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Basic reproductive rate, Epidemic threshold and Herd immunity
Modelling the dynamics of a disease gives clues on some of its key characteristics, by assessing such questions as (sic): “Can the infection be stably maintained in the population? Is it endemic or epidemic? What is the time course […] of the infection when introduced into a virgin population?” [180]. Notably, the ‘Basic Reproductive Rate’, or basic reproduction number, usually noted R0, is a prominent concept in infectious diseases modelling [4, 5]. This number represents the average number of subsequent infection caused by a single infected individual introduced in a fully naïve, susceptible population. If R0 < 1, the invasion will fail and the pathogen will disappear from the population, and if R0 > 1, the pathogen will become either endemic or epidemic. For a simple SIR model with no demography, we have R0 = 0 : (6)
Estimating the R0 of a pathogen gives serious clues to answer the three previous questions. Even if the first theoretical basis of a quantitative estimation of herd immunity have been made before the introduction of R0 in the context of infectious diseases [178,181], the basic reproductive rate is closely related to the “Epidemic Threshold”, the maximum frequency of susceptible that mustnot be exceeded in a population in order to ensure the herd immunity of the population and prevent the spread of the disease [6–9]. Staying in the context of a SIR model, this threshold is Pc = 1 1 R0 :.
Detecting Pathogens Interactions
Identifying interactions is one of the main objective of statistical analysis in this field. Some works already focused on statistical ways to identify interactions between pathogens from population-level data. One of them, which has been a major inspiration for this PhD, is the work of Shrestha et al. [63]. Using a two pathogen model including various interaction mechanisms, they produced epidemiological time series. Then, they inferred the nature of the interactions in the system with partially observed Markov processes [66, 196, 197]. This method tries to fit the data with a ‘process’ model and an observation model. The observation model describes the way data are collected from the reality, and the process model describes the epidemiological and demographic processes ruling the system.
This method, which is a confirmatory approach, is effective but relies on knowledge or hypothesis of both biological and demographic processes, and observation bias. In their paper, this distinguishes itself by the use of the very same model to produce the data and as process model in the analysis. Thus their is no doubt that the process model can reproduce the ‘reality’, i.e. the simulated dynamics. The main point of the inference is then to estimate the parameters used in the model to produce the data, these including the interaction parameters. Once the interaction parameters are estimated, one can conclude about the nature of the interaction existing in the data.
Such approach has been used by the same authors [46] to identify the interaction between Influenza and Pneumococcal Pneumonia. They developed a two pathogen SIRS model with three possible interaction mechanisms. Either (1) individuals infected with pneumococcal pneumonia contribute more to pneumococcal transmission if they have been recently infected with influenza, either (2) individuals recently infected with influenza are more susceptible to pneumococcal pneumonia, either (3) individuals infected with pneumococcal pneumonia are more likely to be reported, if recently infected with influenza. Their main result was that that influenza infection increase susceptibility to pneumococcal pneumonia 100-fold.
Implications for Public Health
Acquiring the ability to broadly explore potential interactions, and thus identify unexpected interaction, might be of great help for Public Health. It has been proven that pathogen-pathogen interactions may affect the course of the disease at the population level, and it is possible that such interactions interfere with Public Health policies. Ecology does not lack of example of unexpected results of human intentional or non-intentional intervention on ecosystem. Invasive species and non-target effect of biological pest control are a flagrant example of such deleterious outcomes [200, 201].
Several authors already rose the issue of potential unexpected consequences of Public Health policies. Elimination of a disease may free a niche for another pathogen to replace it [50]. If this hypothesis has been rejected in the early years of the debate [202], it is nowadays gaining currency.
Emergence of a pathogen in the niche of smallpox, declared eradicated in 1979 [203], is one of the most often invoked risk [51–53]. The same issue arises for the recently eradicated rinderpest [54], or close-to-eradication pathogens such as measles [55]. However, most of these questions are not directly related to interactions between pathogens, as they focus on the potential emergence of a new, previously unknown, pathogen to occupy a vacant niche.
This issue is close to the principle of competitive exclusion [204], stating that two species with the exact same niche cannot coexist at the same place and time, and that two species with overlapping niches will compete in a way that the best competitor will out-populate the other. But if this competition is altered by any mean (including human intervention), the excluded competitor may re-invade the system. Yet we saw in section 2 of this introduction that competition, e.g. for susceptible individuals, occurs between pathogens. Thus similarly, the release of this competition due to the decline or eradication of a pathogen achieved by Public Health policies could facilitate the spread of its competitors, i.e., other pathogens.
Moreover, other types of interactions may interfere with Public Health. Several authors stated that infection by helminths Ascaris lumbricoides reduce the risk of suffering a severe cerebral malaria in case of simultaneous infection by Plasmodium falciparum, the main agent of human malaria [56,57]. More generally, simultaneous infection by helminths appears to reduce the severity of cerebral and mild malaria [58] and malaria-related acute renal failure and jaundice [59].
Thus, reducing the incidence of helminths, e.g. with targeted Public Health policies, could increase the burden of malaria. Cross-protection occurs more often in related pathogens. Strong cross-immunity between antigenically similar strains of influenza is responsible for the evolutive dynamics of the virus [205,206] and the difficulty to eradicate the virus with vaccination [207–209]. For other pathogens such as dengue, the interaction pattern between strains is more complex, with short-term, temporary, cross-immunity and long-term higher susceptibility to severe form of the disease in case of reinfection [60–62]. Human intervention within such complex system may have unexpected consequences, and it is essential to invest the potential collusion between pathogen-pathogen interactions and Public Health policies. As experiment with Public Health are unthinkable, the need for theoretical models is here vital.
The objectives of this PhD
The objective of this PhD thesis is, in a first time, to review the evidences of intra- and inter-host interactions between pathogens, and to categorize them. This will be the object of interactions. Being based on a large set of evidences of the four main kind of isolated pathogen-pathogen interactions, it will show how these interactions may occurs simultaneously.
Among other things, it rises the importance of the “realized susceptible pool”, i.e. the real number of individuals that are available for a pathogen, all interactions with other pathogens taken into account.
Chapter 2 will focus on the dynamical impacts of interactions between pathogen, and their detection from epidemiological data, using a two-pathogen model and several promising statistical causality tools. The aim of this chapter will be to develop and test exploratory approaches that could become standard, easy-to-use tools to test for the existence of interactions within any set of pathogens infecting the same population. It will yet bring out the difficulties of creating such framework firstly because of the lack of visible impact on incidence data of numerous interactions and secondly because of the limitation of ‘simple’ exploratory approaches.
Lastly, in chapter 3, a four-pathogen model will be used to study the specific case of dengue, a vector-born disease with four interacting serotype. More precisely, the problematic of the introduction of vaccines currently being developed will be the point of interest. In this chapter we will see that the homogeneity of the efficacy of such vaccine against the various serotype should be the main focus of the future development of the vaccine, as an heterogeneous vaccine could perturb the balance between serotypes and cause strongly deleterious effects before stabilization
of the system.
Table of contents :
Synthèse en Français
1 Introduction
1.1 Modéliser les épidémies
1.2 Interactions entre pathogènes
1.3 Interactions et Santé Publique
1.4 Les objectifs de la thèse
2 Une nouvelle définition de la susceptibilité
2.1 Interactions multiples
2.2 Conséquences pour la Santé Publique
3 Détection des interactions entre pathogènes
3.1 Le modèle
3.2 Causalité de Granger
3.3 Transfert d’Entropie
3.4 Application
3.5 Discussion
4 Interactions et Santé Publique : cas de la vaccination contre la Dengue
4.1 Le modèle
4.2 Discussion
5 Conclusion
5.1 Perspectives
Introduction
1 Modelling Infectious Diseases
1.1 Basic reproductive rate, Epidemic threshold and Herd immunity
1.2 Other developments of Epidemiology
2 Pathogen-pathogen Interactions
3 Detecting Pathogens Interactions
3.1 Correlation and Causality
4 Implications for Public Health
5 The objectives of this PhD
Chapter 1 Interactions between pathogens and the need for a new definition of population susceptibility
1.1 Introduction
1.2 Parasite-parasite Interaction Mechanisms
1.2.1 Cross-immunity
1.2.2 Immune cross-regulation
1.2.3 Immunosupression
1.2.4 Reducing availability of susceptible individuals
1.2.5 Increased availability of susceptible individuals or perturbation of behavioral resistance
1.3 Simultaneous Parasite-parasite Interactions: a Review of (non-existing) Studies .
1.3.1 Immunity suppression and cross-immunity
1.3.2 Immunity suppression and cross-regulation
1.3.3 Immunity suppression and permanent reduction of susceptible abundance
1.3.4 Cross-immunity and temporary decrease of susceptible abundance
1.3.5 Cross-immunity and permanent reduction of susceptible abundance
1.3.6 Cross-regulation and temporary reduction of susceptible abundance
1.4 Simultaneous Pathogen Interactions and Public Health Strategies
1.5 How could we consider the myriad of interactions? Perspectives for a Global Health 19
Chapter 2 Detecting interactions between pathogens
2.1 Introduction
2.2 Methodology
2.2.1 The Model
2.2.2 Granger Causality
2.2.3 Transfer Entropy
2.3 Results
2.3.1 Model Behaviour
2.3.2 Granger Causality
2.3.3 Transfer Entropy
2.4 Discussion
Chapter 3 Vaccine Heterogeneity and Serotype Interactions
3.1 Introduction
3.2 Methods
3.3 Results
3.4 Discussion
Conclusion
1 Results of the PhD
1.1 Review of the Literature
1.2 Identifying Interactions
1.3 Interactions and Public Health Policies
2 Contextualisation of the Findings
3 Perspectives for this PhD
Lessons from this PhD
Bibliography
