus, in the present chapter, we aimed to:

Model parameters and assumptions

As discussion in the previous chapter, backyard chicken trade network may contribute to HPAI H5N1 spread via chicken catching activities of poultry traders.

Besides trade networks, the virus can also transmit spatially to nearby villages by other means. The spatial transmission of avian influenza was studied in different levels of population, for examples, within flock (Tiensin et al., 2007b), between farms (Boender et al., 2007b) and between villages [START_REF] Bett | Transmission Rate and Reproductive Number of the H5N1 Highly Pathogenic Avian Influenza Virus During the December 2005-July 2008 Epidemic in Nigeria[END_REF].

In our case, the unit of interest is village as we assumed that the chickens raised in each household are homogenously mixed since the chickens are free to roam around without any fences in day time (Choprakorn and Wongpichet, 2007). Thus, our local spatial transmission of HPAI H5N1 is between villages.

To let the virus spread between villages, we put 'transmission kernel ( () hr )' into our model. We adopted equation defining transmission probability used by Boender et al., 2007a:

0 0 ( ) 1 ( / ) h hr r r    (2.1.1)
We also adopted into our model the values of default equation constants: 0 h = 0.002 day -1 , 0 r = 1.9 km and  = 2.1 since the original equation was developed for avian influenza in the poultry-dense areas as in our study. Whereas, Euclidian distance between all villages ( r ) in our study area was calculated by daisy function in package 'cluster' of programing language R. Up to this point, we assumed that HPAI H5N1 virus can spread from an infected village to other uninfected villages by two means: (i) via traditional backyard chicken trade network and (ii) by spatial transmission due to other possible routes such as wild birds, fighting cocks or other anthropogenic activities. We then introduced transmission kernel to determine local transmission probability of the pathogen between villages. The graphical explanation of how a village gets infected is illustrated in Figure 17. In the next step, a mathematical model would be developed based on the stochastic trade network model obtained from the last chapter and taking into account also model parameters and assumptions explained in this section.

Mathematical Model

A stochastic susceptible-infectious-removed (SIR) model was built in this section in order to illustrate how HPAI H5N1 spread in backyard chicken populations in Phitsanulok province, Thailand. In our case, a stochastic model must be developed instead of a deterministic one because our population size does not fit mean field theory. The mean field theory is, generally, valid in only large size population [START_REF] Mckane | Stochastic models in population biology and their deterministic analogs[END_REF] whereas the exchange of chickens between different compartments in our study was occurred with only small number of chickens. Hence, the stochastic version is reasonably applied.

To model the infectious spread of HPAI H5N1 in backyard chicken population in Phitsanulok province, we applied an SIR model on all 1,045 villages in the province. Based on the model built in chapter 1, backyard chicken population in each village was divided into different compartments: young chicken (YC), stocked chicken (SC) and ready-to-sell chicken (RC).

Total population

Initially, each village's compartment was divided, according to infectious status, into susceptible compartments (SYC, SSC and SRC) and infectious compartments (IYC, ISC and IRC). Total number of susceptible chickens (S) in each village was the accumulated number of chickens in all susceptible compartments.

Total number of infectious chickens (I) in each village was the accumulated number of chickens in all infectious compartments and total number of chickens (N) in each village was the combination of susceptible chickens and infectious chickens in the village.

Susceptible compartments

In the compartment of SYC, chickens were daily moved out of the compartment by infected with HPAI HN51 (SYCi), died from other causes (SYCm) and grown up (SYCg). However, number of chickens was compensated by input chickens (SYCip) obtained from newborn chickens produced by stocked chickens inside the village or imported chickens. Where  is disease transmission rate; Where ,, j n t IT is the infectious status of poultry trader j that visit village n on day t;  is the probability that a village visited with an infected poultry trader would become infected. Once a trader visited an infected village, it was immediately infected and it kept being infected for 5 consecutive days.

5 5 , , ,t , , ,t 1 1 1 1 ( 0 1) ( 0 0) N N j n t j j n t j n n IV IT IV IT                    (2.3.9)
Where ,, j n t IV   is the infectious status of village n that was visited by trader j on day t -τ; 𝑁 is total number of villages visited by trader j on day t -τ and  is number of day before day t. Parameter ,, j n t IV is 1 if it is infected and otherwise is 0.

Transmission rate due to local transmission of the disease between villages (Pc2) was the product of infectious status of the village (IV) (0 = not infected, 1 = infected) and transmission kernel (h(r)).

Sensitivity analysis of parameters related to HPAI H5N1 outbreaks

However, some parameters in the model in 2.3 must be performed a sensitivity analysis before adding into the model because the actual values of the parameters

have not yet been studied in this area especially in the level of village. These parameters include: disease transmission rate (  ), mortality rate (  ) and transmission rate by visit of infected trader ( ). Also, the zone of initial infected village must be effectively chosen. The explanations on how sensitivity analysis was performed are as follows.

Mortality rate due to avian influenza infection

Mortality rate due to avian influenza infection ( ) is inversely proportional to infectious period ( T ) [START_REF] Sertsou | Key transmission parameters of an institutional outbreak during the 1918 influenza pandemic estimated by mathematical modelling[END_REF] as shown in the following equation:

1 T   (2.6.1)
Regarding HPAI H5N1 infection, the infected chickens generally died in a short period within 2-4 days after infection [START_REF] Lee | Characterization of highly pathogenic H5N1 avian influenza A viruses isolated from South Korea[END_REF][START_REF] Bouma | Estimation of transmission parameters of H5N1 avian influenza virus in chickens[END_REF]. Thus, we chose T at the average value which was 3 days (  = 1/3). However, we still conducted a sensitivity analysis on  to see the effect on the model if this parameter was changed. The values of  in this analysis were 1/2, 1/3, 1/4, 1/5, 1/6 and1/7 2.4.6 and it was simulated for 1,000 simulations. Each  value was tested for its disease spread probability, number of accumulated infected villages, daily infectious villages and number of infectious days.

Disease transmission rate

Transmission rate (  ) of HPAI H5N1 virus in Thailand was previously estimated within flocks of backyard chickens by Tiensin et al., 2007b. The  value ranged between 0.60 and 2.18 /day depending on infectious period. Nonetheless, the value of transmission rate between villages in backyard chicken population in Thailand has not yet been revealed.

We hereby performed a sensitivity analysis on this value based on an available value obtained the study of Tiensin et al., 2007b. The sensitivity analysis was performed upon the model and parameters explained in section 2.3. To cover the values obtained from the previous study, we made analysis to the values of  at 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 and 5.0. Each  value was put into equations 2.3.4-2.3.6 and it was simulated for 1,000 simulations. Each  value was tested for its disease spread probability (number of simulations which the spread of the disease occurred), number of accumulated infected villages, daily infectious villages and number of infectious days. The  value that yields highest disease spread probability was chosen in order to highlight the effect on the spreading probability.

Transmission rate by visit of infected trader

The trade of chickens related with the spread of HPAI H5N1 was previously explained in term of social network [START_REF] Soares Magalhães | Associations between attributes of live poultry trade and HPAI H5N1 outbreaks: a descriptive and network analysis study in northern Vietnam[END_REF][START_REF] Soares Magalhães | Live poultry trade in Southern China provinces and HPAIV H5N1 infection in humans and poultry: the role of Chinese New Year festivities[END_REF]) not compartmental dynamic model. Thus, transmission rate caused by visit of infected trader ( ) was not known. In our sensitivity analysis, we tested wide range of  values to find the best fit with our model. The  values we tested include: 0.001, 0.005, 0.01, 0.05, 0.1, 0.5 and 1. The sensitivity analysis was performed upon the model and parameters explained in section 2.3. Each  value was put into equations 2.3.8 and it was simulated for 1,000 simulations. Each  value was tested for its disease spread probability, number of accumulated infected villages, daily infectious villages and number of infectious days. The  value that yields highest number of accumulated infected villages was chosen.

Zone of initial infected village

In the dynamic trade model in chapter 2, backyard chickens were traded within the modeled trade zone consisting of villages located in Phitsanulok city area and its vicinities (672 villages). In the infectious model developed in the present chapter, we initialized the infection by infecting only one chicken out of all 1.6 million chickens in the province. Thus, it is important to specify the village which that first infected chicken was raised in. In this sensitivity analysis, we proposed 3 zones that the initial infected village could locate in: (i) all modeled trade zone (672 villages), (ii) Muang district (174 villages) and (iii) outside Muang district (498 villages). The sensitivity analysis was performed upon the model and parameters explained in section 2.3.

One village in each zone was randomly selected and one chicken inside the village was infected on day 17. Each zone was simulated for 1,000 simulations and it was tested for its disease spread probability, number of accumulated infected villages, daily infectious villages and number of infectious days. The zone that yields highest number of accumulated infected villages was chosen.

Totally, 23,000 simulations were run in all sensitivity analysis. All obtained values were used in the model explained in section 2.3 as well as all control measure simulations.

Mathematical modeling of different scenarios of control measures

In the baseline model, the HPAI H5N1 virus was assumed to spread by 2 means: via backyard chicken trade and via local transmission between infected and uninfected villages. We, thus, further simulated different control measures regarding these two ways of virus transmission. Three different levels of control measures were tested: (i) allow all traders, (ii) allow only local traders (TS and HT) and (iii) ban all traders. The control measures were tested based on infectious dynamic model explained in section 2.3. All parameters were remained unchanged except the one modified in each control strategy. Each control measure was run for 1,000 simulations. Then, disease spread probability, number of accumulated infected villages, daily infectious villages and number of infectious days were measured. The control measures tested are as follows:

Allow all traders

Firstly, we aimed to show the efficiency of control measures without any animal movement control policies. Therefore, we allowed all poultry traders regardless the distances they can travel to catch chickens.

No additional control measures

The baseline model was regarded as 'no additional control measure' and used as baseline to compare with results obtained from different control measure simulations.

Disinfect traders' vehicles and facilities

The vehicles and facilities used in chicken catchments can contaminate and bring the virus from one place to another place. The previous study suggested that daily disinfection of 80% visiting traders reduced the mean epidemic size by 0.50-0.77 (Fournié et al., 2013). Hence, we assumed in this study that disinfecting of traders' vehicles and facilities can reduce the probability of disease transmission by chicken trading activities by 0.50. We modified equation 2.3.8 as follow:

, , , 1 0.50

n t j n t Pc IT     (2.7.1)

Disinfect poultry areas in the farm households

The use of disinfectant in the farm household can lower the risk of infection as mentioned in a previous study that the risk of HPAI H5N1 infection was decreased with odd ratio of 0.48 where the owners used disinfectant to clear their poultry areas [START_REF] Paul | Risk factors for highly pathogenic avian influenza (HPAI) H5N1 infection in backyard chicken farms, Thailand[END_REF]. Thus, we assumed in our study that the probability of disease transmission reduced by 0.48 if the farmers disinfect poultry area in the farm households. We modified equation 2.3.10 as follow:

, , 2 ( ) 0
.48

n t n t Pc IV h r    (2.7.2)

Disinfect both traders' vehicles and facilities and poultry areas in the farm households

In this point, we intended to find out the combination effect obtained from the two control measure stated earlier. We hereby used equation 2.7.1 and 2.7.2 together in the model.

Allow only local traders (TS and HT)

Here, we cut the long-range trading organized by traders of traders (TT).

Backyard chicken trade can be performed only within limited radius of 7 km around the trader's location. The simulations were done to illustrate the effect of animal movement control under the compromised situation. The trade was still allowed but within the authorized distances and only trader slaughterhouses (TS) and household traders (HT) were allowed to do the business.

No additional control measures

The baseline model as in 2.5.1.1 was modified by totally eliminating the role of TT.

Disinfect traders' vehicles and facilities

The model as in 2.5.1.2 was modified by totally eliminating the role of TT and the equation 2.7.1 was still applied for the other traders.

Disinfect poultry areas in the farm households

The model as in 2.5.1.3 was modified by totally eliminating the role of TT and the equation 2.7.2 was still applied.

Disinfect both traders' vehicles and facilities and poultry areas in the farm households

The model as in 2.5.1.4 was modified by totally eliminating the role of TT.

Ban all traders

This control measure is the strongest one for poultry traders as all trades in all distances were totally prohibited. The simulations were built to show the efficiency of the policy which was not compromised to the traditional life style but more effective in disease control.

Control measure simulations

When all poultry traders were allowed to traded and traveled in any distances they wished, disease spread probability was 0.43-0.44. The most effective control measure was disinfecting both traders' vehicles and facilities and poultry areas in the farm households. This measure reduced average number of accumulated infected villages to 542.8 villages (95% CI = 481-601) and, simultaneously, average number of daily infectious villages to 41.2 villages (95% CI = 36. 1-45.6). Compared to baseline model (no control measures), this measure reduced 8.8% of average number of accumulated infected villages and 8.0% of average number of daily infectious villages.

After the TTs were banned to do the trades and only TSs and HTs did their business in a limited radius of 7 km, the most effective control measure was still disinfecting both traders' vehicles and facilities and poultry areas in the farm households. Average number of accumulated infected villages found from implementing this control measure was 497.1 villages (95% CI = 91.6-584.0) with average number of daily infectious villages of 38 villages (95% CI = 6.8-45.2).

Compared to baseline model, the partially banned measure reduced 16.5% of average number of accumulated infected villages and 15.2% of average number of daily infectious villages. However, based on CI, it was noticeable that the lower bound of CI decreased dramatically from 524.2 to 91.6 villages in case of average number of accumulated infected villages and from 39.4 to 6.8 villages in case of average number of daily infectious villages.

In the strongest control measures, all poultry traders regardless distances traveled to catch chickens were banned to do the business. Without any other control measures, average number of accumulated infected villages was pushed down to 413.7 villages (95% CI = 28.9-495.0) with average number of daily infectious villages of 32.9 villages (95% CI = 2.1-39. Regarding average number of infectious days in the modeled area, the values ranged from 64.8 to 81.8 days in case poultry traders were totally or partially allowed to do their business (the value of baseline model was 69.5 days) and the values dropped to 40.7-42.9 days when all chicken trades were totally prohibited. In village level, each village was consecutively infected for 11.4-15.7 days except when all poultry trades were banned and control measure of disinfecting poultry areas in the farm households was implemented (the value of baseline model was 15.1 days). In this particular case, the average number of infectious days was only 5.8 days (95% CI 110 = 0.4-9.7). Details on control measure simulation results are illustrated in Table 14-16.

Table 14: 1 Accumulated infected villages, 2 Confidence interval, 3 Daily infectious villages, 4 Infectious days in the model zone, 5 Infectious days in each village

Discussion and conclusion

The infectious models developed in this chapter were all based on the stochastic dynamic trade model of backyard chickens obtained from the previous chapters.

Here, we involved HPAI H5N1 related parameters to show how the virus spread in these backyard chicken populations via traditional trade networks as well as local spread by other means such as free-grazing ducks, wild birds and anthropogenic activities. To make the model as realistic as possible, sensitivity analysis was performed on transmission parameters. After the model was formed, several control strategies were tested upon the model. The model was developed in worst case scenario in order to illustrate clearly how HPAI H5N1 spread in the province and how control measures effectively halt the outbreaks.

Regarding sensitivity analysis of the model parameters, decreasing mortality rate due to avian influenza infection ( ) resulted in elevating of both disease spread probability and accumulated number of infected villages. Decreasing  was in turn to increase the value of infectious period ( T ) which allowed the disease to spread longer and wider. The chosen value of  at 1/3 /day which is corresponding to infectious period of 3 days yield almost 50% disease spread probability and almost 600 accumulated infected villages. Compared to infectious period of 7 days, our chosen value yield 72.6% disease spread probability and 87.8% accumulated number of infected villages. Thus, the value of  at 1/3 /day are high enough to use in our simulations.

The increase of disease transmission rate (  ) firstly increased disease spread probability until the peak at 1.5 /day and subsequently disease spread probability gradually decreased as we increased  . It means that if we allow the disease to spread too fast, susceptible populations will decreased too fast as well resulting in less probability in disease spread. According to worst case scenario, the chosen value of  was at 1.5 /day. This value was reasonable compared to the  got from contacted chickens in an experiment which the value was range from 0.44 to 1.3 /day [START_REF] Bouma | Estimation of transmission parameters of H5N1 avian influenza virus in chickens[END_REF]. In our case, the value was slightly higher because we modeled under the worst case scenario which allowed the disease to spread out as much as possible and, at the same time, the parameters must be still realistic. Nonetheless, the  value was found as high as 2.18 /day (95% CI = 1.94-2.46) in another study conducted within flocks of backyard chickens in Thailand (Tiensin et al., 2007a). As we studied the spread of the virus among compartments within villages, the chicken density at village level was lower than within flocks. Thus, our  was lower than the previous study.

The value of transmission rate by visit of infected trader ( ), which defines amount of chickens in the village that are infected after the visit of an infected trader, has never been studied in the traditional trade network of backyard chickens. In our sensitivity analysis, accumulated number of infected villages increased as the value of increased until the peak at  of 0.01 and then gradually decreased as  increased.

The explanation of this scenario was similar to the case of  . In this case, if we allow the infected trader to infect too many chickens in the village, number of susceptible chickens will decrease too fast and the infection in the village will stop faster resulting in less number of infected villages at the end of simulation. As we intended to model in worst case scenario, the value of  at 0.01 was eventually chosen. It means approximately 1% of chickens in the village were stochastically infected once an infected trader visited the village. However, the value we got (0.01) was still in line with the values (0.0-0.3) used in the infectious model of a previous study conducted in Vietnam on the networks of live bird markets and poultry traders (Fournié et al., 2013). In fact, the value of  is, generally, assumed and applied in case by case basis.

Thus, the value works well in one study might not be inferable to another.

The zone chosen, according to worst case scenario, for an initial infected village (Muang district) was as what we firstly expected. Muang district is a plain and urban area that most poultry traders are located in. Thus, the probability that the virus begins to spread from this area is high. Our chosen zone was agreeable with the previous risk factor study performed in the same province which indicated that densely populated areas with short distances to large cities were account as high risk areas for HPAI H5N1 spread [START_REF] Paul | Anthropogenic factors and the risk of highly pathogenic avian influenza H5N1: prospects from a spatial-based model[END_REF].

In our baseline model outputs, we illustrated a high spreadability of HPAI H5N1 virus in backyard chicken populations in Phisanulok province. We initially seeded the virus into just only one chicken and, later on, the virus spread to 57% of the villages located in the province (595/1,045) within 65 days and each village kept infecting up to 46 days. The previous simulation model also infected one chicken flock and up to 514 flocks were subsequently infected [START_REF] Patyk | An epidemiologic simulation model of the spread and control of highly pathogenic avian influenza (H5N1) among commercial and backyard poultry flocks in South Carolina, United States[END_REF]. Our result was thus in line with the previous study as we regarded a village as a homogenous population equivalently to a flock.

Compared our results to the real outbreak situations in the same province in the initial year of epidemics ( 2004), from January to December 2004 (one year period), 106 distinct villages infected with HPAI H5N1 were officially reported in Phitsanulok province, Thailand (official data). As we put no control measures in the baseline model and we model under worst case scenario, our number of infected villages ( 595) is apparently more than the actual number of infected villages in reality. As intensive control measures were strongly applied at the time of epidemic in the real situation, the number of infected villages was intuitively low. However, the model fitting reality by taking into account the control measures which were really applied is recommended to develop in further study and their effectiveness can be compared with ours.

Upon our baseline model, different levels of control measures were tested.

Disease spread probability ranged from 0.43 to 0.48 in case that poultry trades were partially or totally allowed and the value dropped sharply to 0.15-0.16 when all poultry trades were completely prohibited. Moreover, average number of accumulated infected villages also decreased by 30.4% after implementing only poultry trader banning policy without any other complementary measures. These results highlight the importance of animal movements in the spread of HPAI H5N1 and other infectious diseases as suggested in previous studies [START_REF] Kilpatrick | Predicting the global spread of H5N1 avian influenza[END_REF][START_REF] Volkova | Sheep movement networks and the transmission of infectious diseases[END_REF]. Banning only long-ranged traders decreased only 4.4% of average number of accumulated infected villages and the disease spread probability was fairly unchanged by this implementation. However, it was observed from confident interval that the lower bound of average number of accumulated infected villages was reduced by 82.5% compared to baseline model when long-ranged traders were banned. This means that in some cases the decrease is very important.

Thus, the partial ban policy has some important effects on stopping the spread of HPAI H5N1. Nonetheless, our main results still suggested a banning policy on all poultry traders regardless distances traveled once outbreaks of the disease occur.

A part from poultry trader banning policy, we also simulated, within each level of banning, three other complementary measures. Disinfecting traders' vehicles and facilities slightly reduced average number of accumulated infected villages by only 0-1.3% whereas disinfecting poultry areas in the farm households decreased average number of accumulated infected villages by 7.9-49.3% (7.9-11.4% excluding the scenario when this measure was implemented while all poultry traders were banned.) and the combination of both control measures decreased average number of accumulated infected villages by 8.8-12.7%. Apparently, disinfecting poultry areas in the farm households was more effective than disinfecting traders' vehicles and facilities and the combination of these two measures was the most effective way to reduce virus spreading from one village to another village while the traders were still present. With the absence of poultry traders, disinfecting poultry areas rescued about half of infected villages.

Overall, the most effective control measure obtained from the models was to ban all poultry traders implemented together with the campaign of poultry area that some live bird markets were still very active in the areas that this kind of markets was completely banned and it was likely that these markets had high impact on disease dynamics. In our case, the same situation may occur if the authorities totally ban all poultry trades. They might secretly trade chickens and keep spreading the virus along their routes. Thus, veterinary authorities must strongly implement the measure once epidemics occur.

Regarding poultry area disinfection, villagers should be educated to routinely clean and disinfect the poultry areas in their households with the supports from governments as these villagers might not be able to afford disinfectants themselves.

A cascade community-based education was conducted in rural Cambodia to improve knowledge and practices of villagers related with backyard poultry biosecurity. This educational campaign started with training few individuals which subsequently trained a large group of people. The campaign successfully improved biosecurity practices in the community level [START_REF] Conan | A community-based education trial to improve backyard poultry biosecurity in rural Cambodia[END_REF]. As evidence in Thailand, village health volunteers play very important roles in HPAI H5N1 surveillance and control [START_REF] Chantong | Poultry raising systems and highly pathogenic avian influenza outbreaks in Thailand: the situation, associations, and impacts[END_REF]. These volunteers live within the villages and know each other well. The authorities can start the training with these people and let them train others in their own villages. However, a previous risk communication study on HPAI H5N1 in Thailand indicated that behavior changes can occur only when practical recommendations were provided [START_REF] Takeuchi | Avian influenza risk communication, Thailand[END_REF]. Hence, the training must be carefully planned before implementing to guarantee the achievement. Also, the follow-up plans should be designed and continuously applied to monitor the sustainability of the program.

The baseline model and control measure simulations performed in this chapter were totally based on stochastic dynamic model of backyard chicken trade obtained from the previous chapter. This trade model was basically simulated for nonepidemic period. The flows of chickens are likely to be dramatically altered when the outbreaks do occur. Thus, the infectious models proposed in the present chapter are mainly applicable at the beginning of the outbreak when the virus is present and spread within the trade networks but not yet diagnosed. Once the virus is notified, our proposed control measures should be promptly implemented.

However, these control measures were modeled without stamping out policy which is currently used. We would like to propose alternative ways in controlling HPAI H5N1 without killing animals. It was indicated in a previous study that mass culling procedures provide a short-term benefit in controlling outbreaks but, in long term, the host will be more genetically susceptible resulting in higher mortality and the virulent of virus is likely to be elevated [START_REF] Shim | Evolutionary repercussions of avian culling on host resistance and influenza virulence[END_REF]. Moreover, a study conducted in Thailand found that proportion of specific Thai indigenous stains of chickens was diminished after several outbreaks of HPAI H5N1 which mass culling was an important part of control policies [START_REF] Duangjinda | Impacts of Avian Influenza outbreaks on indigenous chicken genetic resources in Thailand[END_REF]. Most of HPAI H5N1 confirmed outbreaks in Thailand occurred in backyard chicken populations [START_REF] Chantong | Poultry raising systems and highly pathogenic avian influenza outbreaks in Thailand: the situation, associations, and impacts[END_REF]. Backyard chickens are reared with on biosecurity and they are free to roam around the villages without any fences to scavenging their feeds in daytime and they are kept in houses during nighttime.

Thus, the disease is easily distributed within their populations once they are infected. However, it is not possible to ban the villagers to raise backyard chickens because these chickens have been a part of their lifestyle for a long time. Backyard chickens are reared for many purposes including home consumption, cash income, cock fighting and also for some religious or traditional ceremonies.

In backyard chicken trade, the system is still traditional. The negotiation between farmers and traders is managed orally without any official written contacts.

Poultry traders are the ones who roam around many villages to aggregate backyard chickens and supplied to the wet markets, especially, markets with high demands and purchasing power located in urban areas. In our study, we categorized poultry Ultimately, our results suggest that a complete ban of all poultry traders should be promptly implemented with poultry area disinfection campaign once the outbreak occurs. To achieve this, all traders must be known by veterinary authorities by registration. We thus expect Thai veterinary authorities to consider our suggestions and take them into account as another guideline in controlling HPAI H5N1 and other infectious diseases in poultry populations.

In present study, we recommend to ban backyard traders regardless the distances they travel to collect chickens. However, we have not yet developed a model to see how long and which locations they should be banned. The banned period must not be too short because the disease can spread if it is too short and it should not be too long because the traders could start to trade chickens illegally if it is too long. The appropriate banned period must be considered and modeled in further study.

In future studies, the control measures which are currently implemented by veterinary authorities such as stamping out policy could be taking into account based on the current model. Comparison or combination of our proposed control measure and the current control policies should be conducted to show the effectiveness of each measure and find out the best solution that can be directly applied once the outbreak occurs.

In the present study, the model was developed in non-epidemic period and it can be applied effectively at the beginning of the outbreak. In future study, the effect of epidemics should be taken into account especially the effect of anthropogenic behavior changes. One can elaborately model in different stages of epidemic: initial stage, peak stage, post-epidemic stage to see the different scenarios and find out the most appropriate prevention and control measures that should be applied in each stage of epidemic.

The current model focuses on a province of Thailand. The model can be developed to a larger scale, for examples, regional or national scales. In this case, different trading behavior in different geographic location must be taken into account and also different scale of poultry populations. Moreover, the model can also be applied to Thai neighboring countries which have similar trading behavior.

However, some important different characteristics of trading such as live bird markets must be cautioned and adapted to situation of each country.

125

In our study, a social network analysis was performed in the trade network.

Nonetheless, elaborated analysis on the network has not been conducted. More network parameters can be measured and the network can be infected with HPAI H5N1 as we did in our dynamic model. We can also find the hubs of infection on the network and do a simulation by cutting the connections of the hubs and measure how important these hubs on disease spreading. By using different techniques, we can compare results obtained from each technique and discuss on these results to find the best solution.

Moreover, the network can also be theoretically analyzed by using complex network discipline which is widely used in physics. The complex network makes it possible to reveal some important characteristics of the network once the type of network is identified. This interdisciplinary approach should be also applied in the further study. period. We found average K-core of 1.7 (range: 1-4) and 1.4 (range: 1-3) in Chinese New Year festival and regular period respectively. It was concluded in this study that trading activities of backyard chicken during Chinese New Year festival were significantly higher than in regular time (for weighted degree centrality and for Kcore p-value < 0.001). Thus, movement and trade of backyard chicken during festive period could cause wide spread of the outbreak and we should closely monitor and strengthen HPAI H5N1 surveillance program during Chinese New Year.

List of figures

List of tables

implement some effective strategies in fighting with HPAI H5N1 or other emerging subtypes of avian influenza such as H7N9 in the future.

RésuméL'

  Influenza Aviaire Hautement Pathogène H5N1 (IAHP à H5N1) a été déclaré en Thaïlande lors de plusieurs vagues épidémiques puis lors de cas sporadiques entre 2004 et 2008, et le risque persiste encore en Thaïlande. La plupart des foyers confirmés d'IAHP à H5N1 en Thaïlande ont eu lieu dans les populations de volailles de basse-cour. Les poulets de basse-cour sont élevés pour de nombreuses raisons, y compris pour un revenu supplémentaire. Ce commerce est géré informellement par les collecteurs de volailles qui peuvent être classés en collecteur-abatteur (TS), souscollecteur (HT) et collecteur de collecteurs (TT). Ces collecteurs se déplacent entre villages avec les mêmes véhicules et matériel non nettoyés. Nous avons mesuré leurs activités commerciales dans l'espace et le temps. Nous avons développé un modèle spatial dynamique compartimental et stochastique de la filière de poulet de bassecour dans une province. Nos résultats indiquent que ces échanges commerciaux peuvent contribuer à la propagation d'IAHP à H5N1 grâce au chevauchement des zones de collecte et aux distances parcourues. Des variations temporelles ont été observées lors de certaines grandes fêtes rituelles tel le Nouvel An chinois. Nous avons développé un modèle SIR couplé au modèle de la filière de poulets. Nous avons supposé que la maladie peut se propager par deux moyens : localement entre villages voisins et par les échanges commerciaux. Nous avons utilisé ce modèle infectieux de base pour tester plusieurs mesures de contrôle connexes. Nos résultats suggèrent que lors d'un foyer une interdiction totale et rapide de tous les échanges de volailles devrait être mise en oeuvre ainsi qu'une campagne de désinfection. Mots Clés: influenza aviaire, poulet de basse-cour, épidémiologie, modèle mathématique, Thaïlande Résumé Substantiel L'Influenza Aviaire Hautement Pathogène H5N1 (IAHP à H5N1) a été déclaré en Thaïlande lors de plusieurs vagues épidémiques entre 2004 et 2006 puis lors de cas sporadiques en 2007 et en 2008. Depuis cinq ans, il n'y a plus de notifications officielles de foyers d'IAHP à H5N1 tandis que le risque persiste ; la maladie est toujours dans les pays voisins. Ainsi, en 2014 (jusqu'au 16 Avril 2014), l'IAHP à H5N1 a été signalé chez les volailles dans trois pays de l'ASEAN Cambodge, le Laos et le Vietnam et des cas humains mortels ont également été signalés au Cambodge et au Vietnam. Ainsi, le risque de réintroduction de la maladie en Thaïlande n'a pas disparu.

I

  am very grateful to Professor Dr. Xavier Malher, Dr. Véronique Chevalier and Assistant Professor Dr. Charin Modchang for their participation and their valuable comments and suggestions in my PhD committee meetings in the first and second year of my thesis. I would like to contribute my sincere gratitude to Associate Professor Dr. Parntep Ratanakorn, Dean of Faculty of Veterinary Science, Mahidol University for giving me permission to leave my work for study and all of my colleagues at the Monitoring and Surveillance Center for Zoonotic Disease for Wildlife and Exotic Animals, Faculty of Veterinary Science, Mahidol University for supporting my works and working in my position during my study leave.

Figure 1 :

 1 Figure 1: Outbreaks of HPAI H5N1 in poultry notified to the OIE from the end of 2003 to 15 March 2014 (source: OIE, 2014).

Figure 2 :Figure 3 :

 23 Figure 2: Number of confirmed human H5N1 cases by month of onset reported to WHO as of 25

4 .

 4 Wave IV (24 -29 July 2006): the outbreaks were reported from only backyard chickens and laying hens. Afterward, there were three and four outbreaks reported in 2007 and 2008 respectively and no epidemics of HPAI H5N1 have been notified since 2009. Temporal pattern of the outbreaks between 2004 and 2007 is illustrated in Figure 4.

Figure 4 :

 4 Figure 4: Temporal pattern of HPAI H5N1 outbreaks in Thailand during 2004 -2007 (source: Burgos et al., 2008)

Figure 5 :

 5 Figure 5: Distribution of HPAI H5N1 outbreaks during 4 epidemic waves in Thailand during 2004 -2006 (source: Chantong and Kaneene, 2011).

  kernel was used together with simulation model based on poultry population in flock level in Great Britain in 2006 and current control interventions were evaluated. Thus, spatial SIR model is a useful tool to illustrate how diseases spread within and between populations in the same geographic area, and beyond, to identify risk areas and to evaluate control measures. However, mathematical modeling was involved only in the step of quantifying transmission parameters in the study of HPAI H5N1 epidemics in Thailand. Tiensin et al., 2007b estimates transmission rate (β) and basic reproduction number ( 0 R ) of HPAI H5N1 transmission within flock level during epidemics in 2004 and Marquetoux et al., 2012 finds out the same parameters in subdistrict level for the epidemics during July 2004 -April 2005.

  in Thailand occurred mostly in backyard chicken populations. The control measures applied by Thai government generally focused on the chickens reared in the villages. In fact, these chickens are also moved by the traditional trading activities which are currently overlooked by related authorities.More understanding on the mechanism driving the trade and trade pattern in space and time would be used as basic knowledge in designing appropriate control measures for this trade system and further strengthen overall control strategies once the outbreaks emerge.This chapter aimed to:1. Comprehensively understand how backyard chickens are produced and managed within the village, the amount of chickens produced and sold in different periods of the year as well as factors influencing production and selling of chickens in traditional trade chain.2. Study, in details, on trading behaviors of poultry traders regarding their facilities, locations, types of business, trading performance and seasonal trade patterns.3. Quantify backyard chicken trade patterns in both space and time dimensions by using mathematical modeling technique based on official data and field observations. The obtained quantified model would be further used as basis for HPAI H5N1 control measure scenario testing.

  Phitsanulok province is a province located in the Yom-Nan River basin of the upper central region of Thailand. The province is still driven by agricultural activities with about sixty percent of population working in this sector. Backyard chicken is the prominent poultry population in this province. Based on data collected in 2005, backyard chickens represent 94% of poultry flocks in Phitsanulok and they are about half (47%) of chicken heads in the province(NSO, 2009).

  province which was surveyed and recorded in the database of DLD in March 2012 during the 'x-ray' campaign. The details of poultry survey in this database are shown in

  interviewed on their chicken rearing behavior. Information recorded on each visit included (i) general data on each catchment regarding number of households visited and number of chickens collected and (ii) detailed data on each household visited regarding general information of chickens' owners, number and age of chickens (less than 5 months and more than 5 months) reared in the household, number and age of chicken sold, price of chickens and their plan on chicken production before Chinese New Year. The survey form is shown in Annex 4: Original version of survey form on the observation of traders' activities (in Thai) and Annex 5: Translated version of survey form on the observation of traders' activities (in English). of backyard chickens in space and time was simulated in a compartmental stochastic dynamic model. Backyard chickens in each village were considered as a whole homogeneous population, as these chickens are traditionally raised without any cages or fences and they thus mix together during daytime (Choprakarn and Wongpichet, 2007). The model was divided into 2 main parts: village and trader. Each village was then subdivided into 3 compartments: (i) young chickens (defined as chickens aged < 5 months old), (ii) ready-to-sell chickens and (iii) stocked chickens. The village part of the model was run simultaneously in all 1,045 villages located in the Phitsanulok province. Traders were also categorized into 3 types including (i) trader-slaughterhouse (TS), who collects chickens from villages and slaughters himself; (ii) household trader (HT), who collects chickens from villages and sells to other traders; and (iii) trader of trader (TT), who aggregates chickens collected by HTs and slaughters them. In backyard chicken trade, backyard chickens in ready-to-sell chicken compartment had possibility to flow into either compartments of TS or HT. All chickens collected in HT compartments were then aggregated into the compartments of TT. At the end, all chickens from the compartments of TS and TT were slaughtered and sent to market vendors, restaurants and consumers. The conceptual model explaining what happens in both village and trader part and how they connected is shown in Figure 6.

Figure 6 :

 6 Figure 6: A conceptual model representing the organization of traditional live backyard chicken trade in one village located in Phitsanulok province, Thailand.

  is number of grown-up chickens in village n on day 1; ,1 n SC is the number of chickens in the stocked chicken compartment in village n on day 1; ,1 n RS is the number of chickens in the ready-to-sell chicken compartment in village n on day 1; ,1 n nbc is the total number of chickens in village n on day 1. The values were obtained from active HPAI H5N1 surveillance program (x-ray campaign) in March 2012; py is the proportion of young chickens in the overall population and pst is the proportion of young chickens moved into the stocked chicken compartment.

,

  Sixty percent of traders (12/20) located in Muang district and the traders situated in remote areas (Nakhon Thai and Chattrakarn districts) stated that they sell chickens in the local markets without any connections with urban area due to difficulty and high cost in transportation and insufficient profit compared to cost and time spent. Hence, we delimited the simulated trade area to only plain area in Muang district and its suburban districts (672 out of 1,1045 villages). However, the simulation in the village part was still performed in all villages located in Phitsanulok province. Three types of vehicles used in transporting chickens: motorcycle (6/20), threewheeled motorcycle (5/20) and pick-up truck (11/20). On average, traders went to villages to catch chickens 3.8 days a week. Concerning festival effects, Sixty-five percent (13/20) of traders caught and traded more chickens during Chinese New Year and 55 percent (11/20) traded more chickens also during other festivals. There were four other festivals mentioned by traders including Qingming festival, Thai New Year, Hungry Ghost festival and international New Year. Thus, we categorized behavior of chicken catching activities of traders into 3 types consisting of type A: catch the same amount of chickens all year round, type B: catch more chickens only during Chinese New Year and type C: catch more chickens in all festivals. The questionnaire results on traders' characteristics are shown in Erreur ! Source du renvoi introuvable..

  Totally, the traders visited 42 households located in 38 villages during 2 weeks of intensive observation. In each day, traders visited, on average, 2.0 houses which were located in 1.8 villages and caught 40 chickens. The traders caught 20 chickens per household (for TS and HT) or per trader (for TT) approximately with range of 15-25 chickens. Details of chicken catching activities of traders in the intensive survey are shown in Annex 6: Summary of chicken catching activities of traders. With the intensive survey data, we fitted number of chickens collected from each village and we found that it distributed according to Poisson distribution as shown in Figure 7. Thus, we simulated number of chickens collected from each village in our model during normal period using Poisson distribution with a lambda (  ) of 16.5. We used the same distribution for Chinese New Year period and other festivals. According to data obtained from questionnaires, traders collected chickens at an average of 55.2 chickens per village during Chinese New Year and collected half amount (27.5) chickens during other festivals. So, we set lambda of Chinese New Year and other festivals at 55.2 and 27.5 respectively.

Figure 7 :

 7 Figure 7: Theoretical distribution fitting on number of chickens caught from each village

Figure 8 :

 8 Figure 8: Simulated temporal pattern of average number of backyard chicken population within villages for three different compartments (young, ready-to-sell and stocked chicken) in a yearround (365 days).

Figure 9 :

 9 Figure 9: Simulated temporal pattern of backyard chicken trade for three different types of slaughterhouse traders (TSs) (type A, B and C) and of all STs in a year-round (365 days).

Figure 10 :

 10 Figure 10: Simulated temporal pattern of backyard chicken trade for three different types of household traders (HTs) (type A, B and C) and of all HTs in a year-round (365 days).

Figure 11 :

 11 Figure 11: Simulated temporal pattern of backyard chicken trade for three different types of trader of traders (TTs) (type A, B and C) and of all TTs in a year-round (365 days).

Figure 12 :

 12 Figure 12: The map of Phitsanulok province and geographic locations of three different types of simulated traders and of the villages in their catchment area (delimited within a 7 km radius from the trader's location defined by a circle around each trader). This Figure uses 1 trader-of-trader (TT) with its household-traders (HTs) and 8 slaughterhouse traders (TSs) as an example.

Figure

  Figure 13: (a) Histogram of total number of visits made by slaughterhouse traders (TSs) and household traders (HTs) to all villages and (b) histogram of number of distinct villages visited per traders in a year-round period (days 1-365). The plots were illustrated from average values of 1,000 simulations.

  average distance TSs and HTs traveled to collect chickens was 4.4 km (95% CI = 4.2-4.5) in all modeled periods.

Figure 15 :

 15 Figure 15: Bivariate plots of distances traveled to collect chickens (x-axis) and number of chickens collected (y-axis) during the Chinese New Year (days 17-31), the Hungry Ghost Festival (days 228-242), and normal periods (days 336-350). Three plots on the left represent situations of traderslaughterhouses (TSs) and household traders (HTs), and three plots in the right-hand side depict situations of traders of traders (TTs). The plots were illustrated from average values of 1,000 simulations

Figure 16 :

 16 Figure 16: A sociogram of the simulated network (469 nodes, 961 ties) of traditional backyard chicken trade in Phitsanulok province, Thailand in one year period (365 days). Each node represents a village. Light blue nodes indicate the villages with slaughterhouse traders (TS). Green, yellow and red nodes show the villages with traders (HT) belonging to the sub-networks of TT1, TT2 and TT3 respectively.

Figure 11 .

 11 Figure 11.Focusing on temporal variation influenced by major ritual festivals, STs and HTs increased amount of chickens collected by 387% and it was 364% in case of TT during a short 15 days period prior to Chinese New Year festival. This finding is relevant with studies carried out in other countries[START_REF] Van Kerkhove | Poultry movement networks in Cambodia: implications for surveillance and control of highly pathogenic avian influenza (HPAI/H5N1)[END_REF] Soares Magalhaes et al., 2012). The number of villages visited by STs and HTs also increased significantly during the Chinese New year. In other festivals (depicted by Hungry Ghost festival), number of chickens collected by STs and HTs compared with normal period increased by 150% and it was 146% in case of TT. Number of villages visited fell in between the results found in normal period and Chinese New Year festival.

  date, various types of mathematical modelling have been applied in epidemiological study of HPAI H5N1 in poultry population[START_REF] De Jong | Modelling control of avian influenza in poultry: the link with data[END_REF]. For example,[START_REF] Bett | Transmission Rate and Reproductive Number of the H5N1 Highly Pathogenic Avian Influenza Virus During the December 2005-July 2008 Epidemic in Nigeria[END_REF] calculated transmission rate and reproductive number of the epidemics in Nigeria during 2005-2008 and it was found that the control measures implemented during the second phase of the epidemics were more effective than those implemented during the first phase. Hence, the model can be used as a tool in evaluating control measures that have already been applied by authorities or even suggested the better one. Moreover, some models especially focused on backyard chicken populations, for instances, Elbakidze, 2008 developed an SIR model together with economic costminimization framework as well as spatial modeling technique for backyard chicken flocks and the study indicated that the substitute strategies in this case were to reduce the length of asymptomatic and symptomatic periods and to reduce also inter-flock contact rates. Patyk et al., 2013 provided detailed and informed input parameters for HPAI H5N1 simulations in both commercial and backyard chicken populations in South Carolina, United States. Subsequently, a stochastic model was constructed using these parameters and this model was intended to use as a baseline in evaluating various control measures in the future. As per these examples, mathematical model can also be useful in suggesting guideline in implementing further control measures based on simulation results.

1 .

 1 Simulate how HPAI H5N1 spread along traditional backyard chicken trade chain and also taking into account the local spread from the infected village to their neighboring villages. 2. Compare different scenarios of control measures regarding live backyard chicken trade and local spread of the disease. The current chapter consists of 6 sections including (i) model parameters and assumptions that explains what parameters and assumptions we used in our model construction, (ii) Mathematical model which illustrates how we constructed SIR model upon stochastic trade network model, how we performed sensitivity analysis on HPAI H5N1 transmission parameters and how we evaluated different control measures, (iii) sensitivity analysis of parameters related to HPAI H5N1 outbreaks which makes our parameters valid and realistic, (iv) mathematical modeling of different scenarios of control measures that simulates different control measures based on baseline infectious model (v) results derived from sensitivity analysis, model output and control measure selection and (vi) discussion and conclusion which takes into account our results and the results from literatures together to finally make our own conclusion.

Figure 17 :

 17 Figure 17: Mechanism of how a village gets infected.

Figure 18 :

 18 Figure 18: Conceptual SIR model representing how HPAI H5N1 spreads in traditional live backyard chicken trade in one village located in Phitsanulok province, Thailand.

  due to local transmission of the disease between villages in village n on day t; and BN is a function for sampling from a binomial distribution.Transmission rate due to chicken trade (Pc1) was the product of infectious status of visiting traders (IT) (0 = not infected, 1 = infected) and transmission rate by visiting of infected traders ( ).

  /day representing T at 1-7 days. The sensitivity analysis was performed upon the model and parameters explained in section 2.3. Each  value was put into equations 2.4.4-

Figure 19 :

 19 Figure 19: HPAI chronological infectious map of Phitsanulok province depicted from an SIR model simulation. Blue and red dots represent HPAI H5N1 uninfected and infected village respectively.

  1). Compared to baseline model, the completely banned measure reduced 30.5% of average number of accumulated infected villages and 26.5% of average number of daily infectious villages. When control measure of disinfection poultry areas in the farm households was implemented, average number of accumulated infected villages was dramatically reduced to 209.9 villages (95% CI = 15.0-346.2) and average number of daily infectious villages decreased to only 16.6 109 villages (95% CI = 1.1-27.7). Compared to baseline model, this measure reduced 64.7% of average number of accumulated infected villages and 62.9% of average number of daily infectious villages. The results on disease spread probability and mean number of accumulated infected villages is graphically illustrated in Figure 20.

Figure 20 :

 20 Figure 20: Disease spread probability and mean number of accumulated infected villages resulting from different control measure simulations.

  The present chapter simulated an SIR model upon a stochastic dynamic trade model of backyard chickens reared in Phitsanulok province, Thailand. After sensitivity analysis was done, the baseline model showed high spreadability of HPAI H5N1 in the study area i.e. only one initial infected chicken can ultimately result in almost 600 infected villages in the province. This baseline model was, later on, used in control measure simulations. Our results suggest that a complete ban of all poultry traders should be implemented with poultry area disinfection campaign once the outbreak occurs.Chapter of conclusion and perspectives120 HPAI H5N1 was firstly recognized in Thailand in January 2004 and the country subsequently faced multiple waves of outbreaks in poultry populations during 2004-2006 followed by some sporadic cases in 2007 and 2008. Since then, there were not any notifications of the outbreaks up to present. Over five years of HPAI H5N1-free status in Thailand, the disease has still been being reported from Thai neighboring countries. In 2014 (as of 16 April 2014), HPAI H5N1 was reported in poultry in 3 ASEAN countries i.e. Cambodia, Laos and Vietnam (OIE, 2014) and the fatal human cases were also reported from both countries (WHO, 2014). Thus, the risk of disease remerging in Thailand has not yet been vanished.

traders into 3

 3 types according to their trading behaviors including (i) traderslaughterhouse (TS), who collects chickens from villages and slaughters them himself; (ii) household trader (HT), who collects chickens from villages and sells to other traders; and (iii) trader of trader (TT), who aggregates chickens collected by HTs and slaughters them. Activities of these traders are risky for the spread of HPAI H5N1 since they travel from on villages to villages and to slaughterhouse with the same unclean vehicle and facilities. Thus, their trade patterns in space and time are necessary to be elaborately studied. With questionnaires, field observations and official backyard chicken census data, we successfully developed a compartmental stochastic dynamic model explaining how backyard chicken spatiotemporally flow within villages and along traditional trade chain as shown in chapter 1. The results of our model took into account the temporal variations of backyard chicken trade due to dramatic demand of chickens during some important ritual festivals in Thailand and highlighted the consequences in all compartments. We identified 5 important festivals that directly influence the demand of chickens including Chinese New Year in February, Qingming Festival and Thai New Year in April, Hungry Ghost festival in August and International New Year in December.The temporal variation of backyard chicken populations in village compartments was observed in ready-to-sell compartment. Number of chickens in this compartment sharply dropped down during the period of Chinese New Year and slightly decreased during the other festivals before being compensated to the initial level at the end of the year. At the same time, it was found in the trader compartments that the activities of all traders were peaked during Chinese New Year period with high activities during other festivals. Besides Chinese New Year, the present study is the first to reveal the importance of other festivals which backyard chicken trading activities were also higher than normal period.Spatially, poultry traders visited about three-fourth of villages located in the modeled area. Moreover, the catchment areas of these traders were partially overlapped with each other. On average, on village was visited by two traders. These overlapped catchment areas are likely to put more risk in the spread of HPAI H5N1 once the disease occurs. Regarding distances traveled by traders to catch chickens, TSs and HTs collect chickens only within average distance of 4.4 km radius around their houses due to their limited budgets and types of vehicles used in chicken catchment i.e. motorcycle and three-wheeled motorcycle whereas TTs, who normally use pick-up trucks as their vehicles, can travel to catch chickens up to 25 km approximately around their locations and TTs, apparently, transported many more chickens per one catchment compared to TSs and HTs. Thus, types of vehicles determined distances traders can travel and number of chickens they are capable to transport. Due to the distance traveled by traders, we classified TSs and HTs as 'short distance traders' and TTs as 'long distance traders'. It was evident in chapter 1 that the structure of poultry networks in Thailand may contribute to HPAI H5N1 spread through overlapped catchment areas of poultry traders (TSs and HTs) and long distance trading of TTs. It was also highlighted the temporal variations of live poultry movements, which were concentrated during the 15 days prior to Chinese New Year festival and, to a lesser extent, during four other festivals. In chapter 2, we developed an infectious model of HPAI H5N1 upon the compartmental stochastic dynamic model of traditional backyard chicken trade built in chapter 1. An SIR model was employed in this chapter and all compartments in chapter 1 were then subdivided according to infectious status into susceptible, infectious and removed compartments. The virus was initially seeded in a village located in Muang district area and then it was assumed to spread by two means: local spread (determined by transmitted kernel) to its neighboring uninfected villages and spread by poultry traders.Before a baseline infectious model was simulated, a sensitivity analysis was performed on various parameters as these parameters were firstly studied in this type of population. After conducting sensitivity analysis, we got baseline model with high spreadability of HPAI H5N1 virus (44%) in backyard chicken populations in Phisanulok province as the virus spread to 57% of the villages located in this province within 65 days and each village kept infecting up to 46 days approximately after only one village was firstly infected.Then, different scenarios of related control measures were simulated upon the baseline model. We found that banning only long distance traders reduced number 123 of accumulated infected villages by only 4.4% while banning all traders regardless the distances traveled to catch chickens decreased the same indicator by 30.5% and disease spread probability also decreased by this measure for 3 times compared to the baseline model. Besides poultry trader banning policy, other complementary control measures were also simulated. Our results indicated that combination of disinfecting poultry areas in the farm households and disinfecting traders' vehicles and facilities was the most effective way to reduce virus spreading from one village to another village at the time which the traders were still active. With the ban of poultry traders, disinfecting poultry areas rescued about half of infected villages. On overall, the most effective control measure obtained from our simulations was to ban all poultry traders regardless the distances traveled implemented together with the campaign of poultry area disinfection. This measure reduced disease spread probability and also average number of accumulated infected villages by more than 60% compared to the baseline model and it was only control measure which decreased average infectious days in each village to less than one week. Nonetheless, our study has not yet taken into account mass culling policies which require many other hypotheses to be involved.One limitation of this study is that the stochastic dynamic model of backyard chicken trade was simulated during non-epidemic period. Thus, the infectious model and control measure simulations which were developed upon the trade model were also applicable for the beginning of the outbreak when behaviors of traders are still unchanged. Once the present of suspected outbreak is notified, our proposed control measures should be promptly implemented. However, some control measures proposed in our study can be routinely practiced, for examples, disinfection of trader's vehicles and facilities.

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 :Figure 7 :Figure 8 :Figure 9 :Figure 10 :Figure 11 :Figure 12 :Figure 15 :Figure 17 :Figure 19 :Figure 20 :

 1234578910111215171920 Figure 1: Outbreaks of HPAI H5N1 in poultry notified to the OIE from the end of 2003 to 15 March 2014 (source: OIE, 2014). ........................................................................ 20 Figure 2: Number of confirmed human H5N1 cases by month of onset reported to WHO as of 25 February 2014 (Source: WHO, 2014). ........................................................ 21 Figure 3: Global distribution of human H5N1 cases and deaths since 2013 as of 8 January 2014 (source: CDC, 2014) ....................................................................................... 22 Figure 4: Temporal pattern of HPAI H5N1 outbreaks in Thailand during 2004 -2007 (source: Burgos et al., 2008) .................................................................................................. 23 Figure 5: Distribution of HPAI H5N1 outbreaks during 4 epidemic waves in Thailand during 2004 -2006 (source: Chantong and Kaneene, 2011). ........................................... 24 Figure 6: A conceptual model representing the organization of traditional live backyard chicken trade in one village located in Phitsanulok province, Thailand. .... 46 Figure 7: Theoretical distribution fitting on number of chickens caught from each village ...................................................................................................................................... 61 Figure 8: Simulated temporal pattern of average number of backyard chicken population within villages for three different compartments (young, ready-to-sell and stocked chicken) in a year-round (365 days). ............................................................ 63 Figure 9: Simulated temporal pattern of backyard chicken trade for three different types of slaughterhouse traders (TSs) (type A, B and C) and of all STs in a yearround (365 days). ................................................................................................................... 66 Figure 10: Simulated temporal pattern of backyard chicken trade for three different types of household traders (HTs) (type A, B and C) and of all HTs in a year-round (365 days). ............................................................................................................................... 67 Figure 11: Simulated temporal pattern of backyard chicken trade for three different types of trader of traders (TTs) (type A, B and C) and of all TTs in a year-round (365 days). ....................................................................................................................................... 68

( 1 ,Annex 1 :

 11 000 simulations/scenario). .............................................................................................. 112 Publication and international presentations Objective: The objective of this work is to model trade in this sector in time and space from the data collected in the field. Result of this spatial dynamic model should help to optimize monitoring and control measures for avian influenza and other infectious disease.Survey: Given the importance of the spread of the disease within villages and knowledge of geographical coordinates, the village was chosen as epidemiological unit. Phitsanulok province was chosen to be the study area because this province had the highest number of AI outbreaks in the first and second wave of the epidemic. Data were collected on 52,180 flocks in 1,035 villages and 20 collectors. Also, the data from comprehensive active surveillance and poultry census was used. The field surveys allowed quantifying exchanges between different actors of the sector (live poultry movements in time and space).

Field

  Name of trader: ………………………………………………………………………………………………………………………………………………. Catchment time: from…………….………to………………………… Duration…………..…..……hours….………………..……..minutes Number of traders in this catchment: ………………….………………Male………………..…... Female…………………………….. Number of households collected: ……………………….……… Number of village collected: ………………………………………… Total number of chicken: ……………………….. Average number of collected chicken/ household: ………………..………… What happens with chicken at the end of this catchment? …………………………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………..…….…………………………………………………… …………………………………………………………………………………………………………………………………………………………………………… ………………..…. Detailed data on each household visited  Household No………… Name of owner: ………………………………………………………………………………………………………………………………………………….. Address: ……………Moo……….Street ………………T.………………………………A…………………….….Village code: …………..……… Geographic location: …………………………………………………………………………………………………………………………………………… Number of all chicken in this household: …..………………….Cock: ………………….Hen: ………..………Chicks: ………………….  Number of young chicken (less than 5 months): ………………………………………………………………….  Number of old chicken (more than 5 months): ……………………………………………………………………  Desired age of selling: …………………………………months Number of chicken caught at this catchment:..……….Cock: …….………Hen: …………..  Number of chickens aged less than 3 months ………………………………………………………………..…….  Number of chickens aged between 3 and 5 months …………………………………………………………….  Number of chickens aged between 5 months and 1 year……………………………………………………….  Number of chickens aged more than 1 year …………………………………………………………………...…….  The oldest chickens caught at this catchment age……….years………months (Number:…………….) Total weight ……………… Kg Price ……………….. Baht / Kg Total price……………… Baht Special plan for Chinese New Year: ………………………………………………………………………………………......................................................................... ..................................................................................................................................................................

4

 4

Table 1 : HPAI H5N1 control measures implemented by Thai government during epidemics in 2004- 2008 (source: Burgos et al., 2008)

 1

		January 2004	July 2004	July 2005	2006 and onwards
	Case definition Poultry with clinical	Flock having	Poultry death rate >	Poultry death rate >
		signs 1 and sudden	poultry death rate >	1% for commercial	1% for commercial
		death of almost	10% in one	farms and > 5 % for	farms and > 5 % for
		100% OR	day	backyard poultry	backyard poultry,
		Cumulative			plus detection of
		mortality rate more			clear clinical signs
		than 40% within 3			of disease at arrival
		days without
		noticeable signs
	Culling	Pre-emptive culling	Pre-emptive culling	Pre-emptive culling	Stamping out in the
		in 5km radius	in 1km radius	in 1km radius	affected premises
		around case with	around case.	around case.
		75-100% 2 of market
		price compensation	Destruction of	Destruction of
			products	products
			and materials	and materials
	Movement	50km radius around	5km radius around	10km radius around	Quarantines,
	restrictions	infected areas	infected areas	infected areas	zoning
					and movement
			Sampling before	Movement of ducks	control inside the
			movements	restricted in 3	province/regions.
				provinces
	Hygiene	Thorough	Registration of	Thorough	Free-ranging ducks
		disinfection of	fighting cocks	disinfection of	activities forbidden;
		affected premises,		affected premises,	dipping/spraying of
		all infected and	Ban on exhibition	all infected and	incoming vehicle
		contaminated	and cockfighting	contaminated	tires
		materials in risk		materials in
		areas		risk areas

  action, number of new infected cases per unit of time is written in the form of iS  where  is the effective contact rate which represents average number of; i is percentage of infected individuals in total population and S is number of susceptible individuals. The term

					i  represents
	average potentially infective contact with infected individuals per one susceptible
	per unit of time. Thus, in case of only one infective present in the population, the
	infective can only infect the same number of susceptible individuals (  per unit of
	time) regardless the size of population (Chalvet-Monfray, 2006).
	However, in 1970s, Anderson and May proposed deterministic models based
	on hypothesis of pseudo-law of mass action. In contrast to law of mass action,
	number of new infected cases per unit of time in pseudo-law is in the form of		IS
	where  is a coefficient, I and S are number of infected and susceptible individuals
	respectively. The total population ( N ) is made up with the combination of I and S .
	Hence, the form	IS  can be rewritten in the form of		NiS	. Under this hypothesis, one
	infective individual can infect more susceptible individual as size of population
	increases (Chalvet-Monfray, 2006). Compare to law of mas action,

N

 

Table 2 : Types and numbers of poultry in Phitsanulok province recorded in the database of 'x-ray' campaign in March 2012

 2

	Type of poultry	Individual Animal Number	Percentage	Farm Number	Percentage
	Backyard chicken	1,661,168	42.9	37,337	87.4
	Egg-type chicken	261,467	6.8	513	1.2
	Meat-type chicken	541,375	14.0	277	0.6
	Breeder of meat-type chicken	36,484	0.9	41	0.1
	Breeder of egg-type chicken	2,912	0.1	36	0.1
	Duck	1,369,521	35.4	4,513	10.6
	Total	3,872,927	100.0	3,872,927	100.0

Table 3 : Parameters used in constructing compartmental stochastic dynamic model of live backyard chicken flows in Phitsanulok province, Thailand Parameters Value Origin

 3

	Village part
	Proportion of young chickens in total population(py)	0.55	Field observation
	Daily probability of young chickens to leave the young chicken compartment (p)	1/(5×30)	Chopakorn and Wongpichet, 2007
	Proportion of young chickens that flow into the stocked chicken compartment (pst)	0.5	Field observation
	Daily probability of retired stocked chickens to leave the stocked chicken compartment (sst)	0.1/(5×30)	Trader interviews
	Daily probability of mortality (m)	0.5/(5×30)	Chopakorn and Wongpichet, 2007
	Trader part
	Lambda of number of villages visited by a trader
	during normal period (  NBV) 1	0.85	Trader interviews
	Number of villages visited during festival periods	1-3	Trader interviews
	Lambda of number of chickens collected per village per day during normal period (  C)	16	Trader interviews
	Lambda of number of chickens collected per village per day during Chinese New Year (  CNY)	55.3	Trader interviews
	Lambda of number of chickens collected per village per day during other festivals (  OF)	55.3/2	Trader interviews
	Minimum number of chickens in the villages that traders prefer to visit	100	Field observation
	Number of non-repeated day	15	Field observation

1

Lambda corresponds to the mean of Poisson distribution

  in villagenon day 𝑡 that leave the compartment. On average, these two flows compensate each other and make the population stable. The parameter p is the daily probability of the chickens that leave compartment. The function BN is a function for sampling from a binomial distribution.The parameter m is the daily probability of chicken mortality.

	Where			, nt
	n t YC	1  	, n t YC inputYC outputYC ,   n t n t ,	(1.2.1)
	 outputYC ~BN YC , p n,t n,t		(1.2.2)
	, n t inputYC	 ~, , n t BN YC p		(1.2.3)
	Where	, nt YC is the number of chickens in village n on day 𝑡;	, nt inputYC is the
	number of newborn or imported chickens in village n on day 𝑡;	, nt outputYC is the
	number of chickens Daily mortality of chickens in the compartment followed binomial distribution
	(outputYCM) with probability m .
	 outputYCm ~BN outputYC ,m n,t n,t		(1.2.4)
	Where			, n t
	Daily probability of chicken growing up was number of all chickens moved out
	from the compartment (outputYC) excluding dead chickens (outputYCm).
	outputYCg	, n t	,  n t outputYC outputYCm n t ,	(1.2.5)
					50

outputYCm is the number of dead chickens in village n on day t.

4.1.5.2.1 Trader type A:

	, 0 jt  NV n U is uniform distribution of integral. , , , j t j n t HT C Where c  is lambda of number of chickens collected per village per day during (1.5.2)   1.4.1.5.1.3 Trader type C: normal period (without festivals).
	Where the total number of chickens collected by , jt TS is the total number of chickens collected by j HT on day t; ,, j n t C is the number of , jt HT is Trader type C visited 1-3 villages according to uniform distribution of integral Number of chickens collected by trader type B was according to CNY  during during Qingming Festival and Thai New Year (day 81-105), Hungry Ghost Festival 1.4.1.5.2.2 Trader type B: Refer to ,, j n t RC in (1.5.6); 𝑛 = , jt V (1.5.12)
	chickens collected by (day 228-242) and International New Year (day 351-365). During other periods, these , jt NV is the number of type A. traders behaved like trader type B. Chinese New Year period (day 17-31). In other periods, the traders acted like trader Where , jt V is village visited by j TS or j HT on day t.
	villages visited by	j TS or	j HT on day t.
	1.4.1.5.1 Number of villages visited by each trader each day         , ~1,3 ; 81,105 228, 242 351,365 jt U t    ; otherwise (1.5.4)   ; 17,31 CNY t ; otherwise (1.5.9) (1.5.10)   NV t , , j t j t V U AV    (1.5.13)
	(1.5.5) Where CNY Where , jt AV is a set of villages available for j TS or
	AV	, j t		 VR VN V t  , ' \ ; ' j t j t 	    1, 15 ; 	AV	, j t	  ; otherwise (1.5.15)	(1.5.14)
	j AV VR 	j			(1.5.15)
	, , j n t Where ~min C		Pois	  t 	,	RC	, , j n t		(1.5.6)
	C	, , j n t		TS		, , j n t	for chickens collected by	jt , TS ; otherwise (1.5.8)	(1.5.7)
	C	, , j n t		HT	, , j n t	(1.5.8)
	  NBV is number of chickens in ready-to-sell compartment of village n  ,3 (1.5.3) Pois  ,,  j n t       81,105 228, 242 351,365  , ~min Where RC jt NV ; t OF t     ; otherwise (1.5.10) (1.5.11)
	Where NBV visited by j Where OF  is lambda of number of chickens collected per village per day TS or  is lambda of number of villages visited by a trader during normal during Qingming Festival and Thai New Year (day 81-105), Hungry Ghost Festival
	period. Noted that lambda corresponds to the mean of Poisson distribution. (day 228-242) and International New Year (day 351-365).
	1.4.1.5.1.2 Trader type B: Number of chickens collected by trader type A was according to c  during 1.4.1.5.3 Identification of villages visited by each trader each day
	Trader type B visited 1-3 villages according to uniform distribution of integral normal period. As per our assumption, each TS and HT can visit only villages located within a
	during Chinese New Year period (day 17-31). During other periods, these traders radius of 7 km from his location and we put more condition to make our model more
	behaved like trader type A. t c  	(1.5.9)
				NV	jt ,
	, j t jt NV U n TS    0	C	, , j n t t 	; otherwise (1.5.3)	(1.5.1) (1.5.4)
										53

j TS on day t; j TS or j HT from village n on day t and Due to the organization of their activities over time, we further categorized traders into 3 types; type A: catch the same amount of chickens all year round, type B: catch more chickens only during Chinese New Year and type C: catch more chickens in all festivals. 1.4.1.5.1.1 Trader type A: Number of villages visited by trader type A in each day followed Poisson distribution of NBV  and maximum number of villages visited was set at 3 villages.     , ~1,3 ; 17,31 1.4.1.5.2 Number of chickens collected by each trader each day Number of chickens collected daily by TS or HT followed Poisson distribution of t

 or as available in the ready-to-sell compartment of the village (RC). j HT on day t.

1.

 is lambda of number of chickens collected per village per day during Chinese New Year period (day 17-31).

1.4.1.5.2.3 Trader type C:

Number of chickens collected by trader type C was according to OF  during Qingming Festival and Thai New Year (day 81-105), Hungry Ghost Festival (day 228-242) and International New Year (day 351-365). In other periods, the traders acted like trader type B.

realistic. The additional conditions are the villages for visiting each day must not be visited in the last 15 days and number of chickens available in the ready-to-sell compartment of the village must be higher than 100 chickens. If these two additional conditions are not valid that day, any villages located within a radius of 7 km from his location can be chosen. j HT to visit on day t. j VR is the villages situated within radius of 7 km from the location of j TS or j HT ; t VN is the villages with more than 100 chickens on day t and ,' jt V is the village visited by j TS or j

Table 4 : Questionnaire results on traders' characteristics.

 4 Chinese New Year,2 Other festivals,3 Household trader,4 Slaughterhouse trader, 5 Trader of trader, 6 Motorcycle, 7 Pick-up truck, 8 Three-wheeled motorcycle, 9 Not available The period that traders prepared to catch more chickens and sell during festivals was in average 15.7 days approximately before each festival. Hence, we increased chicken catching activities of the traders during 15 days before each festival

	as follows: Chinese New Year period: day 17-32, Qingming Festival and Thai New
	Year: day 81-106, Hungry Ghost Festival: day 228-243 and International New Year:
	day 350-365. The days stated here are according to Gregorian calendar starting from
	January 1 to December 31.

1

Table 5 : Chicken catching day of traders in the intensive survey during a 2-week-period.

 5

	Week	Day	HT5	HT6	TS3	TT2
	1			x 1	x	x
					x	x
			x	x		x
				x	x
	2				x
					x	x
				x	x	x
			x	x	x	x
				x	x	x
	Total		2	6	8	6

Table 5 : Chicken catching day of traders in the intensive survey during a 2-week-period.

 5

	Week	Day	HT5	HT6	TS3	TT2
	1			x 1	x	x
					x	x
			x	x		x
				x	x
	2				x
					x	x
				x	x	x
			x	x	x	x
				x	x	x
	Total		2	6	8	6

1

Trader went to catch chickens.

Table 6 . Compartment Average number of chickens per village per day (1 simulation) Average number of chickens per village per day (1,000 simulations)

 6

		Median	Min	Max	Median	Min	Max
	Young chickens	873.61	872.81	874.7	874.30	874.27	874.39
	Ready-to-sell chickens 350.00	339.67	359.28	351.10	340.15	360.56
	Stocked chickens	360.90	357.67	362.23	361.00	357.67	362.67

Table 6 : Average number of chickens per village per day in each village compartment, as derived from stochastic temporal simulations.

 6 According to Figure8, the average number of chickens per village in the compartments of young chicken and stocked chicken is stable throughout the year, with approximately 875 and 360 chickens. However for the ready-to-sell compartment, this number sharply decreased to 340 chickens during the period of Chinese New Year, before gradually climbing up to the initial level (360 chickens) at the end of the year. As the distribution of chickens in these compartments is not normal, median value is used instead of mean.

	Compartment

Average number of chickens per village per day (1 simulation) Average number of chickens per village per day (1,000 simulations)

		Median	Min	Max	Median	Min	Max
	Young chickens	873.61	872.81	874.7	874.30	874.27	874.39
	Ready-to-sell chickens 350.00	339.67	359.28	351.10	340.15	360.56
	Stocked chickens	360.90	357.67	362.23	361.00	357.67	362.67

Table 7 .

 7

	1 simulation	1 simulation
	1,000 simulations	1,000 simulations
	1 simulation
	1,000 simulations

Table 7 : Average number of chickens caught per trader per day for each type of traders, as derived from stochastic temporal simulations.

 7

1

Trader-slaughterhouse, 2 Household trader,

3

Trader of trader.

Trader Trader type Number of chickens caught per trader per day (1 simulation) Average number of chickens caught per trader per day (1,000 simulation)

			Median	Min	Max	Median	Min	Max
		A	15	0	52	14.39	12.81	15.50
	TS 1	B C	14 17	0 0	177 172	13.10 13.78	11.80 12.66	111.32 110.07
		All	13.25	2.5	91.88	13.01	12.11	74.04
		A	12	0	66	11.46	9.64	14.26
	HT 2	B C	14 16	0 0	185 170	13.06 13.71	11.76 12.33	108.76 112.52
		All	12.13	2	85	11.46	10.38	74.5
	TT1 3	All	97	16	680	91.65	83.03	596
	TT2	All	164	68	793	156.46	148.18	646.55
	TT3	All	87	22	313	82.85	78.76	278.1
	TT all	All	115	62	573.67	110.25	104.81	503.04
								66

Table 8 : Summary of outcomes generated from 1,000 simulations of the stochastic dynamic model for live poultry flows in traditional backyard chicken trade chains in Thailand during normal periods, Chinese New Year festival, and Hungry Ghost Festival.

 8

	During normal period (15 days), TSs and HTs visited half of the villages
	available in the study area (309 of 672) and collected large numbers of chickens
	(6,737; 95% CI = 6,007-8,478) during this short period. Then, 76.5% (5,152/6,737) of
	these collected chickens were further aggregated by TTs (95% CI = 4,569-5,761). In
	the same period, each trader visited 13 villages on average (95% CI = 12.7-13.1) and
	caught about 15 chickens approximately from each village visited (95% CI = 15.0-
	15.6).
	Distances traders traveled to purchase chickens and the number of chickens
	collected in different periods of the year is depicted in Figure 15. TSs and HTs
	collected approximately 41.5 chickens each time during the Chinese New Year
	festival (95% CI = 18.8-54.4), and only 20.0 (95% CI = 15.4-25.6) and 15.3 chickens
	(95% CI = 15.0-15.6) during the Hungry Ghost Festival and normal periods

1 Trader-slaughterhouse, 2 Household trader,

3

Trader of trader.

  disinfection. This measure decreased disease spread probability by 65.9% and it reduced average number of accumulated infected villages by 64.7% compared to baseline model's values. Furthermore, this control measure is the only one that can decrease average infectious days in each village by 62.8% (from 15.6 to 5.8 days) whereas this value ranged from 11.4-15.7 days in other control measure simulations.

	Nevertheless, Fournié et al., 2013 indicated in a study conducted in Vietnam

Table 1 :

 1 HPAI H5N1 control measures implemented by Thai government during epidemics in 2004-2008 (source: Burgos et al., 2008) ........................................................ 25

Table 2 :

 2 Types and numbers of poultry in Phitsanulok province recorded in the database of 'x-ray' campaign in March 2012 .................................................................... 43

Table 3 :

 3 Parameters used in constructing compartmental stochastic dynamic model of live backyard chicken flows in Phitsanulok province, Thailand.................................... 47

Table 4 :

 4 Questionnaire results on traders' characteristics. .............................................. 58

Table 5 :

 5 Chicken catching day of traders in the intensive survey during a 2-weekperiod. ..................................................................................................................................... 59

Table 6 :

 6 Average number of chickens per village per day in each village compartment, as derived from stochastic temporal simulations. .................................. 62

Table 7 :

 7 Average number of chickens caught per trader per day for each type of traders, as derived from stochastic temporal simulations. ............................................. 65

Table 8 :

 8 Summary of outcomes generated from 1,000 simulations of the stochastic dynamic model for live poultry flows in traditional backyard chicken trade chains in Thailand during normal periods, Chinese New Year festival, and Hungry Ghost Festival. ................................................................................................................................... 73

Table 9 :

 9 Sensitivity analysis results of mortality rate (ϒ) (day -1 ) related with HPAI H5N1 spread in backyard chicken populations in Phitsanulok province, Thailand.The results based on 6,000 simulations (1,000 simulations/scenario). ......................... 103

Table 10 :

 10 Sensitivity analysis results of disease transmission rate (β) (day -1 ) related with HPAI H5N1 spread in backyard chicken populations in Phitsanulok province, Thailand. The results based on 7,000 simulations (1,000 simulations/scenario). ....... 103

Table 11 :

 11 Sensitivity analysis results of initial HPAI H5N1 infected village in Phitsanulok province, Thailand. The results based on 3,000 simulations (1,000 simulations/scenario). ......................................................................................................... 104

Table 12 :

 12 Sensitivity analysis results of transmission rate by visit of infected trader ( ) related with HPAI H5N1 spread in backyard chicken populations in Phitsanulok province, Thailand. The results based on 7,000 simulations (1,000 simulations/scenario). ......................................................................................................... 104

Table 13 :

 13 Results of HPAI H5N1 infectious model simulations in backyard chicken populations in Phitsanulok province, Thailand. The results based on 1,000 simulations. .......................................................................................................................... 106

Table 14 :

 14 Results of HPAI H5N1 control measure simulations when all traders were allowed to trade in Phitsanulok province, Thailand. The results based on 4,000 simulations (1,000 simulations/scenario). ........................................................................ 110

Table 15 :

 15 Results of HPAI H5N1 control measure simulations when only local traders (TS and HT) were allowed to trade in Phitsanulok province, Thailand. The results based on 4,000 simulations (1,000 simulations/scenario). ............................................. 111

Table 16 :

 16 Results of HPAI H5N1 control measure simulations when all traders were banned in Phitsanulok province, Thailand. The results based on 10,000 simulations

2 ข้ อมู ลในวั นตามผู ้ จั บไก่ ข้ อสรุ ปของการจั บไก่ ครั ้ งนี ้

  จ านวนไก่ ที ่ คาดหวั งว่ าจะเชื อดต่ อวั น ………..………….ตั ว  จ านวนไก่ เฉลี ่ ยที ่ เชื อดจริ งต่ อวั น ………..………….ตั ว  ได้ มี การน าไก่ จากแหล่ งอื ่ นนอกจากไก่ ที ่ ออกไปจั บเองมาเชื อดด้ วยหรื อไม่ ⃝ ไม่ ⃝ใช่ โปรดระบุ แหล่ ง มี การน าไก่ จากแหล่ งอื ่ นเข้ ามาเชื อดบ่ อยแค่ ไหน…………………………………………ครั ้ ง/สั ปดาห์ o จ านวนเฉลี ่ ยของไก่ ที ่ น าเข้ ามาแต่ ละครั ้ ง ……………….………….ตั ว  ระยะเวลาเฉลี ่ ยและพิ สั ยที ่ เก็ บไก่ ที ่ เชื อดแล้ วก่ อนส่ งตลาด …………………………[ชั ่ วโมง] [วั น]  ไก่ ที ่ เชื อดแล้ วส่ งไปขายที ่ ใด ……………………………….…………………….......... ผู ้ จั บไก่ ท าความสะอาดยานพาหนะที ่ ใช้ ในการจั บไก่ ……………………… ครั ้ ง/ [สั ปดาห์ ] [เดื อน]  น ้ ายาท าความสะอาด ⃝ใช้ ⃝ ไม่ ใช้ ถ้ าใช้ ชนิ ดของน ้ ายาท าความสะอาดที ่ ใช้ ………………………  ความเข้ มข้ น ………………………………………………………………………..…………………….……………….  ผู ้ จั บไก่ ท าความสะอาดกรงจั บไก่ และอุ ปกรณ์ ……………………… ครั ้ ง/ [สั ปดาห์ ] [เดื อน]  น ้ ายาท าความสะอาด ⃝ใช้ ⃝ ไม่ ใช้ ถ้ าใช้ ชนิ ดของน ้ ายาท าความสะอาดที ่ ใช้ ………………………  ความเข้ มข้ น ………………………………………………………………………..…………………….……………….  ผู ้ จั บไก่ ท าความสะอาดพื ้ นที ่ ขั งไก่ ……………………… ครั ้ ง/ [สั ปดาห์ ] [เดื อน]  น ้ ายาท าความสะอาด ⃝ใช้ ⃝ ไม่ ใช้ ถ้ าใช้ ชนิ ดของน ้ ายาท าความสะอาดที ่ ใช้ ………………………  ความเข้ มข้ น ………………………………………………………………………..…………………….………………. ราคาในช่ วงตรุ ษจี น ราคาซื ้ อ …………………บาท/กิ โลกรั ม ราคาขาย …………………บาท/กิ โลกรั ม ราคาที ่ แพงในตลาด …………………บาท/กิ โลกรั ม  ราคานอกช่ วงตรุ ษจี น (ช่ วงปกติ ) ราคาซื ้ อ …………………บาท/กิ โลกรั ม ราคาขาย …………………บาท/กิ โลกรั ม ราคาที ่ แพงในตลาด …………………บาท/กิ โลกรั ม ผู ้ จั บไก่ ได้ จั บไก่ จ านวนมากกว่ าปกติ หรื อไม่ ในช่ วงก่ อนตรุ ษจี น ⃝ ใช่ ⃝ ไม่ ใช่  เพื ่ อเตรี ยมไก่ ขายในช่ วงก่ อนตรุ ษจี น ผู ้ จั บไก่ ต้ องเตรี ยมจั บไก่ เพิ ่ มนานแค่ ไหน …….………… [สั ปดาห์ ] [เดื อน]  จ านวนเฉลี ่ ยของไก่ ทั ้ งหมดที ่ จั บต่ อครั ้ งในช่ วงก่ อนตรุ ษจี น …….………….ตั ว  ระยะเวลาเฉลี ่ ยที ่ ขั งไก่ ไว้ เพื ่ อขายในช่ วงตรุ ษจี น ………………………… [วั น] [สั ปดาห์ ] [เดื อน]  มี เทศกาลอื ่ นอี กหรื อไม่ ที ่ มี ความต้ องการไก่ ของผู ้ บริ โภคมากกว่ าปกติ อย่ างเช่ นตรุ ษจี น ⃝ มี ⃝ ไม่ มี หากมี เทศกาลใดบ้ าง ………………………………………………..…………………………………………..…… และผู ้ จั บไก่ มี การเตรี ยมการส าหรั บเทศกาลนั ้ นๆ อย่ างไร หากเคย กี ่ ครั ้ ง ……………………… เมื ่ อใดและพื ้ นที ่ ใดบ้ าง………………………………………..…………………. จ านวนผู ้ จั บไก่ ในครั ้ งนี ้ …………คน ชาย…………คน หญิ ง…………คน ชื ่ อผู ้ จั บไก่ ……………………………………………………. เวลาจั บไก่ เริ ่ ม ………………………น. เสร็ จ ………………………น. รวมเป็ นเวลา…………ชั ่ วโมง………….นาที จ านวนบ้ านที ่ เข้ าจั บไก่ ในครั ้ งนี ้ …………………… หลั ง จ านวนหมู ่ บ้ านที ่ เข้ าจั บไก่ ในครั ้ งนี ้ …………………… หมู ่ บ้ าน จ านวนไก่ ที ่ จั บได้ ทั ้งหมด ………… ตั ว จ านวนเฉลี ่ ยและพิ สั ยของไก่ ที ่ จั บต่ อบ้ าน ………… ตั ว (……………-……………..) หลั งจากสิ ้นสุ ดการจั บไก่ ครั ้ งนี ้ ผู ้ จั บไก่ น าไก่ ไปไว้ ที ่ ใด และมี แผนจะท าอย่ างไรกั บไก่ ต่ อไป ชื ่ อเจ้ าของบ้ าน ….……………………………………………………………………………………………………………………………….. บ้ านเลขที ่ ……………หมู ่ ที ่ ……………ต าบล.……………………อ าเภอ…………………………….รหั สหมู ่ บ้ าน ……………… ตั ว ตั วผู ้ ……………… ตั ว ตั วเมี ย ……………… ตั ว ลู กเจี ๊ ยบ ……………… ตั ว  ไก่ อายุ น้ อยกว่ า 5 เดื อน จ านวน ……………… ตั ว ……………… ตั ว ตั วผู ้ ……………… ตั ว ตั วเมี ย ……………… ตั ว  ไก่ ที ่ จั บ อายุ น้ อยกว่ า 3 เดื อน จ านวน ……………… ตั ว  ไก่ ที ่ จั บ อายุ มากกว่ า 3 เดื อน แต่ ไม่ เกิ น 5 เดื อน จ านวน ……………… ตั ว  ไก่ ที ่ จั บ อายุ มากกว่ า 5 เดื อน แต่ ไม่ เกิ น 1 ปี จ านวน ……………… ตั ว  ไก่ ที ่ จั บ อายุ เกิ น 1 ปี จ านวน ………… ตั ว (ไก่ ที ่ จั บ อายุ มากที ่ สุ ด………ปี …………เดื อน จ านวน …………… ตั ว) น ้าหนั กรวม ……………… กิ โลกรั ม ราคา ……………… บาท/กิ โลกรั ม ได้ เงิ น ……………… บาท โดยปกติ มี แผนการเลี ้ยงไก่ เพื ่ อเตรี ยมรั บความต้ องการจ านวนไก่ ที ่ เพิ ่ มขึ ้นช่ วงตรุ ษจี นหรื อไม่ ⃝ มี ⃝ ไม่ มี ถ้ ามี โปรดระบุ

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	…………………………………………………………………………………………………………………………………………………………… o ที ่ อยู ่ ……
	……………………………………………………………………………………………………………………………………………………… รายละเอี ยดบ้ านที ่ ขายไก่ ในครั ้ งนี ้
	…………………………………………………………………………………………………………………………………….……………. บ้ านที ่ 1
	 ผู ้ จั บไก่ ส่ งไก่ ไปเชื อดที ่ โรงเชื อด/ผู ้ เชื อดไก่ …………………….แห่ ง
	ที ่ ใดบ้ าง โปรดระบุ ………………………………………………………………………………………………………………………………………………………
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	……………………………………………………………………………………………………………………………………………………… ช่ วงที ่ มี การระบาดของไข้ หวั ดนกในประเทศไทย
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	มาดรการด้ านความปลอดภั ยทางชี วภาพ จ านวนไก่ ที ่ จั บในครั ้ งนี ้
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	 ผู ้ จั บไก่ มี การปรั บตั วอย่ างไรกั บนโยบายห้ ามการเคลื ่ อนย้ ายไก่ ระหว่ างการระบาดของไข้ หวั ดนก

 (B) ผู ้ จั บไก่ ที ่ ไม่ ได้ เชื อดและช ำแหละไก่ เอง  ระยะเวลาเฉลี ่ ยที ่ ขั งไก่ ไว้ ก่ อนส่ งเชื อด …………………………[ชั ่ วโมง] [วั น]  168 แผนการจั บไก่ ในช่ วงก่ อนตรุ ษจี น  ราคาไก่   เคยมี การระบาดของไข้ หวั ดนกในพื ้ นที ่ บ้ านของผู ้ จั บไก่ หรื อไม่ ⃝ เคย ⃝ ไม่ เคย  หากเคย กี ่ ครั ้ ง ……………………… เมื ่ อใดบ้ าง……………………………..………………………..………………….  เคยมี การระบาดของไข้ หวั ดนกในพื ้ นที ่ ผู ้ จั บไก่ เข้ าไปจั บไก่ หรื อไม่ ⃝ เคย ⃝ ไม่ เคย  ……………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………  เมื ่ อเกิ ดการระบาดของไข้ หวั ดนกในพื ้ นที ่ นานเท่ าไร จึ งสามารถกลั บการจั บไก่ ขายได้ ตามปกติ ……………………………………………………………………………………………………………………………………………… แบบฟอร์ มภาคสนามที ่ ……………………พิ กั ดภู มิ ศาสตร์ ………………………………………………………………………ชื ่ อไฟลเส้ นทาง……………………… ………………… จ านวนไก่ ทั ้งหมดในบ้ านนี ้ ………………………………………………………………………………………........................................................................................

February 2014 (Source: WHO, 2014).

Clinical signs were defined as severe respiratory signs, with excessively watery eyes and sinusitis, cyanosis of the combs, wattle and shanks, edema of the head, ruffled feathers with diarrhea and nervous system disruption signs. ,

During 23 January-10 February 2004, the compensation was raised to 100% of market value because of the widespread of the outbreaks. Afterward, the compensation was turned into the normal rate at 75% of market price[START_REF] Heft-Neal | Supply Chain Auditing for Poultry Production in Thailand[END_REF].Besides the main control measures, DLD also implemented an intensive active surveillance called 'The x-ray campaign'. The campaign was run biannually in the months at risk which past outbreaks occurred or the months of increased poultry

Accumulated infected villages,

Confidence interval,

Daily infectious villages,

Infectious days in the model zone,

Infectious days in each village

The Society for Veterinary Epidemiology and Preventive Medicine (SVEPM) AnnualConference, 26-28 March, 2014, Dublin, Ireland (Poster presentation)

Trader did not collect chickens but collected ducks instead.

Acknowledgements

grateful to Mr. Moncef Meddeb, Ms. Wanpen Siripat and Ms. Salisa Limsakul and all staffs at French Embassy in Thailand for their kind supports and managements. Also, I thank CROUS and Campus project. I especially thank Dr. Christian Ducrot and Dr. Gwenael This PhD project was funded by French scholarship via French embassy in Thailand and partially supported by INRA and VetAgro Sup. The project was a Franco-Thai research collaboration between Thai and French institutes. In French side, Professor Dr. Karine Chalvet-Monfray is the main supervisor. The project was mainly conducted at VetAgro Sup Campus Vétérinaire de Lyon. In Thai side, the project was co-

some data previously collected by traders' behaviors. Also, backyard chicken census data was provided by

Introductory Chapter

(95% CI = 1.1-1.5) during normal period and Huger Ghost festival and number of traders increased to 1.5 (95% CI = 1.2-1.7) during Chinese New Year festival. Here, we further divided each compartment into three different infectious status compartments as illustrated in Figure 18. Young chicken compartment was divided into compartments of Susceptible Young Chicken (SYC), Infectious Young Chicken (IYC) and Removed Young Chicken (RYC). The compartments of stocked chicken and ready-to-sell chicken were also divided in the same way. Consequently, chickens in each village were divided into 9 compartments: Susceptible Young Chicken (SYC), Infectious Young Chicken (IYC) and Removed Young Chicken (RYC), Susceptible Stocked Chicken (SSC), Infectious Stocked Chicken (ISC) and Removed Stocked Chicken (RSC), Susceptible Ready-to-sell Chicken (SRC), Infectious Readyto-sell Chicken (IRC) and Removed Ready-to-sell Chicken (RRC).

The model was run on daily basis for one-year period (365 days: start from January 1 to December 31). As the model is stochastic, we make in 1,000 simulations.

Initially, all chickens were classified as susceptible and then some of them were infected as we would explain in 2.3.3. The conceptual SIR model is illustrated in Figure 18. Mathematical equations explaining how the infectious model was constructed are as in 2.3.1-2.3.4. in village n on day t and , nt SYCip is the number of newborn or imported chickens in village n on day t.

Chickens in the compartment of SSC left the compartment daily by infected with HPAI H5N1 (SSCi), died from other causes (SSCm) and retired from the compartment (too old to produce new generation) (SSCr). At the same time, some grown-up chickens (SSCg) were daily added into the compartment. SSCg is the number of grown up chickens that are imported into the compartment in village n on day t.

In the compartment of SRC, chickens daily left the compartment by infected with HPAI H5N1 (SRCi), died from other causes (SRCm) and sold to poultry traders (SRCc). This compartment gained some daily additional chickens from grown-up chickens (SRCg) and retired chickens (SSCr).

(S ,1 e )

Infectious compartments

As stated earlier, all chickens were, at day 1, put into susceptible compartments and let the model run without infection until day 16. Since Chinese New Year festival was regarded as a risky period, the infection started on day 17 (beginning of the increase in chicken catching activities for Chinese New Year Festival). On day 17, only one chicken in the province was initially infected. Afterward, the infected model was run simultaneously until day 365.

In the infectious compartments (IYC, ISC and IRC), chickens daily moved into these compartments by infected with HPAI H5N1 (SYCi, SSCi and SRCi) and chickens daily moved out of these compartments by daily mortality (IYCm, ISCm and IRCm). In addition, chickens in IRC also left the compartment by being sold to the traders (IRCc).

No additional control measures

The baseline model as in 2.5.1.1 was modified by totally eliminating the role of all poultry traders.

Disinfect poultry areas in the farm households

The model as in 2.5.1.2 was modified by totally eliminating the role of all poultry traders and the equation 2.7.2 was still applied.

Results

Sensitivity analysis

According to criteria stated earlier and based on  value of 1/3 /day, the chosen  was 1.5 /day since this value provided the highest disease spread probability at 0.46 (95% CI = 0.43-0.50). The  value of 0.01 that yields the highest average number of accumulated infected villages at 464.7 villages (95% CI = 66.7-534.6) was chosen to be transmission rate by visit of infected trader.

The zone of Muang district was chosen to be the zone which the initial infected village was located in since this zone gave the highest disease spread probability at 0.44 (95% CI = 0.41-0.47) as well as the highest average number of accumulated infected villages at 596.1 villages (95% CI = 531.7-650.0). Details on sensitivity analysis results are shown in 102 In order to illustrate how HPAI H5N1 spatially spread from the index village to other villages in the province, a simulation was chosen and plotted in a map. In this simulation, HPAI H5N1 began infecting a village in Muang district on day 17 and the snap short of disease infection progress was taken every 10 days. The peak number of infectious village was on day 77 at 434 villages and the disease disappeared within 134 days. The infectious map is depicted in Figure 19.

. In order to illustrate how HPAI H5N1 spatially spread from the index village to other villages in the province, a simulation was chosen and plotted in a map. In this simulation, HPAI H5N1 began infecting a village in Muang district on day 17 and the snap short of disease infection progress was taken every 10 days. The peak number of infectious village was on day 77 at 434 villages and the disease disappeared within 134 days. The infectious map is depicted in Figure 19.

List of figures and tables

Model: Compartments represented a group of chickens which can be moved from village to collector, then from collector to slaughterhouse. The model also accounted for the age of chickens. The model is a compartmental model. Given the size of the exchanges between the actors, the model is a stochastic model to simulate the variability in trade. The aim of the model is not exactly represent a comprehensive manner all trade but represent a likely situation. Thus, the contact network is drawn from the information obtained in the field. Field data were used to simulate a likely network. Modelling was carried out in two steps. The first step consisted in setting initial conditions of the network by combining field data with simulation. The second step was a stochastic dynamic modelling of chicken movements in the networks.

Results and discussion:

As first result, we can compare between the results obtained by using the observed network and those obtained using the simulated networks.

The model reproduces the observed data: the stimulation can mimic the reality and