David Gramaje

Massimiliano Morelli

Lars Hestbjerg Hansen

Ifigeneia Kyrkou

Taneli Pusa

Lea Ellegaard-Jensen

Marie-France Sagot

Pierce's Disease of Grapevines: A Review of Control Strategies and an Outline of an Epidemiological Model

Keywords: Xylella fastidiosa, grapevine, Pierce's disease, control strategies, prophylactic, therapeutic, epidemiological model, Homalodisca vitripennis

Xylella fastidiosa is a notorious plant pathogenic bacterium that represents a threat to crops worldwide. Its subspecies, Xylella fastidiosa subsp. fastidiosa is the causal agent of Pierce's disease of grapevines. Pierce's disease has presented a serious challenge for the grapevine industry in the United States and turned into an epidemic in Southern California due to the invasion of the insect vector Homalodisca vitripennis. In an attempt to minimize the effects of Xylella fastidiosa subsp. fastidiosa in vineyards, various studies have been developing and testing strategies to prevent the occurrence of Pierce's disease, i.e., prophylactic strategies. Research has also been undertaken to investigate therapeutic strategies to cure vines infected by Xylella fastidiosa subsp. fastidiosa. This report explicitly reviews all the strategies published to date and specifies their current status. Furthermore, an epidemiological model of Xylella fastidiosa subsp. fastidiosa is proposed and key parameters for the spread of Pierce's disease deciphered in a sensitivity analysis of all model parameters. Based on these results, it is concluded that future studies should prioritize therapeutic strategies, while investments should only be made in prophylactic strategies that have demonstrated promising results in vineyards.

INTRODUCTION

Pierce's disease (PD) is a disease that affects grapevines (Vitis vinifera). The disease is prevalent across the United States (US), from Florida to California, and threatens the country's $30 billion wine industry [START_REF] Sanscartier | Glassy-winged sharpshooter population survey and Xylella fastidiosa detection[END_REF]. Since the 1880s, PD has caused the decline of more than 35,000 acres of vineyards in Southern California (SC) [START_REF] Galvez | The threat of Pierce's disease to midwest wine and table grapes[END_REF]. The aetiological agent of PD is a gram-negative, plant-pathogenic bacterium, Xylella fastidiosa subsp. fastidiosa (Xff ; [START_REF] Davis | Pierce's disease of grapevines: isolation of the causal bacterium[END_REF]. The species X. fastidiosa (XYLEFA) comprises three well-established subspecies, which infect different plant hosts [START_REF] Almeida | How do plant diseases caused by Xylella fastidiosa emerge?[END_REF][START_REF] Marcelletti | Genome-wide comparison and taxonomic relatedness of multiple Xylella fastidiosa strains reveal the occurrence of three subspecies and a new Xylella species[END_REF], while the existence of a fourth and a fifth subspecies is in dispute [START_REF] Marcelletti | Genome-wide comparison and taxonomic relatedness of multiple Xylella fastidiosa strains reveal the occurrence of three subspecies and a new Xylella species[END_REF][START_REF] Giampetruzzi | Genome-wide analysis provides evidence on the genetic relatedness of the emergent Xylella fastidiosa genotype in Italy to isolates from Central America[END_REF]. Generally, XYLEFA is characterized by a wide plant host range, currently reported to include more than 300 different plant species belonging to 187 genera and 68 families [START_REF] Stancanelli | Assessing the risk posed to plant health by Xylella fastidiosa in the European Union[END_REF]. While not all of these hosts are susceptible to PD, XYLEFA negatively affects the yields of many economically important crops other than grapevine, such as almond, mulberry, peach, olive, citrus, and plum [START_REF] Stancanelli | Assessing the risk posed to plant health by Xylella fastidiosa in the European Union[END_REF]. Until recently, the pathogen was primarily found in the US, but in 2013 the first European outbreak was recorded in olive trees in Apulia, Italy [START_REF] Saponari | Identification of DNA sequences related to Xylella fastidiosa in oleander, almond and olive trees exhibiting leaf scorch symptoms in Apulia (Southern Italy)[END_REF]. Lately, numerous XYLEFA incidents in France and Spain are being reported (Godefroid et al., 2018 and references therein).

XYLEFA is transmitted to host plants by specialized insect vectors [START_REF] Janse | Xylella fastidiosa: its biology, diagnosis, control and risks[END_REF]. All vectors proven to transmit the pathogen belong to the groups of spittlebugs and sharpshooter leafhoppers [START_REF] Almeida | How do plant diseases caused by Xylella fastidiosa emerge?[END_REF]. Specialized XYLEFA vectors can inject the pathogen directly into the xylem of the host plant via their sucking mouthparts and as a result of their general feeding habits [START_REF] Redak | The biology of xylem fluid-feeding insect vectors of Xylella fastidiosa and their relation to disease epidemiology[END_REF]. In principle, any xylem-sap feeding insect could be a specialized vector in new areas of entry (Almeida et al., 2005a). Plant hosts susceptible to XYLEFA are often heavily colonized by the pathogen [START_REF] Hill | Multiplication and movement of Xylella fastidiosa within grapevine and four other plants[END_REF]. However, the mechanisms of specific interactions among XYLEFA subspecies and their susceptible hosts have yet to be resolved [START_REF] Rapicavoli | Xylella fastidiosa: an examination of a re-emerging plant pathogen[END_REF]. [START_REF] Killiny | The exopolysaccharide of Xylella fastidiosa is essential for biofilm formation, plant virulence, and vector transmission[END_REF] propose that the production of exopolysaccharides could be a determinative factor of the bacterium's virulence since exopolysaccharides help XYLEFA colonize its two habitats: the foregut of its vectors and the xylem of its plant hosts [START_REF] Chatterjee | Living in two worlds: the plant and insect lifestyles of Xylella fastidiosa[END_REF]. More specifically, XYLEFA exopolysaccharides seem to be responsible for the appearance of water stress symptoms along with plant-derived physiological responses, such as extensive tylose and gum production [START_REF] Hopkins | Xylella fastidiosa: xylem-limited bacterial pathogen of plants[END_REF][START_REF] Choi | Water deficit modulates the response of Vitis vinifera to the Pierce's disease pathogen Xylella fastidiosa[END_REF]. Examples of plant defense response mechanisms include cell-wall remodeling and upregulation of plant hormone pathways and defense-related recognition receptors [START_REF] Rodrigues | RNA-Seq analysis of Citrus reticulata in the early stages of Xylella fastidiosa infection reveals auxin-related genes as a defense response[END_REF][START_REF] Giampetruzzi | Transcriptome profiling of two olive cultivars in response to infection by the CoDiRO strain of Xylella fastidiosa sub sp. pauca[END_REF][START_REF] Zaini | Molecular Profiling of Pierce's Disease Outlines the Response Circuitry of Vitis vinifera to Xylella fastidiosa Infection[END_REF], while the various virulence factors of XYLEFA have been extensively reviewed elsewhere [START_REF] Rapicavoli | Xylella fastidiosa: an examination of a re-emerging plant pathogen[END_REF].

XYLEFA poses a significant threat to susceptible host plants and agriculture worldwide [START_REF] Almeida | How do plant diseases caused by Xylella fastidiosa emerge?[END_REF]. This threat is compounded by the bacterium's high levels of genetic plasticity [START_REF] Nunney | Large-scale intersubspecific recombination in the plant-pathogenic bacterium Xylella fastidiosa is associated with the host shift to mulberry[END_REF] and the fact that in the first stages of infection the hosts do not display any symptom [START_REF] Hopkins | Seasonal concentration of the Pierce's disease bacterium in grapevine stems, petioles, and leaf veins[END_REF][START_REF] Almeida | How do plant diseases caused by Xylella fastidiosa emerge?[END_REF]. The European Food Safety Authority (EFSA) Plant Health Panel has therefore recommended that the European research community intensify studies on the epidemiology and control of XYLEFA (EFSA PLH Panel, 2015a). Several intervention strategies have already been addressed to prevent, suppress, and eliminate the pathogen in vineyards, but as yet there is no strategy available that can cure infected plants in the field (EFSA PLH Panel, 2015a).

This review addresses all the strategies that have been proposed thus far. These strategies are divided into groups A and B. Group A lists only prophylactic strategies, i.e., strategies to avoid infection incidents in vineyards, and Group B includes therapeutic strategies, i.e., strategies suggested for controlling the Abbreviations: XYLEFA, Xylella fastidiosa; Xff, Xylella fastidiosa subsp. fastidiosa; PD, Pierce's disease; GWSS, glassy-winged sharpshooter; SC, Southern California.

pathogen and excluding it from an infected vineyard. Tables 1,2 list all the promising strategies in groups A and B, respectively and include the current status of each strategy and most recent citations. Furthermore, the Xff epidemiological model has been developed to describe the disease dynamics of Xff in vineyards. The Xff epidemiological model identifies key parameters in the spread of PD that should be pursued by current and future intervention strategies. The framework of this model may assist the future design of more complex models of Xff and XYLEFA disease dynamics.

GROUP A: PROPHYLACTIC STRATEGIES

Prophylactic practices against PD are typically aimed at either inoculum reservoirs or modes of dispersal of the pathogen in vineyards, i.e., host plants and insect vectors [START_REF] Almeida | Transmission of Xylella fastidiosa to grapevines by Homalodisca coagulata (Hemiptera: Cicadellidae)[END_REF]. When prophylactic measures deal with alterations to cropping techniques, a combination of practices is highly recommended for optimal results (EFSA, 2016). A summary of all types of prophylactic strategies discussed below is illustrated in Figure 1A.

Control of Insect Vectors

Maintaining the insect vector populations at low levels has traditionally been attempted via foliar and soil-applied insecticide treatments (Almeida et al., 2005a;EFSA, 2015). Vinegrowers have often combined insecticides with a specific type of insect traps, known as yellow sticky traps, either to indicate the necessity for or monitor the efficiency of insecticides in the field (EFSA, 2016). Moreover, in Californian nurseries citrus plants have typically been fumigated with insecticides [START_REF] Ancona | Xylella fastidiosa: a model for analyzing agricultural biosecurity[END_REF]. The basic vector of Xff in vineyards is the glassy-winged sharpshooter [Homalodisca vitripennis, formerly known as H. coagulata (GWSS)] [START_REF] Hopkins | Xylella fastidiosa: cause of Pierce's disease of grapevine and other emergent diseases[END_REF]. Given that the vast majority of control strategies against Xff vectors aim at GWSS, this review focuses on GWSS exclusively. Many studies have tracked the susceptibility of GWSS to different classes of insecticides, in particular neocotinoids, butenolides, pyrethroids, carbamates, and organophosphori (e.g., Bextine et al., 2004a;[START_REF] Prabhaker | Susceptibility of immature stages of Homalodisca coagulata (Hemiptera: Cicadellidae) to selected insecticides[END_REF][START_REF] Tubajika | The effects of kaolin, harpin, and imidacloprid on development of Pierce's disease in grape[END_REF]. Imidacloprid, a systemic neocotinoid, has proven most efficient against GWSS due to its persistence in the plant tissue, its systemic activity and its selectivity for xylem and phloem-feeding insects [START_REF] Daugherty | Is vector control sufficient to limit pathogen spread in vineyards?[END_REF]. Regardless of its apparent success, imidacloprid has adverse effects on bee health and it is going to be banned within the European Union by the end of 2018 (EFSA, 2018).

A recent report on systematic monitoring for insecticide resistance in GWSS has detected a pattern of decreasing susceptibility in the vector to most insecticides applied in the last 14 years [START_REF] Perring | Monitoring for insecticide resistance in the glassy-winged sharpshooter in California[END_REF][START_REF] Perring | Monitoring for insecticide resistance in the glassywinged sharpshooter in California[END_REF]. Nonetheless, the higher flow of GWSS recorded in 2017 does not appear to be due to the development of resistance to insecticides [START_REF] Perring | Monitoring for insecticide resistance in the glassywinged sharpshooter in California[END_REF]. Nevertheless, given the prolonged employment of insecticides, resistance development in the target insects is to be expected in addition to environmental contamination with insecticide residues and effects on non-target organisms [START_REF] Pimentel | Environmental and economic costs of the application of pesticides primarily in the United States[END_REF]. Despite those issues, insecticides continue to play a central [START_REF] Daugherty | Is vector control sufficient to limit pathogen spread in vineyards?[END_REF][START_REF] Redak | Management of insecticide resistance in glassy-winged sharpshooter populations using toxicological, biochemical, and genomic tools[END_REF] Kaolin-based products Tested in the vineyard [START_REF] Tubajika | The effects of kaolin, harpin, and imidacloprid on development of Pierce's disease in grape[END_REF] role in the control of PD, especially in the case of commercial nurseries [START_REF] Redak | Management of insecticide resistance in glassy-winged sharpshooter populations using toxicological, biochemical, and genomic tools[END_REF]. Vine-growers often carry out within-vineyard sprays to supplement coordinated, area-wide insecticide sprays [START_REF] Rapicavoli | Xylella fastidiosa: an examination of a re-emerging plant pathogen[END_REF]. Three alternatives to insecticides for GWSS have already been described however. The first is Surround WP (Engelhard Corporation, Iselin, New Jersey, US), a kaolin-based product. Vineyard trials showed that coating vines with white kaolin both sabotages GWSS preference for grapevine and increases GWSS mortality after 48 h' exposure [START_REF] Wood | Scientists sharpen strategies to sabotage glassy-winged sharpshooter[END_REF][START_REF] Tubajika | The effects of kaolin, harpin, and imidacloprid on development of Pierce's disease in grape[END_REF]. The second alternative is harpin, a proteinbased elicitor that induces the hypersensitive response of plants and is produced by certain phytopathogenic bacteria. Harpin was included in the field study by [START_REF] Tubajika | The effects of kaolin, harpin, and imidacloprid on development of Pierce's disease in grape[END_REF]. Similar to kaolin, the results of harpin applications in the field suggest that vines treated with this protein have a lower chance of developing PD. Nevertheless, harpin appears to be less lethal to GWSS compared to kaolin. The third alternative is a unique tactic tested by [START_REF] Blua | Impact of a screen barrier on dispersion behavior of Homalodisca coagulata (Hemiptera: Cicadellidae)[END_REF]. In order to physically impede GWSS from entering a field, the researchers assessed the impact of a 5-m-high screen barrier on GWSS dispersal and demonstrated that only 6% of GWSS released outside the barrier were able to fly over it and enter the field.

In addition to the above-mentioned conventional methods, there are various organic approaches to control the spread of XYLEFA vectors. One example is mimetic technology, which involves the development of peptides that closely resemble the natural substrates of proteins vital for the survival of an unwanted pest organism. The host organism is then engineered to express the mimetic peptide, which is lethal to the pest. With regard to PD, mimetic insecticidal peptides have been produced in order to control GWSS [START_REF] Federici | The alimentary track of the glassy-winged sharpshooter as a target for control of Pierce's disease and development of mimetic insecticidal peptides for glassy-winged sharpshooter control[END_REF]. The aim was to make peptides that could bind to transport proteins in the GWSS midgut microvillar membrane or to GWSS salivary enzymes. The best candidate target so far is V-ATPase c, a protein that affects H+/K+ transport, which in turn maintains insect gut pH [START_REF] Federici | The alimentary track of the glassy-winged sharpshooter as a target for control of Pierce's disease and development of mimetic insecticidal peptides for glassy-winged sharpshooter control[END_REF]. Tests are still ongoing to ensure the efficiency of the constructed antibody peptides. Long-term plans include the expression of any successful peptides in transgenic vines [START_REF] Federici | The alimentary track of the glassy-winged sharpshooter as a target for control of Pierce's disease and development of mimetic insecticidal peptides for glassy-winged sharpshooter control[END_REF]. Another example is paratransgenic control or paratransgenesis. Paratransgenesis utilizes either genetically modified symbionts or commensal bacteria as vehicles of delivery of anti-pathogen molecules within the insect gut. Subsequently, these molecules block any transmission of the bacteria concerned [START_REF] Hurwitz | Paratransgenic control of vector borne diseases[END_REF]. With respect to PD control, more than one bacterial candidate has been investigated. In one case, the commensal Pantoea agglomerans E325 was chosen, since it is able to persist within the foregut of GWSS [START_REF] Arora | Paratransgenic Control of Pierce's disease[END_REF] and deliver anti-Xylella effector proteins [START_REF] Lampe | Native secretion systems for the grapevine endophyte Pantoea agglomerans useful for the delivery of anti-Xylella effector proteins[END_REF]. P. agglomerans E325 has been engineered to express melittin and a scorpine-like molecule, two antimicrobials that are toxic for XYLEFA [START_REF] Arora | Paratransgenic Control of Pierce's disease[END_REF]. The manipulated GWSS were less capable of carrying the pathogen than the control GWSS and failed to infect naïve grapevines with Xff [START_REF] Arora | Paratransgenic Control of Pierce's disease[END_REF]. In another case, a bacterial symbiont of GWSS that can survive within vines, Alcaligenes xylosoxidans denitrificans, was selected as the vehicle of delivery [START_REF] Miller | Insect-symbiotic bacteria inhibitory to Xylella fastidiosa in sharpshooters[END_REF][START_REF] Lauzon | Paratransgenesis to control Pierce's disease: the 'social life' of Alcaligenes xylosoxidans denitrificans[END_REF]. The latest reports confirm that A. xylosoxidans denitrificans survives in GWSS for just 5 weeks (Bextine et al., 2004b;[START_REF] Ramirez | Fate of a genetically modified bacterium in foregut of glassy-winged sharpshooter (Hemiptera: Cicadellidae)[END_REF]. RNA interference also has temporary effects. [START_REF] Falk | RNAinterference and control of the glassy-winged sharpshooter and other leafhopper vectors of Pierce's disease[END_REF] investigated various mRNAs that, if blocked by RNA interference, would kill or reduce the survival and/or fecundity of GWSS. The final report concluded that no in vitro feeding or transgenic vine essays with RNA-interference-inducers could have consistent phenotypic expression on exposed GWSS [START_REF] Falk | RNA-interference and control of the glassy-winged sharpshooter and other leafhopper vectors of Xylella fastidiosa[END_REF].

Besides biotechnological efforts, naturally occurring parasites have been considered in the "organic combat" against PD. The treatment of PD via augmentation of natural enemy populations of its insect vectors has generally been a very popular approach. [START_REF] Hunter | Glassy-winged sharpshooter iridovirus pathogen[END_REF] examined the potential of a whitefly iridovirus (WFIV). By infecting GWSS with WFIV via microinjection and sprays, they succeeded in negatively impacting the vector's fecundity and longevity. They also observed that adult GWSS that acquired the iridovirus could pass it on to other healthy individuals and perhaps lay infected eggs. Following that, [START_REF] Hunnicutt | Genome sequence and molecular characterization of Homalodisca coagulata virus-1, a novel virus discovered in the glassy-winged sharpshooter (Hemiptera: Cicadellidae)[END_REF] isolated an ssRNA virus, Homalodisca coagulata virus-1 (HoCV-1) after detecting sequences of the virus in expressed sequence tag libraries from GWSS. HoCV-1 was able to establish infection regardless of the host plant species or the developmental stage and sex of GWSS, and its host range extended to other sharpshooter species [START_REF] Hunnicutt | Prevalence and natural host range of Homalodisca coagulata virus-1 (HoCV-1)[END_REF]. Although, infections did not always lead to acute mortality, HoCV-1 coupled with other preventive strategies or engineered to deliver toxic peptides and/or induce systemic RNA interference (RNAi) was able to curb GWSS populations significantly [START_REF] Bextine | Identification and whole extraction of Homalodisca coagulata virus-1 (HoCV-1) from texas glassywinged sharpshooter populations[END_REF]. Such combination of strategies is presently being explored [START_REF] Falk | Development and use of recombinant Homalodisca coagulata virus-1 for controlling the glassy-winged sharpshooter[END_REF][START_REF] Kamita | Selective disruption of GWSS maturation and reproduction by RNAi[END_REF]. Along with HoCV-1, GWSS harbors a dsRNA virus of the genus Phytoreovirus designated as H. vitripennis reovirus. Even though H. vitripennis reovirus is widely distributed among GWSS populations in the US, it has caused no detectable decline in them, thus the contribution of this virus to the biocontrol of GWSS is questionable [START_REF] Stenger | Population genetics of Homalodisca vitripennis reovirus validates timing and limited introduction to California of its invasive insect host, the glassy-winged sharpshooter[END_REF].

Other parasites with the potential to regulate GWSS are entomopathogenic fungi, but current knowledge about these fungi is limited. [START_REF] Kanga | Fungal pathogens of the glassy-winged sharpshooter Homalodisca coagulata (Homoptera: Cicadellidae)[END_REF] suggest that the fungi FIGURE 1 | Summary of all types of prophylactic and therapeutic strategies against PD presented in this paper. Prophylactic strategies address healthy vines in an attempt to prevent PD (A), while therapeutic strategies address Xff-infected vines in order to cure them of PD (B).

Pseudogibellula formicarum and Metarhizium anisopliae are likely candidates for the biocontrol of GWSS. Three more fungal candidates have subsequently been added to the list of potential biocontrols: Hirsutella homalodiscae, Sporothrix spp. and Beauveria bassiana [START_REF] Boucias | Studies on the fungi associated with the glassy-winged sharpshooter Homalodisca coagulata with emphasis on a new species Hirsutella homalodiscae nom[END_REF][START_REF] Dara | Evaluation and molecular characterization of Beauveria bassiana for the control of the glassywinged sharpshooter (Homoptera: Cicadellidae) in California[END_REF][START_REF] Lietze | Transmission of the mycopathogen, Hirsutella spp., to nymphs and adults of the glassy-winged sharpshooter, Homalodisca vitripennis (= coagulata), in the greenhouse[END_REF]. The latest case study refers to the fungus Isaria poprawskii and investigated its pathogenicity to GWSS [START_REF] Cabanillas | Pathogenicity of Isaria poprawskii (Ascomycota: Hypocreales: Cordycipitaceae) against the glassy-winged sharpshooter, Homalodisca vitripennis (Hemiptera: Cicadellidae), under laboratory conditions[END_REF]. In vitro trials showed that the fungus is virulent and pathogenic to GWSS nymphs and adults. Ultimately, the study deemed I. poprawskii to be a promising biocontrol agent of GWSS because it can cause natural epizootics, has a spectrum that encompasses more than one Xff insect vectors, is heattolerant, and is easy to culture. Surprisingly, the potential of entomopathogenic bacteria against GWSS, such as the widely-applied Bacillus thurigiensis, remains unexplored and should be addressed.

In addition to viral and microbial enemies, the utility of other GWSS enemies has been investigated. [START_REF] Fournier | Identifying key predators of the various glassy-winged sharpshooter lifestages[END_REF] embarked on a large-scale project with the aim of determining any important predators during the various life stages of GWSS. The project screened the gut concent of GWSS associated predators by egg-specific monoclonal antibody-based, enzymelinked immunosorbent assays (ELISA), and by PCR assays using GWSS-specific mitochondrial primers. As many as 1,578 fieldcollected spider and insect species were identified as predators [START_REF] Hagler | Gut content examination of the citrus predator assemblage for the presence of Homalodisca vitripennis remains[END_REF]. Results indicated that GWSSs, at any life stage, are not the main prey for the generalist predators examined. No other potential predators, such as birds, have been studied, and a subsequent study has corroborated the finding that arthropod predators may not be useful in GWSS regulation [START_REF] Daugherty | Is vector control sufficient to limit pathogen spread in vineyards?[END_REF]. In addition, multiple egg parasitoids of GWSS have been identified. [START_REF] Triapitsyn | Taxonomy and biology of egg parasitoids of Auchenorrhyncha of economic importance in Taiwan and adjacent countries, and of Proconiine sharpshooters in the New World[END_REF] has produced an exhaustive review that lists more than 20 egg parasitoids of GWSS. A mymarid egg parasitoid, Gonatocerus ashmeadi, has successfully been used for the biocontrol of GWSS in French Polynesia and, consequently, released with G. morgani and G.morrilli in California [START_REF] Grandgirard | Engineering an invasion: classical biological control of the glassy-winged sharpshooter, Homalodisca vitripennis, by the egg parasitoid Gonatocerus ashmeadi in Tahiti and Moorea, French Polynesia[END_REF][START_REF] Grandgirard | Classical biological control of the glassy-winged sharpshooter, Homalodisca vitripennis, by the egg parasitoid Gonatocerus ashmeadi in the Society, Marquesas, and Austral Archipelagos of French Polynesia[END_REF][START_REF] Cdfa | Pierce's disease control program[END_REF].

Control of Non-vine Host Plants and Vine Propagation Material

Xylella fastidiosa subsp. fastidiosa has a very broad host range that includes common cultivars, as well as wild herbs and weeds [START_REF] Purcell | Fate of Pierce's disease strains of Xylella fastidiosa in common riparian plants in California[END_REF][START_REF] Wistrom | The fate of Xylella fastidiosa in vineyard weeds and other alternate hosts in California[END_REF][START_REF] Stancanelli | Assessing the risk posed to plant health by Xylella fastidiosa in the European Union[END_REF]. There have been various reports on host plants that pose a threat to vineyards [START_REF] Purcell | Fate of Pierce's disease strains of Xylella fastidiosa in common riparian plants in California[END_REF][START_REF] Costa | Plant hosts of Xylella fastidiosa in and near southern California vineyards[END_REF][START_REF] Wistrom | The fate of Xylella fastidiosa in vineyard weeds and other alternate hosts in California[END_REF][START_REF] Sisterson | Epidemiology of diseases caused by Xylella fastidiosa in California: evaluation of alfalfa as a source of vectors and inocula[END_REF]. Removal of these undesirable plants that serve as reservoirs for the bacterium or its vectors currently constitutes a major preventive strategy in the field (EFSA PLH Panel, 2015a). In addition, vineyards should be distanced from non-vine plants that can harbor nymphal and adult stages of Xff vectors, such as citrus, alfalfa, almond, maple, cherry, Spanish broom, and western redbud [START_REF] Janse | Xylella fastidiosa: its biology, diagnosis, control and risks[END_REF][START_REF] Sisterson | Epidemiology of diseases caused by Xylella fastidiosa in California: evaluation of alfalfa as a source of vectors and inocula[END_REF]. Even if non-vine host plants are not nececcarily an important source of inocula, they may still serve as a pool of vectors [START_REF] Sisterson | Epidemiology of diseases caused by Xylella fastidiosa in California: evaluation of alfalfa as a source of vectors and inocula[END_REF]. For example, GWSS frequently overwinters in citrus groves located next to vineyards in California (Almeida et al., 2005b). The chances of PD occurring in pest-free areas could be reduced by prohibiting the import of host plants that represent important cultivars (EFSA PLH Panel, 2015a). Furthermore, planting certified nursery plants and growth plants under exclusion conditions (screen-house and greenhouse) could prevent the spread of PD (EFSA PLH Panel, 2015a).

Hot water treatment (HWT) has been the most popular approach to avoid PD occurrence in nurseries, [START_REF] Goheen | Association of a Rickettsialike organism with Pierce's disease of grapevines and Alfalfa Dwarf and heat therapy of the disease in grapevines[END_REF]EFSA PLH Panel, 2015b). There are two different protocols of HWT: a short-duration HWT and a long-duration one [START_REF] Waite | Hot water treatment, trunk diseases and other critical factors in the production of high-quality grapevine planting material[END_REF]. In order to eliminate any Xff infection, grapevine planting material is exposed to longduration HWT (50 • C for 45 min; EFSA PLH Panel, 2015b). The planting material can either be vine cuttings or 1-year-old rooted vines. In both instances, it is of vital importance that the planting material is fully dormant otherwise it could be irreparably damaged (Waite and Morton, 2007 and references therein). That said, some varietal-based sensitivity to HWT does exist and is expressed as slower establishment of the treated cuttings in the field (Waite and Morton, 2007 and references therein). Additionally, the success of such treatment can depend upon many pre-and post-HWT propagation practices. For example, long-term cold storage of treated material that has not been properly soaked or ventilated can cause irreparable damages to the plant (Gramaje et al., 2014 and references therein).

Alterations to Cropping Techniques

Cropping techniques are crucial in the attenuation of plant disease risk [START_REF] Palti | Cultural practices and infectious crop diseases[END_REF]. Specific practices have been recommended to avoid the occurrence or diminish the spread of PD in vineyards. One example is soil and vegetation management, such as regular rototilling and hand weeding to repress nymphal populations of insect vectors that thrive on herbaceous hosts (EFSA, 2016). Regular summer and autumn pruning of symptomless vines might also eliminate PD infections [START_REF] Hopkins | Xylella fastidiosa: cause of Pierce's disease of grapevine and other emergent diseases[END_REF], albeit posing a risk of Xff mechanical transmission should pruning tools not be regularly disinfected [START_REF] Krell | Mechanical and insect transmission of Xylella fastidiosa to Vitis vinifera[END_REF][START_REF] Overall | Seasonal abundance and natural inoculativity of insect vectors of Xylella fastidiosa in Oklahoma tree nurseries and vineyards[END_REF]. Indeed, severe pruning might stop Xff from reaching the grapevine's permanent structure and establishing a chronic infection [START_REF] Hopkins | Xylella fastidiosa: cause of Pierce's disease of grapevine and other emergent diseases[END_REF]. Nevertheless, severe pruning does not significantly contribute to the recovery of vines infected by Xff and should be viewed as a disease strategy of minor efficacy [START_REF] Daugherty | Severe pruning of infected grapevines has limited efficacy for managing Pierce's disease[END_REF]. During the dormant season, entire vines that either have PD symptoms for more than one year or extensive foliar symptoms on most canes and with tip dieback of canes for less than one year must be removed. Such vines are unlikely to recover or produce a significant crop, and roguing them would prevent the rapid spread of PD to adjacent vines [START_REF] Sisterson | Epidemiology of diseases caused by Xylella fastidiosa in California: evaluation of alfalfa as a source of vectors and inocula[END_REF]. Specific destruction protocols toward a better management of infested plant residues and tools are still pending, but some examples for XYLEFA involve autoclaving and incineration [START_REF] Onghia | Xylella fastidiosa and the Olive Quick Decline Syndrome (OQDS). A Serious Worldwide Challenge for the Safeguard of Olive Trees -IAM[END_REF].

Another measure is regulated deficit irrigation. In a study comparing fully irrigated plants to water-stressed ones, [START_REF] Krugner | Plant water stress effects on stylet probing behaviors of Homalodisca vitripennis (Hemiptera: Cicadellidae) associated with acquisition and inoculation of the bacterium Xylella fastidiosa[END_REF] argue that GWSS avoid water-stressed plants and spend shorter periods ingesting their xylem fluid. Thus, provided the grower is aware of the drought-sensitive growth stages of the grapevine varieties, this strategy could be sufficiently effective [START_REF] Krugner | Plant water stress effects on stylet probing behaviors of Homalodisca vitripennis (Hemiptera: Cicadellidae) associated with acquisition and inoculation of the bacterium Xylella fastidiosa[END_REF]. The importance of low plant water content has previously been underlined by [START_REF] Boisseranc | Environmental Variables Influencing the Severity of Pierce's Disease in California Grapevines[END_REF]. In this study, Boisseranc identified high levels of soil dryness, soil sulfur content, vine calcium, and boron content as significantly reducing the predicted risk of PD. Recently, additional variables that negatively correlate to increased PD incidence have been pinpointed, of which cation exchange capacity and low soil pH appear to be the most significant [START_REF] Costello | Environmental variables influencing the incidence of Pierce's disease[END_REF]. All the above-mentioned plant and field variables should be considered and potentially incorporated in the regular management of vineyards to control PD.

Breeding or Engineering PD-Resistant/Tolerant V. vinifera

In grapevine, V. vinifera cultivars are susceptible to PD, while resistance is found in other species that are not of sufficiently high quality for wine production. Thus wild, resistant Vitis spp. have been used in traditional plant breeding experiments with elite cultivars. Lin et al. (2017) report that 15 out of 183 hybrid lines of N18-6 crossed with Flame Seedless developed few to no PD symptoms in greenhouse trials. It is worth noting that N18-6 comes from the cross of DC1-56 (W1521 x Aurelia) x Orlando Seedless (D4-176 x F9-68) and is characterized by a high yield, good flesh texture and flavor. Moreover, N18-6 has been able to survive under high PD pressure in the field. The study is ongoing and is currently focusing on identifying the genetic source of resistance.

Another study, described by [START_REF] Walker | Breeding Pierce's disease resistant winegrapes[END_REF], has discovered the PD resistance gene PdR1 (chromosome 14) in V. arizonica/candicans line b43-17 (alleles PdR1a, PdR1b) and V. arizonica line b40-14 (allele PdR1c). By backcrossing elite grapevine cultivars with the PdR1b gene they succeeded in reaching progeny of 97% V. vinifera. They then refined their selection by evaluating fruit and vine characteristics, performing resistance screenings in the greenhouse, assessing the wine in various wine tastings, and finally establishing field trials. Their most resistant varieties were grown in the field at various PD hotspots in California during a 16-year field trial and have yet to show any PD symptoms. Walker and Tenscher's project, which has been running since 2001, has produced 19 PD-resistant scions and three PD-resistant rootstocks. Research is ongoing to investigate the possibility of breeding PD resistance to grape varieties via other means, such as gene PdR2 (chromosome 8) of V. arizonica/girdiana line b42-26, and V. shuttleworthii [START_REF] Walker | Breeding Pierce's disease resistant winegrapes[END_REF].

A major offshoot of Walker and Tenscher's project has since been initiated [START_REF] Walker | Molecular breeding support for the development of Pierce's disease resistant winegrapes[END_REF]. One of the scopes was to identify more resistance genes that map to regions different to PdR1 (i.e., other than chromosome 14), thus allowing resistance sources to be combined to produce breeding lines of wider resistance to PD [START_REF] Walker | Molecular breeding support for the development of Pierce's disease resistant winegrapes[END_REF]. Five additional resistant accessions, T03-16, ANU67, b41-13, b47-32, and A14, were singled out after screening many different Vitis species. Accession b46-43 was also tested, but ultimately discarded since the mapping results located its resistance source on chromosome 14, the same as for PdR1 (Walker et al., 2017). The mapping experiments are still underway in order to elucidate the origins of the resistance in the rest of the accessions. To date chromosome 14 has been ruled out as a possibility.

Other than for breeding purposes, different transgenic lines of V. vinifera have been produced to protect grapevines from Xff. For example, [START_REF] Kirkpatrick | Evaluation of Pierce's disease resistance in transgenic Vitis vinifera grapevines expressing either grape thaumatin-like protein or Xylella fastidiosa hemagglutinin protein[END_REF] produced Hxf-expressing grapevines, i.e., transgenic grapevine lines that are able to express a Hxf protein in their xylem fluid. The research was based on an earlier finding that Hxf proteins (hemagglutinins) are involved in XYLEFA virulence and cell-to-cell aggregation [START_REF] Guilhabert | Identification of Xylella fastidiosa antivirulence genes: hemagglutinin adhesins contribute to X. fastidiosa biofilm maturation and colonization and attenuate virulence[END_REF]. The conclusion of the study and field trials of transgenic Hxf-expressing grapevines was that even though the Hfx gene seems to delay the spread of XYLEFA, it is unable to provide long-term protection against the bacterium [START_REF] Gilchrist | Evaluation of Pierce's disease resistance in transgenic Vitis vinifera grapevines expressing Xylella fastidiosa hemagglutinin protein[END_REF].

In a different study, Vitis vinifera cvs. "Thompson Seedless" (TS) and Vitis vinifera cvs. "Chardonnay" (CH) were transformed to express the pear fruit PGIP-encoding gene (pPGIP) [START_REF] Agüero | Evaluation of tolerance to Pierce's disease and Botrytis in transgenic plants of Vitis vinifera L. expressing the pear PGIP gene[END_REF]. PGIPs (PG-inhibiting proteins) are produced by plants to block cell wall-degrading enzymes [START_REF] Esquerré-Tugayé | Cell wall degrading enzymes, inhibitory proteins, and oligosaccharides participate in the molecular dialogue between plants and pathogens[END_REF]. The latter are typical effector proteins of plant pathogens [START_REF] Esquerré-Tugayé | Cell wall degrading enzymes, inhibitory proteins, and oligosaccharides participate in the molecular dialogue between plants and pathogens[END_REF]. XYLEFA's arsenal includes a polygalacturonase (Xf PG), which digests cell wall pectin, and several β-1,4-endo-glucanases (EGase), which digest xyloglucan polymers [START_REF] Roper | Xylella fastidiosa requires polygalacturonase for colonization and pathogenicity in Vitis vinifera grapevines[END_REF]. Thus, if allowed to express Xf PG and EGase the bacterium can move around neighboring xylem vessels by degrading the pit membranes separating those vessels [START_REF] Harakava | Molecular studies of the endo-polygalacturonase gene from Xylella fastidiosa. I. Xylella fastidiosa[END_REF]. This process releases nutrients for the pathogen and eventually leads to vessel occlusion and vine death [START_REF] Harakava | Molecular studies of the endo-polygalacturonase gene from Xylella fastidiosa. I. Xylella fastidiosa[END_REF]. Therefore, lines with high (TS-50, , moderate and low (CH-248 and CH-251) PGIP activity were initially trialed by inoculating the vines with Xff under greenhouse conditions. pPGIP succeeded in protecting three lines (TS-50, CH-329, and CH-327) against PD, as these developed only mild symptoms of the disease [START_REF] Harakava | Molecular studies of the endo-polygalacturonase gene from Xylella fastidiosa. I. Xylella fastidiosa[END_REF]. Finally, [START_REF] Dandekar | HNE-CecB chimeric antimicrobial protein and polygalacturonaseinhibiting protein transgenic grapevines field trial[END_REF] selected line TS-50 to establish a seven-year-long field evaluation. For that study, four different constructs of pPGIPplants were planted in two different PD hotspot locations, either as own-rooted plants or as rootstocks, and were mechanically inoculated with Xff [START_REF] Dandekar | HNE-CecB chimeric antimicrobial protein and polygalacturonaseinhibiting protein transgenic grapevines field trial[END_REF]. The results of the study supported the hypothesis that TS-50 rootstocks can sufficiently protect the scion from PD [START_REF] Dandekar | Field testing transgenic grapevine rootstocks expressing chimeric antimicrobial protein and polygalacturonase-inhibiting protein[END_REF].

Plants have developed a first line of defense against invaders, the innate immune response, to detect pathogens and activate defense responses [START_REF] Janeway | Innate immune recognition[END_REF]. The innate response is not always successful, but [START_REF] Dandekar | An engineered innate immune defense protects grapevines from Pierce disease[END_REF] hypothesized that if two different types of it are combined in one construct they will manage to efficiently block a pathogen. To exclude Xff, they constructed a chimeric antimicrobial protein by joining human neutrophil elastase (HNE), a recognition protein, and cecropin B (CB), a lytic peptide [START_REF] Gupta | Compositions and methods for the treatment of Pierce's disease[END_REF]. HNE has the advantage of cleaving the most abundant and accessible protein in Xff membrane, protein MopB [START_REF] Dandekar | An engineered innate immune defense protects grapevines from Pierce disease[END_REF]. Moreover, the interaction between CB and HNE would promote both cleavage (HNE) and lysis (CB) of Xff [START_REF] Dandekar | An engineered innate immune defense protects grapevines from Pierce disease[END_REF]. Later, the construct was reformed to comply with US regulations on genetically modified organisms. HNE was replaced by P14a from V. shuttleworthii, which, like HNE, functions as a serine protease, and CB was replaced by HAT52 and/or PPC20 (Dandekar et al., 2017 and references therein). New constructs and a combination of old and new constructs have been used to transform vines for the 101-14 and 1103 rootstocks [START_REF] Dandekar | Building the next generation chimeric antimicrobial protein to provide rootstock-mediated resistance to Pierce's disease in grapevines[END_REF]. The newly produced transgenic vines are being tested in the greenhouse and in the field [START_REF] Dandekar | Field testing transgenic grapevine rootstocks expressing chimeric antimicrobial protein and polygalacturonase-inhibiting protein[END_REF]. Previous field trials for the old construct (HNE-CB) expressed in a TS rootstock and manually inoculated with Xff have been very promising [START_REF] Dandekar | Field testing transgenic grapevine rootstocks expressing chimeric antimicrobial protein and polygalacturonase-inhibiting protein[END_REF].

Efforts to produce transgenic vines that are resistant to Xff have generally been a favored approach in various studies. For example, vines have been engineered to express gene rpfF for a diffusible signal factor (DSF) synthase RpfF that originates from XYLEFA [START_REF] Lindow | Field evaluation of diffusible signal factor producing grape for control of Pierce's disease[END_REF][START_REF] Beaulieu | Characterization of a diffusible signaling factor from Xylella fastidiosa[END_REF]. The rpfF gene is thus essential for the production of DSF that in turn upregulates factors required for biofilm formation but represses traits necessary for plant colonization [START_REF] Newman | Cell-cell signaling controls Xylella fastidiosa interactions with both insects and plants[END_REF]. Therefore, a high concentration of DSF moleculesin transgenic vines could be expected to change the quorum sensing of Xff and thereby increase attachment and aggregation, and limit systemic spread via the xylem [START_REF] Lindow | Field evaluation of diffusible signal factor producing grape for control of Pierce's disease[END_REF]. DSFproducing transgenic "Freedom" vines were tested in the field and indeed reported to be two to fourfold more resilient to PD after natural or mechanical inoculation with Xff [START_REF] Lindow | Production of Xylella fastidiosa diffusible signal factor in transgenic grape causes pathogen confusion and reduction in severity of Pierce's disease[END_REF]. Presently, the DSF project is undergoing various improvements to enhance the effect of DSF and reduce costs [START_REF] Lindow | Field evaluation of Pierce's disease resistance of various diffusible signal factor producing grape varieties as scions and rootstocks[END_REF]. These involve the application of fatty acids that are homologous to DSF, transformation of many different vine varieties and rootstocks, as well as the use of a variant of gene rpfF, which encodes a protein with sequences that can direct the enzyme to the chloroplast [START_REF] Lindow | Field evaluation of Pierce's disease resistance of various diffusible signal factor producing grape varieties as scions and rootstocks[END_REF]. Interestingly, similar efforts are in progress to transiently express the rpfF gene of the olive-infecting XYLEFA strain CoDiRO in planta using a TMV-based vector [START_REF] D'attoma | Towards a sustainable strategy for Xylella fastidiosa control[END_REF].

Another project dealt with with the generation of transgenic vines that could suppress apoptosis and programmed cell death (PCD), thus rendering the transgenes asymptomatic hosts. Specifically, [START_REF] Gilchrist | Resistance to Pierce's disease by transgenic expression of plant-derived anti-apoptotic genes[END_REF] performed functional cDNA screening to identify anti-PCD genes expressed in grapevines, which yielded 12 genes. Transgenic "Freedom" and TS vines over-expressing a variety of those 12 genes were inoculated under greenhouse conditions and were later shown to harbor Xff concentrations comparable to those in resistant grapevines [START_REF] Gilchrist | Resistance to Pierce's disease by transgenic expression of plant-derived anti-apoptotic genes[END_REF][START_REF] Gilchrist | Systemic control of Pierce's disease by altered expression of anti-apoptotic genes or their RNA-based regulatory elements[END_REF]. Finally, two DNA transgenic sequences, VvPR1 and UT456, were selected as the most effective ones [START_REF] Gilchrist | Pierce's disease control and bacterial population dynamics in winegrape varieties grafted to rootstocks expressing anti-apoptotic sequences[END_REF]. Between 2012 and 2014, transgenic rootstocks of VvPR1 and UT456 were evaluated in two field sites, under both artificial and natural Xff pressure, and found to efficiently protect TS scions against PD (Gilchrist and Lincoln, 2014).

In an effort to provide longer-lasting and more robust protection against PD, Gilchrist et al. (2014) commenced a project with the aim of combining all DNA constructs mentioned in section Breeding or Engineering PD-Resistant/Tolerant V. vinifera in pairs. The combination of transgenes takes place in the rootstock, which was being tested for its efficacy of crossprotecting the susceptible scions 1103 and 101-14 (Gilchrist et al., 2014). Dual construct transgenic plants are currently being mechanically inoculated with Xff and monitored under greenhouse conditions [START_REF] Gilchrist | Transgenic rootstock-mediated protection of grapevine scions by single and stacked DNA constructs[END_REF]. Field experiments were planned for spring 2018 and the long-term objective of the project is to combine more than two constructs in a gene [START_REF] Gilchrist | Transgenic rootstock-mediated protection of grapevine scions by single and stacked DNA constructs[END_REF].

Control via Avirulent XYLEFA Strains

An early report on naturally occurring benign and weakly virulent strains of XYLEFA that could shield susceptible grapevines against Xff can be found in [START_REF] Hopkins | Induced resistance to Pierce's disease of grapevine by weakly virulent strains of Xylella fastidiosa[END_REF]. The hypothesis was that these strains cross-protect susceptible vines and induce systemic acquired resistance if inoculated prior to an infection with a highly virulent Xff [START_REF] Hopkins | Induced resistance to Pierce's disease of grapevine by weakly virulent strains of Xylella fastidiosa[END_REF]. In 2005, an update on the same project expanded the potential of avirulent and benign strains [START_REF] Hopkins | Biological control of Pierce's disease in the vineyard with strains of Xylella fastidiosa benign to grapevine[END_REF], involving six such strains. Strains PD-1, PD91-2, PD94-1, and PD95-6 were weakly virulent and strains Syc86-1 and EB92-1 were avirulent to grapevines [START_REF] Hopkins | Biological control of Pierce's disease in the vineyard with strains of Xylella fastidiosa benign to grapevine[END_REF]. The trials took place both in the greenhouse (6 months) and in three different vineyards (2 years) and involved three different cultivars. Under both conditions, only individuals treated with strain EB92-1 seemed to develop few to no symptoms of PD compared to vines treated with the other five strains [START_REF] Hopkins | Biological control of Pierce's disease in the vineyard with strains of Xylella fastidiosa benign to grapevine[END_REF]. Strain EB92-1 was subsequently selected for further testing in the field. After a fouryear field trial on Pinot Noir and Cabernet Sauvignon cultivars, the results corroborated the finding that EB92-1 can efficiently protect those cultivars against Xff under heavy disease pressure conditions [START_REF] Hopkins | Biological control of Pierce's disease of grapevine with a benign strain of Xylella fastidiosa[END_REF].

Likewise, [START_REF] Burr | Identification of a new virulence factor required for Pierce's disease and its utility in development of a biological control[END_REF] created the Xff disruption strain PD1311 by deleting gene PD1311. PD1311 had previously been discovered to encode a putative acyl-CoA synthetase, and the deletion of this gene was found to render Xff non-pathogenic [START_REF] Burr | Identification of a new virulence factor required for Pierce's disease and its utility in development of a biological control[END_REF]. Further investigation into the role of PD1311 demonstrated that it participates in biofilm formation and aggregation, and influences motility [START_REF] Burr | Identification of a new virulence factor required for Pierce's disease and its utility in development of a biological control[END_REF]. The value of strain PD1311 as a biocontrol agent was also investigated because PD1311 appeared to be avirulent [START_REF] Burr | Identification of a new virulence factor required for Pierce's disease and its utility in development of a biological control[END_REF] and capable of reducing the virulence of Xff in planta [START_REF] Burr | Identification of a new virulence factor required for Pierce's disease and its utility in development of a biological control[END_REF]. By the time the greenhouse inoculation experiments had been concluded, the suitability of strain PD1311 as a biocontrol agent against PD was confirmed and the need for field tests underlined [START_REF] Burr | Development of a biological control for Pierce's disease[END_REF]. Such an approach seems promising and similar studies are underway (Lin and Shi, 2017), although the risk that the avirulent strains may revert to virulent by horizontal gene transfer from Xff should be taken into account.

Control via Other Beneficial Bacteria and Fungi

Plants are naturally colonized by specific beneficial microbes such as plant growth-promoting rhizobacteria and mycorrhizal fungi [START_REF] Van Wees | Plant immune responses triggered by beneficial microbes[END_REF]. This microflora promotes plant health by various mechanisms, including the production of antagonistic substances and induction of systemic resistance against pathogens (ISR) [START_REF] Van Wees | Plant immune responses triggered by beneficial microbes[END_REF][START_REF] Beneduzi | Plant growth-promoting rhizobacteria (PGPR): their potential as antagonists and biocontrol agents[END_REF]. This principle has prompted the search for potential beneficial bacteria and fungi to stop Xff infections of susceptible hosts. The first study on plant endophytes antagonistic toward Xff described 19 absolute inhibitor strains belonging to six different Bacillus RFLP groups, Cellulomonas sp., Rahnella sp., and Streptomyces sp. [START_REF] Kirkpatrick | Characterize and assess the biocontrol potential of bacterial endophytes of grapevines in California[END_REF]. Unfortunately, in planta greenhouse trials using five of these isolates showed that they cannot prevent initial Xff infections [START_REF] Kirkpatrick | Characterize and assess the biocontrol potential of bacterial endophytes of grapevines in California[END_REF].

A follow-up study assessed the six isolates by establishing a field trial. This revealed that two isolates, Cellulomonas sp. and a Bacillus sp. strain, had great potential to suppress Xff [START_REF] Kirkpatrick | Evaluation of grapevine endophytic bacteria for control of Pierce's disease[END_REF]. Subsequently, the putative Cellulomonas sp. strain was sequenced and identified as a Bacillus subtilis strain [START_REF] Kirkpatrick | Evaluation of grapevine endophytic bacteria for control of Pierce's disease[END_REF]. Unfortunately, continuation of the field trials showed that the Bacillus subtilis strain and the other Bacillus sp. strain are unable to provide long-term protection to the inoculated vines [START_REF] Kirkpatrick | Evaluation of grapevine endophytic bacteria for control of Pierce's disease[END_REF]. Other isolates belonging to the genera Pseudomonas, Kocuria, Bacillus, Curtobacterium, Pantoea, Paenibacillus, Stenotrophomonas exhibited a promising inhibition of Xff during in vitro screenings, but subsequent field trials failed due to inadequate inoculations (Kirkpatrick andWilhelm, 2006, 2007). All in all, a significant vine endophyte library has been created by this group. [START_REF] Rolshausen | Greenhouse Evaluation of Grapevine Microbial Endophytes and Fungal Natural Products for Control of Pierce's Disease[END_REF] took the next step and showed successful reduction of PD symptoms by Pseudomonas sp. and Achromobacter sp. These two bacteria were strongly colonizing vines that have escaped PD under great disease pressure and were tested by introducing them in planta via needle inoculation of shoots or vacuum infiltration of vines before the rooting stage.

XYLEFA produces a type of "xanthan gum, " which is suggested to enable the pathogen to adhere, aggregate and ultimately clog the xylem vessels [START_REF] Lee | Control of Pierce's disease through degradation of xanthan gum[END_REF]. A study on xanthan-gum development by XYLEFA has characterized an endophytic bacterium with high gum-degrading activity, Acinetobacter johnsonii strain GX123 [START_REF] Cooksey | Control of Pierce's disease through degradation of xanthan gum[END_REF]. The advantage of this isolate is that unlike other endophytes [START_REF] Hardoim | Properties of bacterial endophytes and their proposed role in plant growth[END_REF] it does not display any plant cellulose-degrading activity, making it safe for in planta tests [START_REF] Cooksey | Control of Pierce's disease through degradation of xanthan gum[END_REF]. Greenhouse tests on oleander plants evinced that the endophyte can reach a higher titer in the plants and spread faster and further from the inoculation site when it is co-inoculated with Xff [START_REF] Cooksey | Control of Pierce's disease through degradation of xanthan gum[END_REF]. A year later, all the inoculated plants displayed PD symptoms, but the symptoms of those co-inoculated with A. johnsonii GX123 were less severe [START_REF] Lee | Control of Pierce's disease through degradation of xanthan gum[END_REF]. The results suggest strain GX123 is a promising biocontrol tool, although more tests are needed to confirm the efficiency of this gum-degrader in vines.

Another virulence factor of Xff targeted by researchers through endophytes is DSF. The role of DSF has already been described above. During a 5-year study, Lindow and his collaborators exploited the role of DSF to highjack cellcell communication in XYLEFA. Among others, they collected grapevines from PD affected vineyards and tomato and cruciferous crop plants infected with pathogens Xanthomonas campestris pv. vessicatoria and X. campestris pv. campestris [START_REF] Lindow | Management of Pierce's disease of grape by interfering with cell-cell communication in Xylella fastidiosa[END_REF]. In all, they unraveled two types of disturbance of the cell-cell signaling by the isolates: DSF degradation and another unidentified mode of DSF inhibition [START_REF] Lindow | Management of Pierce's disease of grape by interfering with cell-cell communication in Xylella fastidiosa[END_REF]. They also isolated endophytes that can produce DSF [START_REF] Lindow | Management of Pierce's disease of grape by interfering with cell-cell communication in Xylella fastidiosa[END_REF]. The DSF-producing strains were all Xanthomonas spp., while the DSF-inhibitory ones belonged to the genera Paenibacillus, Pseudomonas, Staphylococcus, and Bacillus [START_REF] Lindow | Management of Pierce's disease of grape by interfering with cell-cell communication in Xylella fastidiosa[END_REF]). To test the potential of all isolate categories, they co-inoculated vines with Xff plus either the DSF-producing or the DSF-inhibitory isolates in the greenhouse. In spite of their insufficient systemic spread in the vine, all categories reduced PD symptoms, with DSFproducing isolates appearing to perform slightly better than the DSF-inhibitory isolates [START_REF] Lindow | Management of Pierce's disease of grape by interfering with cell-cell communication in Xylella fastidiosa[END_REF]. Thus, all the isolates proved very promising as protective agents for grapevines against Xff [START_REF] Lindow | Management of Pierce's disease of grape by interfering with cell-cell communication in Xylella fastidiosa[END_REF].

Finally, fungal endophytes have also been considered for the protection of vines against PD. First, Rolshausen et al.

(2010) isolated endophytic fungi from PD-escape vines. Later, in vitro studies revealed seven grapevine endophytic fungi, which can significantly inhibit XYLEFA [START_REF] Rolshausen | Fungi antagonistic to Xylella fastidiosa[END_REF]. The fungi belong to the genera Aspergillus, Cochliobolus, Cryptococcus, Discostroma, Geomyces, Phaeosphaeria, and Ulocladium [START_REF] Rolshausen | Fungi antagonistic to Xylella fastidiosa[END_REF]. In planta bioassays showed that Geomyces sp., Cochliobolus sp., and Cryptococcus sp. are able to mitigate PD symptoms under greenhouse conditions [START_REF] Rolshausen | Fungi antagonistic to Xylella fastidiosa[END_REF][START_REF] Rolshausen | Greenhouse Evaluation of Grapevine Microbial Endophytes and Fungal Natural Products for Control of Pierce's Disease[END_REF]. Lastly, the research group investigated the healing potential of natural compounds produced by some of those fungi (further details can be found in the "therapeutic strategies" section below)1 .

GROUP B: THERAPEUTIC STRATEGIES

Curative strategies are crucial for the successful protection of vines against Xff. These strategies are characterized by the fact that they directly target susceptible plants and can both protect and cure sick vines by eliminating Xff. Most therapeutic strategy mechanisms rely heavily on biological control agents, although some exceptions are also reported. Thus, most of the strategies presented below have the advantages of being environmentally friendly, specific and cost effective. Some of them are also based on natural enemies of Xff, which minimizes their ecological impact. This is because Xff 's natural enemies are normally found only where Xff is present and are therefore unable to persist to an ecosystem without it and become invasive. A summary of all types of therapeutic strategies reviewed below is depicted in Figure 1B.

Bacteriophages of Xff

Bacteriophages (phages) are viruses that infect bacteria. Phages are classified into the virulent or the temperate group based on their lifestyle. Phages in the virulent group follow a lytic lifestyle, i.e., they destroy the bacterial cells they infect. A given phage species is capable of infecting one bacterial species with a high degree of specificity, usually in the strain level. Owing to this specificity, different virulent phages are chosen and applied in a cocktail to treat bacterial infections. Generally, a cocktail of distinct phages provides robust protection, due to various available phage receptors, and long-lasting protection due to limited possibilities of resistance development [START_REF] Gill | Phage choice, isolation, and preparation for phage therapy[END_REF]. Phage therapy is still in its infancy as far as the treatment of crop infections is concerned. However, there are many examples of bacteriophages being isolated against plant pathogenic bacteria of crops, and phage cocktail applications are gradually becoming more common (Doss et al., 2017 and references therein). Even though the mechanism of bacteriophage cocktails could fit in either category of the control strategies described in this review, its therapeutic character is emphasized here.

In the case of XYLEFA, a temperate phage was induced from a Xff strain supernatant [START_REF] Summer | Genomic and biological analysis of phage Xfas53 and related prophages of Xylella fastidiosa[END_REF]. Phage therapy applies only virulent phages since temperate phages are unstable and could incorporate into the host genome, accidentally transfer genes (transduction) and/or confer superinfection exclusion [START_REF] Gill | Phage choice, isolation, and preparation for phage therapy[END_REF]. The first virulent phages against XYLEFA have recently been described by [START_REF] Ahern | Characterization of novel virulent broad-host-range phages of Xylella fastidiosa and Xanthomonas[END_REF]. The group isolated four broad-host range phages, i.e., phages that could infect many different strains of XYLEFA and some strains of Xanthomonas species. Two of the isolated phages, Sano and Salvo, belong to the family of Siphoviridae, while the other two, Prado and Paz, belong to the family of Podoviridae [START_REF] Ahern | Characterization of novel virulent broad-host-range phages of Xylella fastidiosa and Xanthomonas[END_REF]. Grapevines were inoculated, either pre or post-Xff infection, with a cocktail of all four phages, using a titer of 1 × 10 10 PFU/ml. In both experiments, the phage cocktail was able to fully protect vines against Xff infection in greenhouse experiments [START_REF] Das | Control of Pierce's disease by phage[END_REF]. In another greenhouse-based study, GWSS were used as vectors of phage Paz. Even though GWSS were able to efficiently acquire phage Paz, they could not transmit it to cowpea plants [START_REF] Bhowmick | Transmission of phage by glassy-winged sharpshooters, a vector of Xylella fastidiosa[END_REF]. All in all, phage therapy is a promising field and more studies are needed to investigate the potential of phages for treating PD and plant bacterial infections in general.

Antagonistic Bacterium Paraburkholderia phytofirmans Strain PsJN

The use of biocontrol bacteria against Xff has been presented in the "preventive strategies" section. Nevertheless, Paraburkholderia phytofirmans strain PsJN is also therapeutic since it has been quite successful in curing infected vines. PsJN was first isolated from onion roots [START_REF] Sessitsch | Burkholderia phytofirmans sp. nov., a novel plant-associated bacterium with plant-beneficial properties[END_REF] and successfully colonized vines epiphytically and endophytically during in planta trials [START_REF] Compant | Endophytic colonization of Vitis vinifera L. by Burkholderia phytofirmans strain PsJN: from the rhizosphere to inflorescence tissues[END_REF]. Although the titer and spread of PsJN within the vines 6 weeks after inoculation resembled that of XYLEFA, population sizes measured 12 weeks after inoculation were quite low [START_REF] Lindow | Comparison and optimization of different methods to alter diffusible signal factor mediated signaling in Xylella fastidiosa in plants to achieve Pierce's disease control[END_REF]. In planta experiments demonstrated that the endophyte can inhibit growth of XYLEFA in various vine cultivars when co-inoculated or even when inoculated 30 days after the pathogen (Lindow et al., 2017a). Another attractive characteristic is that PsJN can control PD not only when inoculated but also when applied foliarly, provided it is combined with a penetrative surfactant [START_REF] Lindow | Comparison and optimization of different methods to alter diffusible signal factor mediated signaling in Xylella fastidiosa in plants to achieve Pierce's disease control[END_REF]. Field experiments and further attempts to decipher how PsJN mediates control of PD are in progress (Lindow et al., 2017a). Results indicate that PD mitigation does not derive from a putative rpfF gene of PsJN. Instead, a small molecule, active in low concentrations may interfere with Xff quorum-sensing regulation and biofilm formation (Lindow et al., 2017a). Furthermore, it is hypothesized that, together with the signaling molecule, PsJN may trigger host immune defense responses (Lindow et al., 2017a).

Natural, Antibacterial Substances

Up to now, the application of chemical compounds has played a leading role in agriculture and been a widespread practice for controlling plant pathogens in the field. However, recent legislation, such as Directive 2009/128/EC (European Parliament Council, 2009), requires the reduction of synthetic pesticides in agriculture owing to their environmental impact and risks to human health [START_REF] Dayan | Natural products in crop protection[END_REF]. Thus, there is a particular requirement to discover and develop more natural pesticides to replace their chemical counterparts [START_REF] Dayan | Natural products in crop protection[END_REF]. Fortunately, the alternative of applying natural product-based compounds is not wholly new to agricultural scientists.

In the case of PD, researchers have tried to identify and evaluate various natural, antibacterial substances against Xff. One such study assessed the use of fungal natural products that can inhibit XYLEFA in vitro [START_REF] Rolshausen | Fungi antagonistic to Xylella fastidiosa[END_REF]. First, radicinin produced by Cochliobolus sp., and later crude extracts from the endophytes Eurotium sp., Geomyces sp., and Ulocladium sp. successfully inhibited XYLEFA in vitro [START_REF] Rolshausen | Evaluation of natural products isolated from grapevine fungal endophytes for control of Pierce's disease[END_REF]. Radicinin is a known, naturally produced fungal compound, and its antibacterial and phytotoxic properties are well described [START_REF] Aldrich | Radicinin from Cochliobolus sp. inhibits Xylella fastidiosa, the causal agent of Pierce's Disease of grapevine[END_REF] and references therein). Radicinin's mode of action against XYLEFA is via a mechanism that involves inactivation of Xff proteases [START_REF] Aldrich | Radicinin from Cochliobolus sp. inhibits Xylella fastidiosa, the causal agent of Pierce's Disease of grapevine[END_REF]. Radicinin is currently being tested for its curing potential in planta under greenhouse conditions [START_REF] Rolshausen | Greenhouse Evaluation of Grapevine Microbial Endophytes and Fungal Natural Products for Control of Pierce's Disease[END_REF].

In another study on antibacterial molecules, [START_REF] Kuzina | In vitro activities of antibiotics and antimicrobial peptides against the plant pathogenic bacterium Xylella fastidiosa[END_REF] screened PD and other XYLEFA strains using various antibiotics and antimicrobial peptides. Earlier, Kirkpatrick et al. had tested the antibiotic tetracycline in vitro [START_REF] Kirkpatrick | Biological, cultural, and chemical management of Pierce's disease[END_REF] and the antibiotic streptomycin in planta [START_REF] Kirkpatrick | Evaluation of bactericides and grapevine endophytes for management of Pierce's disease[END_REF] and found them to be effective against XYLEFA. The study of those antibiotics was moved to the field and a report on their effect is still pending. The study of Kuzina et al. was restricted to in vitro assays, but is still noteworthy due to the extent of the antibacterial molecules tested. Of the 12 antibiotics tested, the best candidates for XYLEFA control were gentamicin (0.5-1 µg/ml), tetracycline (1-4 µg/ml), ampicillin, kanamycin, and novobiocin (4-8 µg/ml), chloramphenicol (1-8 µg/ml), and rifampin (2-8 µg/ml) (ibid). Moreover, out of the 18 antimicrobial peptides tested, only four, namely PGQ, indolicidin, magainin 2, and dermaseptin, strongly inhibited all XYLEFA strains in the study [START_REF] Kuzina | In vitro activities of antibiotics and antimicrobial peptides against the plant pathogenic bacterium Xylella fastidiosa[END_REF]. On the one hand, further studies are necessary to develop the right delivery system of those molecules to grapevines [START_REF] Kuzina | In vitro activities of antibiotics and antimicrobial peptides against the plant pathogenic bacterium Xylella fastidiosa[END_REF]. On the other hand, it is less likely that any antibacterial molecules will be permitted for in planta applications against Xff, because of their adverse killing of other plant beneficial microbes and their use in human therapy.

A similar study investigated the anti-Xylella effect of 12 phenolic compounds in vitro [START_REF] Maddox | Antibacterial activity of phenolic compounds against the phytopathogen Xylella fastidiosa[END_REF]. The researchers studied two PD strains and two strains infecting almond for their sensitivity to caffeic acid, catechin, p-coumaric acid, resveratrol, rutin, sinapic acid, catechol, coumarin, ferulic acid, gallic acid, naringenin, and quercetin [START_REF] Maddox | Antibacterial activity of phenolic compounds against the phytopathogen Xylella fastidiosa[END_REF]. All the tested compounds were able to efficiently inhibit Xff, but catechol, caffeic acid and resveratrol had the greatest effect [START_REF] Maddox | Antibacterial activity of phenolic compounds against the phytopathogen Xylella fastidiosa[END_REF]. Nonetheless, the mechanism of inhibition of those compounds remains unknown. Lastly, potted PD-infected vines were inoculated with the microelement zinc sulfate/oxide [START_REF] Kirkpatrick | Evaluation of bactericides and grapevine endophytes for management of Pierce's disease[END_REF]. The vines were assessed over a three-year period and exhibited noteworthy recovery from PD [START_REF] Kirkpatrick | Evaluation of bactericides and grapevine endophytes for management of Pierce's disease[END_REF]. Even though no results of field studies have been published yet, the use of phenolics may be restricted, owing to their wide range of inhibition that can also impact beneficial microbes of vines.

Other molecules with antibacterial properties have been tested in planta and produced promising results. Nevertheless, the host challenged was not grapevine so they will only be mentioned briefly here. N-Acetylcysteine, a molecule used in medicine to disrupt disulfide bonds in mucus, was able to reduce citrus variegated chlorosis symptoms in planta [START_REF] Co Muranaka | N-Acetylcysteine in agriculture, a novel use for an old molecule: focus on controlling the plant-pathogen Xylella fastidiosa[END_REF]. In another study an antimicrobial peptide from a tarantula spider, gomesin, interfered with two citrus variegated chlorosis strains and reduced their virulence in planta [START_REF] Fogaça | Effects of the antimicrobial peptide gomesin on the global gene expression profile, virulence and biofilm formation of Xylella fastidiosa[END_REF]. Generally, the combination of molecules that can reduce biofilm formation of XYLEFA with antimicrobial compounds is of good potential and should be considered in future. This is significant considering that biofilms greatly increase bacterial resistance to antimicrobial compounds [START_REF] Mah | Mechanisms of biofilm resistance to antimicrobial agents[END_REF]. On the other hand, strategies of biofilm reduction can be efficient during the early stages of XYLEFA infection. In later stages, reduction of virulence has been attempted following the opposite approach, i.e., increased adhesiveness and reduced motility, such as in the study of [START_REF] Lindow | Production of Xylella fastidiosa diffusible signal factor in transgenic grape causes pathogen confusion and reduction in severity of Pierce's disease[END_REF].

Other Defense-Stimulating Compounds

Defense-stimulating compounds have also been included in trials against Xff. The first case study, by [START_REF] Meyer | Exogenous applications of abscisic acid increase curing of Pierce's disease-affected grapevines growing in pots[END_REF], investigated the curative effect of ABA. This is a typical plant hormone that regulates plant growth, seed dormancy, and stomatal function. In addition to these roles, ABA is an important factor in plant responses to a disease. In a greenhouse trial, [START_REF] Meyer | Exogenous applications of abscisic acid increase curing of Pierce's disease-affected grapevines growing in pots[END_REF] applied ABA to grapevines infected by Xff via foliar sprays or soil drenches. The trial ran for three consecutive years and the exogenous ABA applications were performed using one naturally occurring and one synthetic ABA [START_REF] Meyer | Exogenous applications of abscisic acid increase curing of Pierce's disease-affected grapevines growing in pots[END_REF]. The treated vines exhibited significant recovery from PD, and the researchers further noted a significant rise in the phenolic compound concentration in those vines. This implied a positive correlation between successful ABA treatments and the content of phenolic compounds in the sap [START_REF] Meyer | Exogenous applications of abscisic acid increase curing of Pierce's disease-affected grapevines growing in pots[END_REF]. Other than ABA, metal chelators have been recommended for the inhibition of Xff. [START_REF] Koh | Inhibition of Xylella fastidiosa biofilm formation via metal chelators[END_REF] reported that biofilm formation can be blocked via iron chelators such as lactoferrin, EDTA (ethylenediaminetetraacetic acid) and EDDS (ethylenediamine-N, N ′ -disuccinic acid). It was hypothesized that the possible mechanism of action is connected to iron deprivation for XYLEFA [START_REF] Koh | Inhibition of Xylella fastidiosa biofilm formation via metal chelators[END_REF].

This review concerns control strategies already tested but many more studies could serve as a source of inspiration for the development of efficient strategies against Xff. For example, a recent study by [START_REF] Zaini | Molecular Profiling of Pierce's Disease Outlines the Response Circuitry of Vitis vinifera to Xylella fastidiosa Infection[END_REF] has specified various response mechanisms of vines to Xff infection that could be exploited, including accumulation of gamma-aminobutyric acid and upregulation of phytoalexins. As presented in this first section, various prophylactic and therapeutic strategies have already been proposed in order to minimize the effects of Xff in vineyards. A substantial number of these strategies appear promising. To evaluate the efficacy of all current and future approaches, the following section will model the spread of Xff in a population of vines.

XFF EPIDEMIOLOGICAL MODEL

Description of the Xff Epidemiological Model

This section elaborates an epidemiological model of Xff with the aim of deciphering key parameters for the spread of PD. To the authors' knowledge, only one relevant model has so far been published [START_REF] Perring | Treatment thresholds for the glassy-winged sharpshooter based on the local epidemiology of Pierce's disease spread[END_REF]. Given that the model of [START_REF] Perring | Treatment thresholds for the glassy-winged sharpshooter based on the local epidemiology of Pierce's disease spread[END_REF] is still in a preliminary form, the Xff epidemiological model made in the following section was based on a malaria model by [START_REF] Chitnis | Using Mathematical Models in Controlling the Spread of Malaria[END_REF]. To calibrate the present model, SC was used as a reference due to the consistency of studies and the severity of PD there [START_REF] Rapicavoli | Xylella fastidiosa: an examination of a re-emerging plant pathogen[END_REF]. Even though the model presented here is expected to be applicable to any hightransmission region of Xff, it would be advisable to perform these analyses again with suitable parameter values. This will allow users to verify whether the significance of various parameters remains as reported here for the new regions of interest.

Definition of the Vine State Variables of the Xff Epidemiological Model

This model describes the dynamics of a vine population under high PD pressure. The Xff epidemiological model (Figure 2) divides the vine population into three classes: healthy (S h ), latent (L h ), and symptomatic (I h ). A vine becomes latent only after an infected GWSS vector manages to probe the vine and successfully inject Xff into the vine's xylem [START_REF] Killiny | Factors affecting the initial adhesion and retention of the plant pathogen Xylella fastidiosa in the foregut of an insect vector[END_REF]. Generally, a probe involves all GWSS behaviors starting from the penetration of its stylet and ending with stylet withdrawal [START_REF] Sandanayaka | Quantitative comparison of stylet penetration behaviors of glassy-winged sharpshooter on selected hosts[END_REF]. Once in the latent stage, a vine does not yet display any PD symptoms, but harbors sufficient Xff titers to infect a healthy GWSS [START_REF] Hill | Populations of Xylella fastidiosa in plants required for transmission by an efficient vector[END_REF][START_REF] Schaad | Real-time polymerase chain reaction for one-hour on-site diagnosis of Pierce's disease of grape in early season asymptomatic vines[END_REF]. Latent vines can then either recover or start developing symptoms. Vines that enter the latent stage in late summer often recover and revert to the healthy stage if the following winter is cold. Low winter temperatures are hostile to Xff growth and do not allow the pathogen to become established inside the vine [START_REF] Feil | Temperature-dependent growth and survival of Xylella fastidiosa in vitro and in potted grapevines[END_REF][START_REF] Purcell | Paradigms: examples from the bacterium Xylella fastidiosa[END_REF]. Furthermore, severe winter pruning may enhance, but not replace, the curing effect of low temperatures [START_REF] Daugherty | Severe pruning of infected grapevines has limited efficacy for managing Pierce's disease[END_REF]. Vines that entered the latent stage during early spring and summer become symptomatic within two to 12 months [START_REF] Hopkins | Xylella fastidiosa: cause of Pierce's disease of grapevine and other emergent diseases[END_REF]. Symptomatic vines cannot recover and will decline within a year of infection at the earliest [START_REF] Varela | UC IPM Pest Management Guidelines: Grape[END_REF].

Definition of the GWSS State Variables of the Xff Epidemiological Model

As experience in the case of SC, GWSS is the insect vector likely to lead a vine population to a PD epidemic [START_REF] Rapicavoli | Xylella fastidiosa: an examination of a re-emerging plant pathogen[END_REF]. For the Xff model, the GWSS population was divided into two classes: healthy (S v ) and infected (I v ). A healthy GWSS Displayed on each transition between the state variables are the rates at which they happen in the model (see Equations 1-5). The model parameters can be found in Table 4.

would pass into the infected stage only after successfully probing a vine that is either latent or symptomatic. Generally, plants other than vine can also infect GWSS (Almeida et al., 2005a;[START_REF] Janse | Xylella fastidiosa: its biology, diagnosis, control and risks[END_REF]. However, such plant hosts are either nonexistent or inconsiderable sources of infection in SC (Mizell et al., 2008a;[START_REF] Almeida | How do plant diseases caused by Xylella fastidiosa emerge?[END_REF], the region used in this model as a reference. In GWSS, Xff multiplies in the vector's foregut [START_REF] Purcell | Pierce's disease bacterium: mechanism of transmission by leafhopper vectors[END_REF] and can be transmitted by that GWSS in less than an hour [START_REF] Almeida | Transmission of Xylella fastidiosa to grapevines by Homalodisca coagulata (Hemiptera: Cicadellidae)[END_REF]. GWSS has neither transovarial nor transstadial transmission of Xff, but nymphs of the vector may carry Xff, and adults that acquire Xff remain infected for life (Almeida et al., 2005a;[START_REF] Chatterjee | Living in two worlds: the plant and insect lifestyles of Xylella fastidiosa[END_REF]. New GWSS are born at a constant per capita birth rate. For the Xff it was assumed that GWSS are "born" as adults. This is a simplifying but realistic assumption, since the adult stage lasts substantially longer and is generally more active in the dispersal of Xff than any nymphal stage of GWSS (Mizell et al., 2008a;[START_REF] Lauzière | Life history studies of Homalodisca vitripennis (Hemiptera: Cicadellidae), a vector of Pierce's disease of grapevine[END_REF]. The acquisition of Xff appears to have no effect on GWSS longevity or fertility [START_REF] Mizell | Xylella fastidiosa Diseases And Their Leafhopper Vectors[END_REF].

Differential Equations of the Xff Epidemiological Model

To model the spread of Xff in a population of vines, the following system of differential equations was used:

dS v dt = ψ v N v -λ v (t) S v -f v (N v ) S v (1)
dI v dt = λ v (t) S v -f v (N v ) I v (2)
dS h dt = ψ h (N h0 -N h ) -λ h (t) S h + γ L h -µ h S h (3) dL h dt = λ h (t) S h -γ L h -νL h -µ h L h (4)
dI h dt = νL h -(µ h + µ x ) I h (5)
The state variables of the model are shown in Table 3 and the parameters used in the model are shown in Table 4.

Expression of the Differential Equations in the Fractional System

To facilitate analysis, state variables over the total populations were expressed as

i v = I v N v ; s v = 1 -i v ; s h = S h N h0 ; l h = L h N h0 ; i h = I h N h0
in order to arrive at an equivalent system in terms of fractional quantities

di v dt = λ v (t) (1 -i v ) -ψ v i v (6) dN v dt = ψ v N v -f v (N v ) N v (7) ds h dt = ψ h 1 -s h -l h -i h -λ h (t) s h + γ l h -µ h s h (8) dl h dt = λ h (t) s h -γ l h -vl h -µ h l h (9) di h dt = vl h -(µ h + µ x ) i h (10)

N h0

The maximum number of vines, unit

µ v1 Density-independent part of GWSS death rate, time -1 µ v2 Density-dependent part of GWSS death rate, vector -1 × time -1 f v (Nv) = µ v1 + µ v2 N v
Per capita density-dependent death rate of GWSS, time -1 µ h PD-independent death and removal rate of vines, time -1

µ x PD-induced removal rate of vines, time -1 λ v (t) = β hv pσ (L h + I h ) N h
Per capita inoculation rate for GWSS, time -1

λ h (t) = β vh pσ Iv N h
Per capita inoculation rate for vines, time

Baseline Parameter Values

As mentioned earlier, baseline parameter values were chosen that refer to SC. These values are presented below (Table 5) and an explanation given for their selection. All the values utilized are estimates from the literature.

Model Parameters for GWSS

Since vines contract PD only via specialized insect vectors, parameters that describe GWSS behavior are essential to this model. Only the adult stage of the GWSS life cycle was included, thus the birth rate was adjusted to account for egg and nymphal survival. One female GWSS lays 2.1 eggs per day on average during the active oviposition period [START_REF] Sétamou | Biology and biometry of sharpshooter Homalodisca coagulata (Homoptera: Cicadellidae) reared on cowpea[END_REF]. It was assumed that eggs are produced through a constant per capita birth rate, and that 50% of all female GWSS lay eggs every day [START_REF] Sisterson | Egg load dynamics of Homalodisca vitripennis[END_REF]. Based on the values given by [START_REF] Lauzière | Life history studies of Homalodisca vitripennis (Hemiptera: Cicadellidae), a vector of Pierce's disease of grapevine[END_REF], it was estimated that 30% of the total number of eggs would survive due to environmental pressures, such as egg parasitism, rather than greenhouse conditions. Therefore the per

+ µ v2 × N v ).
The density-independent part of the death rate of GWSS, µ v1 , was set at 1/100 per day, which is in agreement with the already reported longevity of this vector [START_REF] Lauzière | Life history studies of Homalodisca vitripennis (Hemiptera: Cicadellidae), a vector of Pierce's disease of grapevine[END_REF]. The density-dependent part, µ v2 , is the parameter that largely controls the equilibrium size of the GWSS population. For most of this analysis, a GWSS population of approximately twice the size of the vine population was used, in conditions when PD is not present. This estimate was based on [START_REF] Krugner | Plant water stress effects on the net dispersal rate of the insect vector Homalodisca vitripennis (Hemiptera: Cicadellidae) and movement of its egg parasitoid, Gonatocerus ashmeadi (Hymenoptera: Mymaridae)[END_REF], the 2016 Citrus Acreage Report (NASS/CDFA, 2017a) and the 2016 Grape Acreage Report (NASS/CDFA, 2017b). To obtain such a size of GWSS population, µ v2 was set accordingly. However, µ v2 was also varied to simulate situations with different numbers of GWSS per vine (spatial distribution of vectors) and to explore how this affects the disease dynamics (Figures 3,4).

The probability of transmission from vine to vector during a probe, β hv , is known as vector acquisition efficiency in the XYLEFA vector literature, and the probability of transmission from vector to vine during a probe, β vh , as vector inoculation efficiency. GWSS acquisition efficiency is poor when the titer of Xff in the vine is low and can increase when probing duration increases, but only for a period of up to 6 h (Almeida and Purcell, 2003 and references therein). GWSS inoculation efficiency for a GWSS individual depends on probing duration [START_REF] Almeida | Transmission of Xylella fastidiosa to grapevines by Homalodisca coagulata (Hemiptera: Cicadellidae)[END_REF]. Nevertheless, the existence of other factors affecting GWSS inoculation and acquisition efficiency should be clarified in order to design successful control strategies [START_REF] Daugherty | Estimating Xylella fastidiosa transmission parameters: decoupling sharpshooter number and feeding period[END_REF]. Both probability values were extracted from the literature [START_REF] Almeida | Transmission of Xylella fastidiosa to grapevines by Homalodisca coagulata (Hemiptera: Cicadellidae)[END_REF].

The number of probes on vines were set per unit of time at σ = 1.5, after combining information on the number of probes [START_REF] Sandanayaka | Quantitative comparison of stylet penetration behaviors of glassy-winged sharpshooter on selected hosts[END_REF] and GWSS preference for vine [START_REF] Daane | Biology and ecology of the glassy-winged sharpshooter in the San Joaquin Valley[END_REF]Mizell et al., 2008a). Moreover, the impact of seasonality and field conditions were also incorporated because they reduce the number of probes a GWSS can perform on a host plant [START_REF] Blua | Dispersion of Homalodisca coagulata (Hemiptera: Cicadellidae), a vector of Xylella fastidiosa, into vineyards in southern California[END_REF]. It should be noted that this definition of σ describes a fairly local situation, where it is FIGURE 3 | Equilibrium prevalence of PD in the GWSS population (A) and in the vine population (B), as a function of GWSS density , i.e., the relation between the equilibrium total number of GWSS, N * and the maximum number of vines N h0 . The equilibrium values are presented using the expression of the state variables in the fractional system. These are infected GWSS over the total number of GWSS i v , healthy vines over the maximum number of vines s h , latent vines over the maximum number of vines l h and infected vines over the maximum number of vines i h . Denoted as N h /N h0 is the number of vines in the population at a given time over the maximum number of vines. To obtain the equilibria at different GWSS densities, a numerical simulation was run with each value, starting from an initial low level of infection (i v = 0.1 and s h = 1) until the system had converged to a steady state. Other parameter values remain as in Table 5. The plot shows that PD becomes endemic at a GWSS density of ∼0.01 GWSS per vine.

assumed that the total number of probes the GWSS population performs is distributed evenly across all vines. Therefore, this model does not account for vector aggregation and swarm behavior, although it is acknowledged that these factors can significantly influence disease spread. This concept also affects the per capita rate of inoculation, λ, which is a function of the number of probes on vines, the proportion of infected vectors, and the probability of transmission per probe.

Model Parameters for Vines

The vine population is an artificial one, and its maximum size N h0 considered to be the number that the vine-grower aims to maintain. Vines are being removed at a constant rate, µ h , because of age and other diseases. The PD-independent death and removal rate of vines, was set at 1.1 × 10 -4 per day to reach an average lifespan of 25 years. This choice is in accordance with practices of Californian vineyards [START_REF] Alston | Economic consequences of Pierce's Disease and related policy in the California winegrape industry[END_REF]. In SC, vine-growers are advised to rogue vines within the first year of PD symptom development [START_REF] Varela | UC IPM Pest Management Guidelines: Grape[END_REF]. Vines start showing symptoms within two to 12 months of infection [START_REF] Hopkins | Xylella fastidiosa: cause of Pierce's disease of grapevine and other emergent diseases[END_REF]. Considering these two factors, the PD-induced death and removal rate of vines, µ x , was estimated to be equal to 1/180 per day, so that the average time it takes for a symptomatic vine to be removed is 6 months. The missing vines, corresponding to the difference between N h0 and N h , are being replaced at a constant per capita rate ψ h . Consequently, in the absence of PD, vines have a stable population level N h < N h0 .

The per capita replacement of missing vines, ψ h , was set at 1/365 per day to reflect viticulture guidelines and nurseries' responsiveness [START_REF] Alston | Economic consequences of Pierce's Disease and related policy in the California winegrape industry[END_REF][START_REF] Daniels | 2018 Pest Management Guide for Grapes in Washington[END_REF]. It was assumed that all vines that enter the population from a nursery are free of Xff. Latent vines recover at a constant rate, γ , or progress to the symptomatic stage at a constant rate, ν. It was gauged that the cold-curing effect and severe winter pruning support a 28% chance of recovery [START_REF] Lieth | Modeling cold curing of Pierce's disease in Vitis vinifera 'Pinot Noir' and 'Cabernet sauvignon' grapevines in California[END_REF][START_REF] Daugherty | Severe pruning of infected grapevines has limited efficacy for managing Pierce's disease[END_REF], thus γ = 0.0033 per day. Alternatively, latent vines become symptomatic in an average of 120 days [START_REF] Li | Citrus and coffee strains of Xylella fastidiosa induce Pierce's disease in grapevine[END_REF], thus the progression from latent to symptomatic vine, ν, was estimated to be 1/120 per day.

Disease-Free Equilibria

The dynamics of the total number of GWSS N v is not affected by the disease. Hence, the equilibrium number of GWSS is always given by dN

v dt = 0 ↔ N v = 0 or N v = ψ v -µ v1 µ v2 .
Clearly, the nontrivial equilibrium exists only if ψ v > µ v1 , and is asymptotically stable. It is denoted by N * v . For the vine, in the absence of disease the only dynamics are:

ds h dt = ψ h (1 -s h ) -µ h s h ,
that is the non-PD-related death and removal, and subsequent replacement. This gives the disease-free equilibrium for vine

s * h = ψ h ψ h + µ h
, which equals approximately 0.96 for the parameter values in Table 5. Taken together, the disease-free equilibrium of the whole system is i v , N v , s h , l h , i h = (0, N * v , s * h , 0, 0).

Basic Reproduction Number

The basic reproduction number R 0 is a metric to determine whether an infection will spread in a healthy population. There 5, in order to confirm the existence of a stable endemic equilibrium. The initial conditions for the state variables (Table 3) were: S h = 10,000; L h = 0; I v = 0; S v = 18,000; I v = 2,000. The plot shows that a stable endemic equilibrium is indeed established within ∼2 years for both the GWSS and vine populations (A,B, respectively).

are different definitions and ways to calculate it. Generally, though, R 0 aims to approximate the number of secondary infections one infected individual will cause when it enters a fully susceptible population. Thus R 0 < 1 would mean the disease will not establish itself. Following [START_REF] Diekmann | The construction of next-generation matrices for compartmental epidemic models[END_REF], the basic reproduction number was calculated using

R 0 = K vh K hv
where K vh and K hv are, respectively, the number of vines one infected GWSS is expected to infect and the number of GWSS to which one infected vine is expected to transmit the pathogen, assuming a completely healthy population. K vh and K hv are given by

K vh = σ β vh µ v1 + µ v2 N * v K hv = σ β hv N * v s * h N h0 1 γ + v + µ h + v γ + v + µ h σ β hv N * v s * h N h0 1 µ h + µ x .
K vh translates as the product of GWSS expected lifetime and the rate at which the vector successfully inoculates a vine. K hv equals the expected time the vine spends at the latent stage multiplied by the number of successful transmissions to a GWSS. The second summand of K hv describes the same, but for the symptomatic stage, multiplied by the probability of transitioning from the latent to the symptomatic stage. Figure 5 displays how the basic reproduction number depends on the probing rate, σ , and GWSS density, i.e., the relation between the equilibrium total number of GWSS, N * and the maximum number of vinesN h0 . Specifically, it shows that a combined increase in GWSS density and probing rate positively affects the chances of establishment of endemic PD in the vine population.

Endemic Equilibrium

An endemic equilibrium is a steady state solution in which the disease will persist in the system. Numerical simulations of this system indicate that there is a unique endemic equilibrium and FIGURE 5 | The basic reproduction number R 0 indicates whether a disease can establish itself in a healthy population through an initial infection. Namely when R 0 < 1, the disease-free equilibrium of the whole system, i v , N v , s h , l h , i h = 0, N * v , s * h , 0, 0 , is stable and a small number of infected individuals will not cause endemic PD. GWSS density is defined as N * /N h0 , which is the relation between the equilibrium total number of GWSS, N * , and the maximum number of vines N h0 . The plot shows how the combined increase in GWSS density and probing rate positively affects R 0 . The rest of the model parameters are fixed to the values given in Table 5.

that it is asymptotically stable when R 0 > 1. To examine how GWSS density affects the equilibria, simulations were performed for different values of GWSS density. For each value of vector density, a numerical simulation was started with a small initial number of infected individuals (i v = 0.1 and s h = 1) and run until sufficient convergence was achieved. The obtained results are displayed in Figure 3 and show that PD becomes endemic at a GWSS density of approximately 0.01 GWSS per vine (Figures 3A,B).

To show that this system indeed reaches an endemic equilibrium for the baseline parameter values of Table 5, a numerical simulation was run starting from a low initial Xff presence in the system (S h = 10,000; L h = 0; I v = 0; S v = 18,000; I v = 2,000). The simulation yielded persistence of Xff in the system and establishment of a stable endemic equilibrium within approximately two years for both the GWSS and vine populations (Figures 4A,B, respectively).

Unfortunately, the aforementioned equilibria could not be solved analytically. Rigorous proof of their existence and type falls outside the scope of this paper.

Sensitivity Analysis and Identification of Key Parameters for PD Control

The aim of this model was to assess the importance of different parameters of PD epidemiology and, through them, suggest which control strategies would be more efficient against Xff spread. To that end, a sensitivity analysis was performed for the model parameters following the approach detailed in [START_REF] Arriola | Sensitivity analysis for uncertainty quantification in mathematical models[END_REF]. The normalized sensitivity index of output u to parameter p is defined as

S up = p u ∂u ∂p (11)
This estimates how the output u changes when small perturbations are made to the value of p. By calculating the sensitivity index for the basic reproduction number, R 0 , it could be determined which parameters of the model are responsible for the initial transmission of Xff. Meanwhile, the sensitivity index was also calculated for the endemic equilibrium and therefore key parameters that induce PD prevalence pinpointed. Given the analytical expression for R 0 , its sensitivity to the 12 parameters of the Xff model could be directly computed. For the endemic equilibrium, a linear system for each parameter was solved first in order to find an expression for S up . This expression was then evaluated at the numerically solved equilibrium value of the state variables. The results of the sensitivity analysis for the different parameters of this model are presented in Tables 6,7.

The most sensitive parameter for R 0 is the number of probes a GWSS performs on a vine per unit of time, σ . The sign of this sensitivity index means that as S R0σ = 1, decreasing (or increasing) σ by 10% would decrease (or increase) R 0 by 10%. In other words, the initial transmission of Xff would decrease (or increase) by 10%. Other noteworthy parameters are the probability of transmission from vine to GWSS during a probe, β hv , and the probability of transmission from GWSS to a vine during a probe, β vh . Similar to σ , these two parameters are positively correlated to R 0 . Finally, the maximum number of vines, N h0 , and the density-dependent part of GWSS death rate, µ 2v , significantly affect R 0 , and are negatively correlated to it. For most of the parameters, the sign of the sensitivity index of R 0 agrees with an intuitive expectation. Exceptions are the rate of progression from latent to symptomatic, ν, the maximum number of vines, N h0 , and the PD-independent death and removal rate of vines, µ h . According to these results (Table 6), the reproduction number increases when the rate of progression from latent to symptomatic decreases. This is because latent vines are a source of infection that cannot be traced and removed by the vinegrower. Thus, the existence of more latent vines in a population would mean more frequent encounters with Xff for GWSS. The reproduction number also increases when the maximum number of vines decreases. This is interpreted as being due to a shrinkage of probing options for GWSS. As the maximum number vines drops, the chances rise that healthy GWSS would end up probing on vines with PD and successfully acquiring the pathogen. Furthermore, the chances that infected GWSS feed on a healthy vine and successfully inoculate Xff also rise, causing an overall increase in transmission. Lastly, the reproduction number increases as the PD-independent death and removal rate increases. This happens because the vine population becomes smaller, which enhances the possibility that GWSS would feed on a vine with PD and acquire the pathogen. However, the increase in death and removal also decreases the lifetime of a vine, which has the opposite effect, so the change in the reproduction number is negligible.

According to the sensitivity index of the state parameter i h for the endemic equilibrium, the most influential model parameter for i h is ψ h (Table 7). The same parameter seems to be quite important for l h , as well. Another noteworthy parameter for i h is µ x and for both i h and l h is ν. At this point, it should be stressed that the three vine state variables of the fractional system, s h , l h and i h , are expressed in relation to the maximum number of vines, N h0 , which is a constant parameter. For this reason, when ψ h changes, s h , l h, and i h change in the same direction (increase or decrease simultaneously). Nevertheless, the reason why there is an increase in s h , l h , and i h when ψ h increases may be difficult to explain. The increase in the per capita replacement rate of vines would lead to an increase in the size of the vine population because the empty spots of the removed vines in the vineyard would be filled in. As a result, there would ultimately be an increase in all three vine stages related to a Xff infection. In situations such as the one analyzed here, i.e., when the disease is established in the population, most of this increase would end up mainly boosting the number of latent and infected vines. This would eventually mean that there are fewer healthy vines in relation to vines harboring Xff and, by extension, more infected GWSS, just as this model predicts (see i v in relation to ψ h ).

Effectiveness of Control Strategies for Regions With High PD Pressure

Subgroups of current control strategies that share a mode of function are defined above. Table 8 links the parameters of this model with all the types of control strategies described in the first part of the review (Tables 1,2).

Based on the results of the sensitivity analysis and on Table 8, it can be deduced that strategies reducing mainly σ , but also β vh and β hv , could undermine an initial Xff spread. Therefore, GWSS control strategies linked with σ are crucial for reducing the incidence of PD in recently invaded areas. Such strategies are those impeding GWSS from feeding on vines or those rendering vines an unpleasant food source for GWSS. Existing strategies that target σ are screen barriers that protect vineyards from GWSSs, coating vines with kaolin and harpin-based products, and regulated deficit irrigation. A strategy that could decrease β vh and β hv is the release of major GWSS predators since their presence would reduce GWSS probing duration on vines. Parameter β vh could also be minimized via paratransgenesis, while β hv appears to be affected by many more strategies. By definition, these involve all prophylactic strategies that breed or engineer resistance/tolerance in vines and that control Xff using avirulent XYLEFA strains, beneficial bacteria and fungi (i.e., preinfection stage). Furthermore, β hv is affected by all therapeutic strategies (i.e., post-infection stage). As regards N h0 and µ 2v , the analysis demonstrated their negative impact on Xff transmission. Unfortunately, N h0 and µ 2v are parameters over which there is no control as they are determined by land availability and vine productivity, and GWSS population dynamics, respectively. These results, though, combined with the literature review indicate a positive connection between mainly ψ h , but also v and the prevalence of PD in a vine population. Moreover, a decrease in µ x is partially responsible for the eventual successful establishment of Xff. Parameter ψ h cannot be managed by a PD control strategy since it strictly depends on the budget of vine-growers and nurseries' responsiveness. Evidently, a strategy directly reducing µ x is the roguing of vines that have developed persistent PD. Parameter v does not relate to any strategy of breeding or engineering resistance/tolerance in vines, or strategies that control Xff using avirulent XYLEFA strains, beneficial bacteria and fungi. This is correct, given that any preventive strategy is not applicable when the vine reaches the symptomatic stage. Conversely, both v and µ x can be controlled by all the therapeutic strategies mentioned.

Overall, this model shows that all studied therapeutic strategies affect three key parameters: β hv , µ x , and v. These parameters appear to contribute by blocking an initial spread of PD and are also extremely promising against Xff establishment in a vine population. Hence, it is suggested that research on and application of those strategies need to be prioritized. For areas in which Xff is not yet persistent in the majority of vines, vine-growers are advised to principally employ strategies that reduce GWSS preference for vines and vine accessibility. Lastly, the model suggests regular inspection of vineyards to monitor PD symptom severity and expeditious removal of problematic vines. This mode of management may significantly impede Xff transmission in a healthy vine population.

GENERAL CONCLUSIONS

There has been a systematic effort to reduce the presence of Xff in vineyards for more than 20 years. To that end, a plethora of approaches has been studied. Considering that the threat of XYLEFA-associated diseases is now increasingly widespread, researchers need to direct their attention toward improving those prophylactic strategies that have already been successful in vineyards. Furthermore, future studies should also focus on therapeutic strategies, such as successful field application of bacteriophage cocktails or other antagonistic microorganisms, since curing infected vines appears to be vital for the survival of the wine industry in PD-demarcated areas. This statement is supported by the results of the numerical simulation of the developed model. It is proposed that alternative strategies, should be designed only when already promising control strategies consistently fail to render the expected results in vineyards. In such an event, researchers should consider the importance of the parameters determined by this model as being crucial to the initial spread and establishment of Xff in a healthy vine population. Nonetheless, it should also be borne in mind that the evaluation of key parameters here was based on a model that considered SC, which is a region facing high PD pressure. Shifts regarding the importance of different parameters are to be expected in areas where PD epidemiology has different characteristics.

FIGURE 2 |

 2 FIGURE 2 | Schematic of the Xff epidemiological model showing the transition of the vine and GWSS populations to different stages due to Xff presence. State variables referring to the stages of GWSS are healthy S v and infected I v . State variables referring to the stages of vines are healthy S h , latent L h and symptomatic I h . Displayed on each transition between the state variables are the rates at which they happen in the model (see Equations 1-5). The model parameters can be found in Table4.

FIGURE 4 |

 4 FIGURE 4 | A numerical simulation of the model, with parameter values given in Table5, in order to confirm the existence of a stable endemic equilibrium. The initial conditions for the state variables (Table3) were: S h = 10,000; L h = 0; I v = 0; S v = 18,000; I v = 2,000. The plot shows that a stable endemic equilibrium is indeed established within ∼2 years for both the GWSS and vine populations (A,B, respectively).

TABLE 1 |

 1 Summary of promising strategies to prevent infection with Xff in vineyards (group A).

	Strategy	Promising case studies	Status of strategy	Latest citations
	Control of insect vectors	Insecticides (esp. neocotinoids)	Applied in vineyards and
			nurseries

TABLE 2 |

 2 Summary of promising strategies to exclude Xff from an infected vineyard (group B).

	Strategy	Promising case studies	Status of strategy	Latest citations
	Bacteriophage cocktails	Lytic phages Sano, Salvo, Paz & Prado	Tested in the greenhouse	Ahern et al., 2014; Das et al.,
				2015
	Antagonistic bacteria	Inoculating with P. phytofirmans strain PsJN	Tested in the greenhouse	Lindow et al., 2015, 2017a
	Natural, antibacterial	Radicinin	Tested in vitro	Rolshausen et al., 2015, 2017
	substances
		Antibiotics tetracycline, gentamicin, ampicillin,	Tested in vitro	Kuzina et al., 2006
		kanamycin, novobiocin, chloramphenicol and
		rifampin
		Inoculating with antibiotic streptomycin	Tested in the greenhouse	Kirkpatrick et al., 2004
		Antimicrobial peptides PGQ, indolicidin,	Tested in vitro	Kuzina et al., 2006
		magainin 2, and dermaseptin
		12 phenolic compounds (esp. catechol, caffeic	Tested in vitro	Maddox et al., 2010
		acid and resveratrol)
		Inoculating with microelement zinc	Tested in the greenhouse	Kirkpatrick et al., 2004
		sulfate/oxide
	Other defense-stimulating	Application of ABA by foliar sprays or soil	Tested in the greenhouse	Meyer and Kirkpatrick, 2011
	compounds	drenches
		Iron chelators lactoferrin, EDTA	Tested in vitro	Koh and Toney, 2005
		(ethylenediaminetetraacetic acid) and EDDS

TABLE 3 |

 3 State variables of the Xff epidemiological model.

	N v	Total number of GWSS
	S v	Number of healthy GWSS
	I v	Number of infected GWSS
	N h	Total number of vines
	S h	Number of healthy vines
	L h	Number of latent vines
	I h	Number of symptomatic vines

TABLE 4 |

 4 Parameters of the Xff epidemiological model.

	ψ v	Per capita birth rate of GWSS, time -1
	ψ h	Per capita replacement rate of (missing) vines,
		time -1

TABLE 5 |

 5 Baseline parameter values applied to calibrate the Xff epidemiological model. 28% chance of recovery once a vine has become latent capita birth rate, ψ v , of GWSS was 0.32 per day and the per capita density-dependent death rate of GWSS was (µ v1

	ψ v	0.32, 2.1 eggs per female per day, 30% of which survive
	ψ h	1/365, giving an average replacement time of 365 days
	N h0	10000
	µ v1	0.01, giving an average lifetime of 100 days
	µ v2	1.55 × 10 -5 , which leads to N * v	N h0 = 2
	µ h	1.1 × 10 -4 , giving an average lifetime of 25 years
	µ x	1/180, giving an expected time of vine removal once symptomatic
		of 180 days
	β hv	0.2
	β vh	0.35
	σ	1.5, GWSS performs 5 probes, 30% of which are on vines
	ν	1/120, average time of progressing 120 days
	γ	0.0033, giving a

TABLE 6 |

 6 Sensitivity indices of the basic reproduction number R 0 to the parameters, evaluated at the values given in Table5.

	R 0

TABLE 7 |

 7 Sensitivity indices of the endemic equilibrium values of the state variables to the parameters, evaluated at the values given in Table5.

		i v	N v	s h	l h	i h
	ψ v	-0.77	1.0	-0.27	0.00079	0.0023
	ψ h	0.7	0.0	0.76	0.55	1.6
	N h0	-0.0038	0.0	1.0	-0.003	-0.0088
	µ v1	-0.00012	-0.032	0.032	-0.000096	-0.00028
	µ v2	-0.0038	-1.0	1.0	-0.003	-0.0088
	µ h	-0.012	0.0	0.00025	-0.0056	-0.036
	µ x	-0.014	0.0	0.048	0.088	-0.72
	β hv	0.77	0.0	-0.77	0.0023	0.0067
	β vh	0.0038	0.0	-1.0	0.0030	0.0088
	σ	0.77	0.0	-1.8	0.0052	0.016
	ν	-0.27	0.0	-0.18	-0.81	0.56
	γ	-0.0011	0.0	0.28	-0.00083	-0.0025

TABLE 8 |

 8 Overview of control strategies and the model parameters that represent them. Control of insect vectors ψ v , µ v1 , σ , β vh , β hv Bacteriophages of Xff β hv , µ x , γ , and v Antagonistic bacteria β hv , µ x , γ , and v Natural, antibacterial substances β hv , µ x , γ , and v Other defense-stimulating compounds β hv , µ x , γ , and v Parameters σ , β vh , β hv, µx, and v, shown by the sensitivity analysis to be key parameters for PD control, are in bold.

	Control strategies	Relevant parameters
	Control of non-vine host plants and vine	None due to model assumptions
	propagation material
	Alteration to cropping techniques	σ , µ x , γ
	Breeding or engineering	β hv , γ
	PD-resistant/-tolerant V. vinifera
	Control via avirulent XYLEFA strains	β hv , γ
	Control via other beneficial bacteria and	β hv , γ
	fungi

Frontiers in Microbiology | www.frontiersin.org

September 2018 | Volume 9 | Article 2141

Readers of this review should be warned that Rolshausen et al. have significantly relied on the Proceedings of Pierce's Disease Research Symposia to publish updates of their project on fungal anti-Xff endophytes. The purpose of this review is to offer the readers a complete and detailed overview of all attempts to control Xff. Thus, even if not always peer-reviewed, the authors believe that overlooking this project from the review would be reductive.Frontiers in Microbiology | www.frontiersin.org

ACKNOWLEDGMENTS

We would like to acknowledge Ariena van Bruggen and Alexander Byth Carstens for contributing to conceiving the original idea for this manuscript. We would also like to thank Julia Harding, Patsy McGaughy, Jennifer Van Court, Andrew Walker, Rodrigo Almeida, Tracy Clevel and Monica Cooper, and Julie McNamara for helpful discussions.

FUNDING This study was funded by the Horizon 2020 Program of the European Commission within the Marie Skłodowska-Curie Innovative Training Network MicroWine (grant number 643063) and the Danish Research Council for Technology and Production Grants DFF-4184-00070 (Phytoprotect).

AUTHOR CONTRIBUTIONS

IK conceived the idea, performed the literature search and collection of data, wrote the review part, designed figures and the model, performed the calculations, contributed to writing the modeling part, and interpreted the results. TP designed the model and the computational framework, ran the model, performed the calculations and analyses, designed figures, contributed to writing the modeling part. LE-J, M-FS, and LH discussed the results and reviewed the manuscript. M-FS and LH were in charge of overall direction and planning.

Conflict of Interest Statement:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.