Peter Richmond
email: peterrichmond@ymail.com

Bertrand M Roehner
email: roehner@lpthe.jussieu.fr

Similarities vs. key discrepancy between tuberculosis and cancer

Keywords: age-specific death rate, death ratio, tuberculosis, cancer

In 2015 in the United States 612,000 persons died from cancer whereas only 470 died from tuberculosis (TB), a disease which was the main cause of death around 1900. How can one explain such a key discrepancy in treatment progress? A statistical comparison between TB and cancer will give some clues. However, TB and cancer also share several important features. Both TB and cancer can affect several organs, e.g. lungs, brain, bones, intestines, skin. What in cancer is called malignant neoplasm (tumor) is called granuloma in TB. By isolating malignant cells (versus bacteria) from the rest of the body, such clusters protect the host's organism but at the same time they are "secure beachheads" from where malignant cells (versus infected macrophages) can wander off to new locations. Thus, metastatic tumors have a TB parallel in the form of secondary granulomas. In order to investigate more closely this parallel we use the age-specific response of organs. Called spectrometric analysis in a previous paper (Berrut et al. 2017), this method provides information about how fast tumors develop and how serious they become. A convenient characterization of the response to TB of organ j is given by the following (age-dependent) death ratio:

T j (t) = (death by TB of type j)/(all TB deaths). The development of cancer tumors can be described by a similar function C j (t). We compare the organs' responses in all cases for which specific death data are available. It appears that for the same organ T j (t) is similar in shape to C j (t). In other words, the idiosyncrasies of each organ are more determinant than the functional differences of TB versus cancer. For instance, with regard to brain tumors, both TB and cancer mortality peak around the age of 10. Such observations may bring to light vulnerabilities in the way the immune system provides protection to various organs.

Introduction

Contrasting death rates In the early 20th century in Europe and the United States tuberculosis was the first cause of death. Cancer came only in fourth position after cardiovascular and cerebrovascular diseases. Nowadays, although remaining a substantial cause of death in old age, tuberculosis has been virtually eliminated in young and middle-aged patients. In contrast, despite intensive research, progress in cancer treatment was much slower.

Fig. 1a,b shows a dramatic difference between the death rate changes of the two diseases. How can one possibly explain it? Before we develop our explanation let us summarize the key points in a few sentences.

• For cancer the incidence rate (i.e. the annual number of new cases in a population of 100,000) is 439 whereas the death rate is 163 1 . This gives a case-fatality ratio (i.e. number of fatalities for 100 persons who became ill) of 163/439 = 37%.

1 These data are given by the US National Cancer Institute for the years 2011-2015. In 1989-1991 there was a measles outbreak which particularly affected California, Chicago and New York. Sources: 1850-1899: Statistique internationale du mouvement de la population (1907);1900[START_REF] Linder | Vital statistics rates in the United States 1900[END_REF][START_REF] Linder | Vital statistics rates in the United States 1900[END_REF][START_REF] Linder | Vital statistics rates in the United States 1900[END_REF]-1960[START_REF] Grove | Vital statistics rates in the United States 1940-1960[END_REF]1961-1967: Mortality statistics in the United States 1967 p.1-7;[START_REF] Grove | Vital statistics rates in the United States 1940-1960[END_REF][START_REF] Leeuwen | Animal models of tuberculosis: zebrafish[END_REF]: CDC Wonder databases, compressed mortality 1968-1978,1979-1998,1999-2016. The respective ICD (International Classification of Diseases) codes for measles are as follows. 1968-1998: ICD8 and ICD9: 055, 1999-2016: ICD10: B05. This is a proportion which is higher than for most infectious diseases. Thus, for measles in the outbreak of 1989-1991 in California and New York it was less than 1%. As a more significant comparison, the case fatality ratio of TB for South African HIV-infested persons is about 20% (Walt et al. 2016). Moreover, for most infectious diseases the case-fatality ratio decreases with age whereas for cancer it increases with age2 . On the contrary, for cancer the case fatality ratio increases with age (Fig. 1d).

• In an epidemic usually only a small proportion of the population is infected by the pathogens in the sense that the others do not produce any antibody. On the contrary, the production of abnormal cells occurs in everyone which means that the infection rate is 100%.

• With respect to infectious diseases any population comprises two components: (i) the susceptibles that is to say the persons who are not immunized and (ii) those Cancer: case fatality ratio (%) Fig. 1d Cancer: case fatality ratio. The case fatality ratio is the ratio: death rate divided by incidence rate. It gives the probability of death for a person who becomes ill in the respective age interval. The fact that the ratio increases with age shows that the organism becomes less and less able to fight the disease successfully. In contrast, for most infectious disease the CF ratio decreases with age. Source: Cancer Research UK. The data are for all forms of cancer (C00-C97), 2013-2015. who are immunized and the proportion of the second group increases (i) with age and (ii) for each age-group in the course of time, at least in the fade-out phase. On the contrary, for cancer the ability to fight the disease decreases with age as shown by Fig. 1d and does not improve in the course of time.

In summary, the previous points together with the upcoming discussion suggest that cancer is fundamentally different from infectious diseases and that human organisms are not well equipped to fight it. Hence the huge difference displayed in Fig. 1a,b.

Natural history of infectious diseases

The history of infectious diseases like smallpox, measles or TB usually comprises 4 phases, each of which may last from a few decades to a few centuries. Despite covering a broad time span of 166 years, the graphs for TB and measles displayed in Fig. 1a,c probably miss the initial epidemic phase.

(TB1) Epidemic phase. When the prevalence of the infectious agent (whether bacteria or viruses) in a population is fairly low, few people have been able to develop an immunity. In this phase the disease manifests itself in the form of periodic epidemic surges.

(TB2) Endemic phase. As the outbreaks become more frequent infection be-comes more prevalent with the result that the disease tends to become endemic. An endemic equilibrium state is reached when the death rate of the disease has become fairly stationary. Whereas for rare diseases such a stationary death rate can be quite low, in some cases of which TB in the 19th century is a good illustration, it can be fairly high. (TB3) Fade-out phase through immunity of survivors and offspring. When the prevalence of a disease is as high as it was for TB in the late 19th century, there are more and more survivors who develop an immunity which means a correlative fall in the number of susceptibles. In this process the transmission of immunity from mother to child through breast-feeding played an important role as was proved by the German biologist Paul Ehrlich in the early 20th century. As a result of a decreasing concentration of pathogens in the environment, the death rate of the disease starts to fall. A "spontaneous" decrease of this kind was indeed observed for measles as well as for TB during several decades prior to the introduction of effective remedies in the 1950s (see Fig. 1a,c).

(TB4) Eradication phase. With the disease held in check by vaccination and other remedies and if there is no other carrier which can constitute a "safe haven" for the pathogens involved, the decrease will go on and will end only when the disease is totally eradicated worldwide, a success so far reached for only a few diseases; back in 1980 smallpox was the first one.

Comparative analysis of cancer vs. TB Now, let us come to the crucial question of why the cancer death rate curve is almost flat. Our reasoning comprises the following steps.

(C1) Deviant cells are ubiquitous It seems natural to admit that the incidence of a disease represents an equilibrium between two opposite forces: the prevalence of infectious agents in the environment and the strength of the immune system with respect to this specific disease. If there are no pathogens there will be no disease. As we have seen, this corresponds to the situation when a disease has been eradicated. Cancer corresponds to a completely opposite situation for the analogue of the pathogens are abnormal cells which grow in a boundless way. As such deviant cells appear continuously in the body of each and every individual, cancer resembles a disease brought about by a highly widespread pathogen.

(C2) Is there a learning curve with regard to the elimination of abnormal cells? Now, we need to gauge the strength of the immune system with respect to cancer cells. Individuals who have recovered from smallpox will never become ill again which means that their immune system has been notably strengthened with respect to this disease. Similarly, it was shown by Paul Ehrling that mice which are fed small but increasing dosages of a poison (e.g. ricin or abrin) become resistant to this poison. Is there a similar strengthening mechanism for the immune system against cancer? It is the task of the killer T-cells to identify and target abnormal cells. This includes cells infected by viruses or bacteria as well as cancer cells. As the first abnormal cells appear soon after birth (as seen by the occurrence of some forms of cancer in newborns), the existence of a learning process would mean that the immune system will be more and more able to remove them. However, the fact that after the age of 10, the death rate of cancer starts to increase and that it continues to go up steadily with age suggests that no equilibrium is reached. In a population of 100,000 30year old persons the immune system will loose its war against abnormal cells in approximately 30 cases; at age 40 and 50 that war will be lost in 60 and 120 cases respectively (for data about age-specific death rates see [START_REF] Richmond | A 2-d classification of diseases based on agespecific death rates[END_REF]. In fact, we do not need to know whether the immune system improves or deteriorates with age; what the previous numbers show is that the imbalance between the rate of apparition of new abnormal cells and the capacity of the immune system to remove them increases with age. In other words, with respect to cancer, the human immune system reveals a structural weakness.

(C3) Cancer in dogs In the previous sentence we used the expression "human immune system" which raises the question of whether this weakness is special to humans or, on the contrary, is shared by other mammal species. It seems that the only animals for which the causes of death are identified with sufficient accuracy are pet dogs and cats. For both adult dogs and cats cancer is the main cause of death. Moreover, Fig. 1e shows that the trend of the age-specific cancer death rate for a group of 345 Rottweiler dogs is mostly upward. Although this is a fairly small group the results give a preliminary indication that the pattern is roughly similar to what is observed in humans. In other words, the weakness of the immune systems is shared by dogs. Probably other mammals would reveal the same pattern if appropriate data were available.

(C4) Poor performance of cancer immunotherapy and chemotherapy For infectious diseases the main method of treatment was to strengthen the immune system through vaccination. Quite understandably, the same approach was tried for cancer. Paul Ehrlich (1854-1915), William Coley (1862-1936) and others developed cancer immunotherapy3 . They were able to prove that the mechanism of removal of abnormal cells by the immune system is fairly similar to the elimination of pathogens. However, despite notable progress (for which Ehrlich was awarded the Nobel prize in 1909), attempted cures were much less successful than for smallpox, rabies or other infectious diseases. Age (year) Cancer death rate (per year of age and 100 in age group) Fig. 1e Cancer death rate for pet dogs as a function of age. The data are based on information provided by veterinarians for a cohort of 345 Rottweiler dogs. With respect to humans the death rate increases more slowly in old age. However, in order to asses more reliably the death rate in old age one would need a larger sample.

Here at the age of 12.5 years there were only 35 dogs still alive. Between the ages of 4 and 10 there is an exponential increase described by µ ∼ exp(αt), α = 0.43 year -1 which corresponds to a doubling time of 1.6 year; this is almost the same as for humans when renormalized with respect to the respective life spans, i.e. 1 dog-year equal some 6 human years. Source: [START_REF] Cooley | Exceptional longevity in pet dogs is accompanied by cancer resistance and delayed onset of major diseases[END_REF].

Ehrlich was not only a pioneer in immunotherapy but also in chemotherapy. Around 1910 he discovered the first effective drug treatment for syphilis. However, when tried for cancer, the approach of chemotherapy once again proved less effective than for infectious diseases.

In short, the component of the immune system tasked with fighting abnormal cells (let us call it the endo immune system) turned out to be weaker and more difficult to strengthen than the component (let us call it the exo immune system) destined to fight pathogens. In a parallel developed below this difference can be seen as similar to the one between fighting a foreign war and a guerrilla war.

In spite of the differences emphasized in the previous discussion, the main argument of our paper is that better insight can be gained by comparing the two diseases. On the one hand, as shown below, they share many similarities but on the other hand with respect to treatment they are dramatically different.

Questions

Here are some of the questions that can be raised.

(1) Both TB and cancer do exist in dormant mode. In latent TB the persons are infected with the TB bacteria which however do not multiply; as a result they are not ill and not contagious. This state can last for years. Even without treatment less than 10% of these persons will develop the disease during their lifetime. Similarly, dormant cancer cells are mutated cells which, however, do not multiply. As explained below dormancy is a very common occurrence in many microorganisms. Would it not be of interest to examine if there are common dormancy mechanisms. TB and cancer might be a good point where to start such a comparative study.

(2) Both TB bacteria and cancer cells form clusters. This is for them a way to be protected against anti-bodies or drugs. However, the death rate differential suggest that TB clusters afford much less effective protection. In a sense this is a network problem in which the bacteria or cancer cells are the nodes; such networks would have the ability to branch out and nucleate to form secondary networks. Naturally, to define such networks in a meaningful way would require a knowledge of key-parameters such as density and interaction strength.

(3) Whether in TB or in cancer, the creation of new clusters (i.e. metastasis) is conditioned by the same steps. (i) First bacteria or cells must be able to leave the initial cluster. In cancer tumors this means being able to cross the extra cellular matrix, a layer of protein molecules which surrounds the tumor and separates it from adjoining tissues. (ii) While on their way the bacteria or cancer cells must either not be detected or be able to ward off anti-body strikes. (iii) Finally, an appropriate niche must be found. Our subsequent analysis suggests that TB myco bacteria and cancer cells have the same preferences, namely the lungs and the other organs that we examine but that they both avoid skeletal muscles. Whether or not we have a good understanding of these steps can be tested through our ability to explain the differential outcomes.

In the next section additional explanations are provided about the mechanisms involved in the previous points.

Similarities between TB and cancer

Treatment

The impressive difference suggested by Fig 1a,b is an enigma for in a sense the situations of the two diseases with respect to treatment appear fairly similar.

• Drugs are available which kill the agents responsible of the disease, Mycobacterium tuberculosis on one hand and cancer cells on the other hand. The mechanism of action of antibiotics and drugs used in chemotherapy are very much the same in the sense that both drugs are only effective when the bacteria or cells are in division stage.

• There are two main mechanisms through which TB bacteria and cancer cells can protect themselves. One is to form tight clusters that anti-bodies cannot penetrate. The second is to form dormant cells which cease dividing but survive in a quiescent state while waiting for appropriate environmental conditions. Among microorganisms this a very common mechanism. For instance, in C. elegans it is called the dauer stage, in the rotifer Brachionus plicatilis the so-called diapausing eggs may remain in an arrested stage for long periods until conditions become more favorable (Garcia-Roger et al. 2005).

In other words, TB and cancer treatments are confronted to similar problems: how to break into clusters and how to get rid of the dormant cells.

It may be tempting to say that in these two tasks antibiotics are doing a better job than cancer chemotherapy drugs. However, this would ignore the fact that between 1850 and 1950 (beginning of antibiotics treatment) TB mortality rate had fallen from 350 to 40 per 100,000.

Worsening environmental factors

If antibiotics were only of marginal importance, what were the other factors? The BCG (Bacille Calmette Guérin) vaccine was first used on humans in 1921 in France but it was not until after World War II that it received widespread acceptance elsewhere. As it arrived at the same time as the antibiotics it can hardly be credited with the sharp reduction since 1850. So, what were the factors at work in the 100 years until 1950? Mainly environmental factors and better living conditions. More specifically, this meant preventing contagion and allowing the organisms of patients to fight the disease in the best conditions possible (sanatorium, rest, healthy apartments).

Why did progress of a similar kind not take place for cancer? This is an interesting but open question. However, it can safely be said that with respect to cancer, environmental conditions rather deteriorated. One may mention food additives, pesticides used in agriculture or X-rays. Except the last one, most of these factors are not easy to quantify. An introductory discussion of the X-ray issue can be found in Roehner (2002, p.42-45).

At first sight it may seem possible to estimate the effect of environmental factors through the incidence rate. However, pre-death medical diagnosis is very dependent upon available identification means. For instance, between 1982 and 1989 the incidence rate of breast tumors smaller than 1cm increased from 10 to 40 per 100,000 women whereas in the same time interval, the incidence of tumors of more than 3cm remained unchanged at a level of 35 per 100,000 [START_REF] Garfinkel | Changing trends. An overview of breast cancer incidence and mortality[END_REF]).

Granulomas versus tumors

The mechanism of TB propagation in an organism can be closely investigated in experimental TB induced in animal models. Zebrafish (Danio rerio) appear as a particularly convenient model [START_REF] Leeuwen | Animal models of tuberculosis: zebrafish[END_REF]. The development of granulomas are a key feature of human TB and zebrafish studies provided a dynamic insight into what, hitherto, was largely seen as static structures. Granulomas are preferentially formed in fatty tissue and they are the first step through which infection can be clearly identified. In short, they play the same role as primary tumors in cancer. Moreover, observations on zebrafish showed that infected macrophages can detach from established granulomas and wander off to other organs to form secondary granulomas. Clearly, such a process parallels the dissemination of cancer cells which leads to secondary tumors. Differences that are more apparent than real At first sight, tuberculosis (TB) and cancer appear as very different diseases. Whereas TB is due to the proliferation of a bacteria, Mycobacterium tuberculosis (MT), cancer results from the boundless reproduction of body cells which have freed themselves from the controls generated by their neighbors. TB starts with a foreign pathogen whereas in cancer it is a body cell which spins out of control.

However, if we look at it more closely, the mechanisms are not too different for indeed through a kind of reprogramming process pathogens are able to twist the behavior of host cells (in the case of viruses) or macrophages (in the case of bacteria) which try to eliminate them. For instance, once a bacterium has been "imprisoned" into a vesicle of a macrophage4 , a common trick (used for instance by MT or Legionella pneumophila) is to prevent the injection into the vesicle of enzymes which would kill the pathogen. In short, by manipulating their host successful pathogens are able to use it as a vehicle for proliferation.

Conversely it was estimated [START_REF] Greenwood | 16% of cancers are caused by viruses or bacteria[END_REF]) that about 16% of worldwide cancers are triggered by viruses or bacteria: for stomach cancer it is Helicobacter pylori, for lymphoma it is the Epstein-Barr virus, for cervical cancer it is the papilloma virus, for liver cancer it is hepatitis B or C.

There are also similarities in subsequent stages.

• One knows that the formation of a tumor is a multistage process; so is also the development of TB as illustrated by the following features. (i) In only 10% of infected persons will TB manifest itself. The other 90% will remain asymptomatic. (ii) As already mentioned as TB develops, one sees the formation of granulomas which are nodules of a diameter of about 3mm in which pathogens and neutralized macrophages are clustered together.

• Primary cancer tumors can develop in many organs. Although pulmonary TB is the most frequent, TB can also develop in several parts of the body: bones, skin, intestines, meningitis, genito-urinary organs. On the other hand there are some locations (e.g. skeletal muscles) where the development of both cancer and TB is uncommon.

• Although fairly rare, TB of the breast (tuberculosis mastitis) does occur and it is far more frequent (about 20 times) in women than in men [START_REF] Wilson | Tuberculous mastitis[END_REF]); it is particularly likely in reproductive age. As a matter of fact, being irregular and hard, TB breast lesions may be indistinguishable from breast carcinoma [START_REF] Baharoon | Tuberculosis of the breast[END_REF].

• One of the most important properties of cancer cells is their ability to spread to other organs where they may form secondary tumors. There is a parallel in TB in the sense that the granulomas can migrate to other organs such as the liver or the kidneys. In developed form such cases are called miliary TB; they represent 20% of the extra-pulmonary cases.

Although too short and schematic, the previous description suggests that it is not completely absurd to think that there may be connections between the development of TB and cancer.

Purpose and method

Purpose

The objective of this paper is very simple. If, as argued above, there is indeed a connection between the growth of TB and cancer in various organs, can it be that these links manifest themselves by similar responses of various organs? How can one design an operational procedure that will unravel such possible links? It turns out that among the set of persons who will develop a cancer during their lifetime the probability C b (t) that this cancer will affect the brain is highest around the age of 10 years: C b (10) = 23% (Fig. 1). At older ages this probability falls off sharply. At the age of 25 it is down to 5%, and at the age of 50 to 1%. Do we currently have a clear understanding of why C b (t) is highest in childhood? To our best knowledge, it does not seem so. Now, as can be seen in Fig. 1, the probability T b (t) for developing TB affecting the brain is also maximum at the age of 10 and falls off in older ages even more sharply than C b (t). Subsequently, for the sake of brevity, a curve such as C b (t) will be called the age-profile of brain cancer.

It could well be that the similarity in the age-profiles C b (t) and T b (t) is merely a coincidence. However, if for a number of other organs the same similarity is observed, it may suggest that some organ-specific factors are at work which account for similar responses for the two diseases.

What can be the practical interest of these observations? Taken alone, they will not give us a full fledged explanation of why such brain diseases appear at that specific age. However, they suggest that the idiosyncrasies of the organ under consideration plays a more important role than the nature of the disease itself. For instance, as far as brain diseases are concerned, the screening defects of the blood-brain barrier may be the key5 . In other words, in this shield versus sword issue, our observation will tend to focus attention on the macrobiological properties of the shield.

Method

In the previous subsection we defined our objective and we broadly delineated how the observation will be organized. Presently, we will explain how in practice it can be implemented.

The main difficulty is the following. As we wish to explore the affinity a disease (α) has for a specified organ (S) we would need incidence data rather than mortality data. As a matter of fact, mortality data mix two very different effects (i) the prevalence of α in S (ii) how effectively this specific disease can be cured. As an extreme case, for a disease whose cure rate is 100% or which simply is not a deadly disease (as for instance is the case of most forms of herpes) it is altogether impossible to get any information about incidence from mortality data.

Because nowadays in all developed countries TB is cured in very effective ways6 , it is impossible to use present-time data for our investigation. On the other hand, if we consider US data from the early 20th century there will also be two difficulties. (i) The international classification of diseases will be very different from the presentday classification and it will be much less detailed. Thus for TB there will be only 5 types and they will include labels such as "Pott's disease" (TB of the spine) or "White swellings" (TB of the joints) with which we are no longer familiar. (ii) In 1910, only 58% of the US population was included in the federal death registration area. This would reduce the number of deaths by a factor of two. Starting from 1933, the death registration area included 100% of the population. This led us to the methodological choice of using data from the period 1934-1945.

In 1934 there were substantial numbers of deaths in almost all types of TB or cancer except for a few. We have been using averages over a number of successive years in order to reduce the statistical fluctuations. Naturally, the fluctuations are conditioned by the number of deaths. As an illustration, one can mention the case of skin TB for which there were less than 10 deaths in almost all age groups except in the oldest ones. In this case the smoothing process required to take averages over 10 successive years that is to say from 1934 to 1943.

Results

If one can assume that the death records have been filed correctly, all disease locations documented in US mortality data are for primary lesions. The comparison between the profiles of TB types and cancer types is shown in Fig. 2a,b. As a matter of curiosity, one may wish to know to what extent the cancer profiles of 1934 differed from those of 2015. Of the 7 profiles, only two were markedly different, namely (i) cancer of the respiratory system and (ii) skin cancer. For (i) in 2015 there was only one peak near the age of 65 The narrow peak centered on the age of 20 does no longer exist. For (ii) it so to say the opposite in the sense that in 2015 in addition to the ratio which surges up beyond the age of 75 there is also around the age of 25 a major peak which reaches the level of 4%.

The TB-cancer correlations are given in the caption of Fig. 2. They show that in 5 of the 7 cases (i.e. 71%) there is a significant correlation. For these 5 cases the average correlation is: r = 0.61 ± 0.11.

In addition two points should be observed.

• Even for the "intestines" and "lymphatic" cases for which there is no correlation the profiles share some common features. Thus, for "intestines" after the age of 25 the two ratios do not fall to zero (as is the case for "brain" or "bones") but increase more or less steadily (applying a smoothing moving average would almost eliminate the ups and downs of the cancer profile). Moreover, an age shift of only 10 years would bring the peaks of the two curves of the lymphatic case together.

• It must be realized that the profiles are of very different shapes which makes similarities arising merely by chance fairly unlikely.

A conjecture to explain the treatment conundrum

Death rate levels versus death profiles What is the present-day situation regarding TB and cancer? As shown in Fig. 3, roughly speaking in terms of order of magnitude TB and cancer death rates differ by a factor 100 at all ages. However, contrary to their levels, the age-profiles of death , 1937-1943. rates are not very different. The parameters of the two laws differ by 20% on average (23% for the exponent γ and 18% for the doubling time T .)

Birth defects versus wear-out

The curves of Fig. 1 suggest that there is a connection in the way TB and cancer lesions develop in different organs. A rough distinction can be made between the lesions (e.g. 2,4,6) which develop mostly in young age (and are likely due to birth defects) and the lesions (e.g. 1,3,5,7) which develop mostly in old age (and are likely due to a wear-out process).

Age (year) Probability of death by given disease (%)

Fig. 2b (continued from Fig. 1a). Comparison between the conditional probabilities represented by the ratios: (deaths by TB type)/(all TB deaths) (blue line with round dots) and (deaths by cancer type)/(all cancer deaths) (red line with squares), USA 1934USA -1943. The left-hand scale refers to TB whereas the righthand scale refers to cancer. The TB ratios represent the conditional probability of dying at a given age from a specified type of TB within the set of all people dying from TB. There is a similar definition for cancer. The 7 cases shown in Fig. 1a,b do not result from a selection; they represent all cases for which data are available. The correlations, confidence intervals (for a probability level of 0.95) and ICD codes are given below in the following form: cor, CI, TB/C. (1) cor = 0.55 (0.17, 0.79), 23/47; (2) cor = 0.67 (0.35, 0.85), 24/subclass of 53; (3) cor = -0.560 (-0.81, -0.24), 25/subclass of 46; (4) cor = 0.46 (0.046, 0.74), 26+27a,b/subclass of 53; (5) cor = 0.91 (0.79, 0.96), 28/52; (6) cor = 0.01 (-0.41, 0.43), 29/72b; (7) cor = 0.56 (0.18, 0.79), 30/46+51. All correlations are significant except (3) and ( 6). Moreover under an age shift of 10 years the two curves of (6) become correlated too. Sources: Bureau of the Census: Mortality Statistics 1934-1936, and Bureau of the Census: Vital Statistics of the United States, Part 1, 1937Part 1, -1943. . Such conclusions would have been impossible to reach by using death rates instead of death ratios. Indeed, as shown in Fig. 2, age-specific death rate curves in the TB TB

Cancer Cancer

One day to 10 years 10 to 100 years Fig. 3 Comparison between the death rates of TB and cancer, USA 1999-2015. Left: age from 1 day to 10 years, right: age over 10 years. Whereas the death levels are very different, the shapes of the agespecific death rates are fairly similar. For all causes of death, in the 0-10 year age range the death rate is an hyperbolic function of age of the form: [START_REF] Berrut | Deciphering infant mortality[END_REF]. For TB: γ = 0.33 ± 0.3, for cancer: γ = 0.43 ± 0.2. In the range 10-100 year, it is the Gompertz law which applies, that is to say an exponential increase: µ ∼ exp(t/τ ). The doubling times T = τ log(2) expressed in years are as follows. TB: T = 9.7 ± 0.8, cancer: T = 7.9 ± 0.7. Source: CDC Wonder database 1999-2015 (underlying causes of death). As of April 2017 the relevant web-address was: https://wonder.cdc.gov adult age-range are increasing exponential functions, a feature that would preclude any shape comparison. On the contrary, the age-profiles of the death ratios have very contrasted shapes that can be compared significantly. The aim of this article was to convey our belief that the age-profiles offer useful "signatures" of the corresponding diseases.

µ b ∼ 1/t γ (

Conjecture for the treatment conundrum

Despite the similarities that we were able to pinpoint in this article, TB and cancer are extremely different in terms of treatment effectiveness. Fig. 1a,b shows that in the past 100 years TB mortality was divided by 1,000 whereas cancer mortality remained basically the same. This is what we call the treatment conundrum. How can it be explained? In the following subsection we propose a testable conjecture.

Army vs. police

In any sovereign country a clear distinction is made between army and police. The role of the army is to ward off foreign attackers and to destroy the forces who were able to penetrate on the national territory. In contrast the action of the police is directed against domestic elements who are sources of disorder or threaten the nation's security. Whereas waging foreign wars is a well defined concept, fighting domestic enemies of the state is a more murky task. The two notions tend to overlap in civil wars or guerrilla warfare. The specificity of guerrilla warfare is that the insurgents hide among the population and are therefore not easy to identify and destroy. There are no definitive victories. Once a region has been cleaned fighting may resume elsewhere.

A similar distinction can be made for the immune system. Bacteria, viruses, fungi, parasites are foreign invaders which will be identified, targeted and destroyed by the lymphocytes (B and T cells), antibody proteins and macrophages. On the contrary, cancer cells are domestic enemies. For the sake of brevity, the part of the immune system which fights foreign invaders will be called the exosystem whereas the part directed against domestic deviants will be called the endosystem 7 .

It may be useful to note that in fact the exo-and endosystems overlap. A clear confirmation is the fact that the BCG vaccine against tuberculosis is a remarkable booster of the immune response to bladder cancer. Since the late 1970s it is known that instillation of BCG into the bladder brings about a local immune reaction against the tumor. Moreover recurrence is prevented in up to 67% of cases (Wikipedia article entitled "BCG vaccine").

A testable explanation of the treatment conundrum

The distinction between the exo-and endosystem suggests a possible explanation.

We have observed that partisan fighters are much more difficult to identify than foreign armed forces. It is natural therefore to make the same assumption for the immune system. More precisely, we make the following assumption.

Exo-endo conjecture For an organism which enjoys optimal living conditions, at any age the exo immune system is more effective than the endosystem in the sense that the natural mortality rate is much higher for endodiseases (like cancer) than for exodiseases (like tuberculosis).

This conjecture explains that the present-day death rate is 1,000 times lower for TB than for cancer but it does not explain why the two rates were almost the same in the early 20th century. This feature can be explained by population movements (particularly rural flight 8 ) followed by a selection process. What do we mean more precisely?

Role of rural flight Unfortunately we do not know early prevalence levels around 1800 respectively in rural and urban places but irrespective of where it was higher the contacts between 7 It would seem that the exosystem has received more attention than the endosystem. On the website of the Nobel Committee there is a fairly detailed presentation of the immune system destined to the general public. In the 5 pages there is only one line which refers to cancer cells. We are told that the killer T cells (one of the two kinds of T cells) are specialized in attacking cells of the body infected by viruses or bacteria as well as cancer cells.

8 In all industrialized countries there were large-scale population migrations from the countryside to cities and their factories.

rural and urban people must have increased the number of cases especially in the cities because of a higher population density (with respect to the influence of density see [START_REF] Li | Effect of population density on epidemics[END_REF]) and poorer living conditions. This resulted in a great TB epidemic observed in all European countries.

As in all epidemics the persons whose immune system was able to protect them survived along with their children. We are not used to view TB as an epidemic but one should remember that from infection to death or recovery the time constant of this disease is of the order of several years. For influenza it is a few weeks that is to say some 50 times less. Whereas an influenza epidemic lasts half a year, a TB epidemic may last 25 years.

The fall of the TB death rate between 1850 and 1950 is often explained by better living conditions. While living conditions may have played a role, in our conjecture the bulk of the decrease was due to the selection process through which people whose immune system could not fight the disease were eliminated. The people who survived were those who had a natural immunity or whose immune system was able to adapt. If this explanation is correct one should observe a correlation between the development of population interaction (particularly the rate of rural flight) and the death rate due to TB.

There remains a question however. Should one not observe a similar selection process with respect to cancer? For such a selection to operate, the persons who have weak immunity should not be able to transmit it to their children. This was indeed the case for TB whose peak rate occurred in the 20-30 age group (see [START_REF] Richmond | A 2-d classification of diseases based on agespecific death rates[END_REF] but is not at all the case for cancer whose death rate is very low for the 20-30 age group and becomes substantial only after the age of 60.

Conclusion

Similarities and differences between TB and cancer

The main message of this paper was to emphasize the similarities between TB and cancer. However, this left open the question of why there was a tremendous difference in the outcome of treatment. To explain it we proposed what we called the exo-endo conjecture. How can it be tested?

The simplest test would be a comparison of mortality rates of exodiseases and endodiseases in other mammals. The Wikipedia article entitled "Cancer in dogs" gives the following information. Dogs can develop a variety of cancers and most are very similar to those found in humans. Cancer is the leading cause of death in dogs. It is estimated that 30% domestic dogs will develop cancer, which is the same incidence as in humans.

A more thorough investigation of the respective frequency of exo-and endo-diseases in mammals will be postponed to a subsequent paper.

Extension of the present study

For the purpose of this paper we had by necessity to use data from the first half of the 20th century because our main requirement was to have enough death cases to keep the statistical fluctuations under control. How can we extend this analysis to a greater number of lesions?

If, instead of using death rates we could use incidence rates the number of cases would be multiplied by a large factor. This factor depends of course upon how lethal a lesion is; for instance lesions of the thyroid can be cured with high probability which means that the incidence rate may be 20 or 30 times higher than the death rate. This will allow an interesting extension.

TB and cancer are not the only diseases which can target different organs; syphilis or diabetes are other examples. This will provide a second extension. It will be interesting to see if there are meaningful connections between such families of diseases.

Appendix A. Importance of thinking by analogy

Readers may wonder what can be gained and learned by emphasizing analogies between TB and cancer. Perhaps the best answer is to observe that throughout the history of science analogies have permitted great progress. This is explained in Appendix A.

It is not always realized that throughout the development of physics from the 16th century up to nowadays physicists have relied on thinking by analogy. The purpose was always the same, namely to establish a bridge between phenomena which were fairly well understood and others which were still mysterious. Seen in this perspective, the role of thinking by analogy should not be limited to physics. In any field, when facing uncharted territory, one needs some guidance. While assistance may come in many different forms, analogy with similar but simpler cases is certainly one of them. As an example Mendel's experiments provided the framework on which the whole field of genetics could develop.

Rigid versus open scientific thinking

At first sight, thinking by analogy may not appear very scientific. It is true that it cannot prove itself to be correct but at least analogy reasoning can lead to fruitful conjectures. It may well be that in their concern to appear highly "scientific", biologists refrain from relying on analogy arguments. The very structure of present-day biological papers, namely: (i) Problem (ii) Material and method (iii) Results and discussion, may be appropriate for well defined issues but not for opening new vistas in unexplored territory. In physics such a rigid framework would be suitable for engineering problems but certainly not for developing the new concepts and ground-breaking ideas of a new field like quantum mechanics. New visions require imagination and creativity and most often such advances are channeled and guided by analogy thinking.

The purpose of the present appendix is to make biologists realize that even in physics, the most successful among scientific fields, analogy has played a great role at some crucial junctures. In the hope that they may convince doubtful readers, we give below a number of illustrations.

Examples of progress brought about by analogy thinking

In the late 16th and early 17th century the question of how two masses can attract one another without apparently any contact was a key issue for astronomy as well as for the question of free fall. From Galileo to Kepler to Newton electrostatic and magnetic attraction provided welcome examples supporting the conjecture of the existence of a gravitational force. Nowadays, the mechanism of gravitational attraction explains many phenomena, from the fall of an apple, to the "fall" of the Moon toward the Earth, to the formation of black holes, to the rotation of spiral galaxies.

Three centuries later, in the discussions which led to the creation of quantum mechanics, the analogy with optics, namely geometrical optics on the one hand and physical optics on the other hand, played a great role for it facilitated the adoption of wave-particle duality.

Fifty years later, in an attempt to describe strongly interacting particles, physicists created what is now called quantum chromodynamics (QCD) and for that purpose, as a blue print, they used quantum electrodynamics (QED), that is to say the study of particles which have only electromagnetic interactions. Some two decades later, Yang-Mills gauge theories took model on gauge invariance in electromagnetism9 , see Yang et al. (1954).

The role of analogy in the history of physics was studied and emphasized by the French physicist Pierre Duhem as attested by the following excerpt (Duhem 1906, p. 140). "The history of physics shows that the search of analogies between different categories of phenomena may have been the most productive of approaches tried by theoretical physics".

It should not come as a surprise, therefore, that when they turn to the fields of biology and medicine, physicists adopt a comparative perspective with the purpose of finding parallels and common rules for apparently unrelated phenomena.

It is hoped that the macro-biological perspective that we develop in the present paper may prove of value in complement to the highly detailed descriptions permitted by the techniques of molecular biology and genetic sequencing.

  Fig.1cNatural history of the death rate of measles in the United States. For 1850-1899 the data are for the state of Massachusetts which is the only state to have data going back to 1850. For 1900-1930 the data are for the registration states. After 1930 the data cover the whole country (except Alaska and Hawaii until statehood). In 1989-1991 there was a measles outbreak which particularly affected California, Chicago and New York. Sources: 1850-1899: Statistique internationale du mouvement de la population(1907); 1900[START_REF] Linder | Vital statistics rates in the United States 1900[END_REF][START_REF] Linder | Vital statistics rates in the United States 1900[END_REF][START_REF] Linder | Vital statistics rates in the United States 1900[END_REF] -1960[START_REF] Grove | Vital statistics rates in the United States 1940-1960[END_REF] 1961-1967: Mortality statistics in the UnitedStates 1967 p.1-7;[START_REF] Grove | Vital statistics rates in the United States 1940-1960[END_REF][START_REF] Leeuwen | Animal models of tuberculosis: zebrafish[END_REF] : CDC Wonder databases, compressed mortality 1968-1978,1979-1998,1999-2016. The respective ICD (International Classification of Diseases) codes for measles are asfollows. 1968-1998: ICD8 and ICD9: 055, 1999-2016: ICD10: B05.

  Fig.2a(continued in Fig.1b). Comparison between the conditional probabilities represented by the ratios: (deaths by TB type)/(all TB deaths) (blue line with round dots) and (deaths by cancer type)/(all cancer deaths) (red line with squares),USA 1934USA -1943. The left-hand scale refers to TB whereas the righthand scale refers to cancer. Sources: Bureau of the Census: MortalityStatistics 1934-1936, and Bureau of the Census: Vital Statistics of the United States, Part 1, 1937-1943.

For instance, it is reported by[START_REF] Dales | Measles epidemic from failure to immunize[END_REF] that for measles during the outbreak of 1989-1991 in California and New York City, the case fatality rate was divided by a factor 100 between the age intervals (0,1 year) and (5 y,15 y).

Interestingly, Ehrlich told his sponsors that cancer research meant basic research and that a cure could not be expected soon.

The diameter of a human macrophage is about 20 micrometers which is 10 times more than the length of MT bacteria.

Some of the "holes" of this barrier are described inKim (2010 p.33-34) and[START_REF] Sorge | Defense at the border: the bloodbrain barrier versus bacterial foreigners[END_REF]. For instance, the barrier can be penetrated by using so-called "Trojan horse" mechanisms.

In 2015 in the US the total number of TB deaths was 470 which is 152 times less than in 1934. In 1910 there were even 2.4 times more TB deaths than in 1934. For cancer it is a different situation in the sense that there were 140,771 deaths in 1934 and 612,207 in 2015.

That is to say the fact that there is a degree of arbitrariness in the definition of the scalar and vector potentials.