Evaluating the importance of within- and between-host selection pressures on the evolution of chronic pathogens

Modeling multiple infection of cells by viruses: Challenges and insights

The multiple infection of cells with several copies of a given virus has been demonstrated in experimental systems, and has been subject to previous mathematical modeling approaches. Such models, especially those based on ordinary differential equations, can be characterized by difficulties and pitfalls. One such difficulty arises from what we refer to as multiple infection cascades. That is, such models subdivide the infected cell population into sub-populations that are carry i viruses, and each sub-population can in principle always be further infected to contain i + 1 viruses. In order to study the model with numerical simulations, the infection cascade needs to be cut artificially, and this can influence the results. This is shown here in the context of the simplest setting that involves a single, homogeneous virus population. If the viral replication rate is sufficiently fast, then most infected cells will accumulate in the last member of the infection cascade, leading to incorrect numerical results. This can be observed even with relatively long infection cascades, and in this case computational costs associated with a sufficiently long infection cascade can render this approach impractical. We subsequently examine a more complex scenario where two virus types/strains with different fitness are allowed to compete. Again, we find that the length of the infection cascade can have a crucial influence on the results. Competitive exclusion can be observed for shorter infection cascades, while coexistence can be observed for longer infection cascades. More subtly, the length of the infection cascade can influence the equilibrium level of the populations in numerical simulations. Studying the model in a parameter regime where an increase in the infection cascade length does not influence the results, we examine the effect of multiple infection on the outcome of competition. We find that multiple infection can promote coexistence of virus types if there is a degree of intracellular niche separation. If this is not the case, the only outcome is competitive exclusion, similar to equivalent models that do not take into account multiple infection of cells. We further find that multiple infection has a reduced ability to allow coexistence if virus spread is spatially restricted compared to a well-mixed system. These results provide important insights when analyzing and interpreting multiple infection models.

Coupled within-host and between-host dynamics and evolution of virulence

Mathematical models coupling within- and between-host dynamics can be helpful for deriving trade-off functions between disease transmission and virulence at the population level. Such functions have been used to study the evolution of virulence and to explore the possibility of a conflict between natural selection at individual and population levels for directly transmitted diseases (Gilchrist and Coombs, 2006). In this paper, a new coupled model for environmentally-driven diseases is analyzed to study similar biological questions. It extends the model in Cen et al. (2014) and Feng et al. (2013) by including the disease-induced host mortality. It is shown that the extended model exhibits similar dynamical behaviors including the possible occurrence of a backward bifurcation. It is also shown that the within-host pathogen load and the disease prevalence at the positive stable equilibrium are increasing functions of the within- and between-host reproduction numbers (Rw0 and Rb0), respectively. Optimal parasite strategies will maximize these reproduction numbers at the two levels, and a conflict may exist between the two levels. Our results highlight the role of inter-dependence of variables and parameters in the fast and slow systems for persistence of infections and evolution of pathogens in an environmentally-driven disease. Our results also demonstrate the importance of incorporating explicit links of the within- and between-host dynamics into the computation of threshold conditions for disease control.

Global stability of an infection-age structured HIV-1 model linking within-host and between-host dynamics

Although much evidence shows the inseparable interaction between the within-host progression of HIV-1 infection and the transmission of the disease at the population level, few models coupling the within-host and between-host dynamics have been developed. In this paper, we adopt the nested approach, viewing the transmission rate at each stage (primary, chronic, and AIDS stage) of HIV-1 infection as a saturated function of the viral load, to formulate an infection-age structured epidemic model. We explicitly link the individual and the host population scale, and derive the basic reproduction number R0 for the coupled system. To analyze the model and perform a detailed global dynamics analysis, two Lyapunov functionals are constructed to prove the global asymptotical stability of the disease-free and endemic equilibria. Theoretical results indicate that R0 provides a threshold value determining whether or not the disease dies out. Numerical simulations are presented to quantitatively investigate the influence of the within-host viral dynamics on between-host transmission dynamics. The results suggest that increasing the effectiveness of inhibitors can decrease the basic reproduction number, but can also increase the overall infected population because of a lower disease-induced mortality rate and a longer lifespan of HIV infected individuals.

A mathematical modelling framework for linked within-host and between-host dynamics for infections with free-living pathogens in the environment

In this study we develop a mathematical modelling framework for linking the within-host and between-host dynamics of infections with free-living pathogens in the environment. The resulting linked models are sometimes called immuno-epidemiological models. However, there is still no generalised framework for linking the within-host and between-host dynamics of infectious diseases. Furthermore, for infections with free-living pathogens in the environment, there is an additional stumbling block in that there is a gap in knowledge on how environmental factors (through water, air, soil, food, fomites, etc.) alter many aspects of such infections including susceptibility to infective dose, persistence of infection, pathogen shedding and severity of the disease. In this work, we link the two subsystems (within-host and between-host models) by identifying the within-host and between-host variables and parameters associated with the environmental dynamics of the pathogen and then design a feedback of the variables and parameters across the within-host and between-host models using human schistosomiasis as a case study. We study the mathematical properties of the linked model and show that the model is epidemiologically well-posed. Using results from the analysis of the endemic equilibrium expression, the disease reproductive number R0, and numerical simulations of the full model, we adequately account for the reciprocal influence of the linked within-host and between-host models. In particular, we illustrate that for human schistosomiasis, the outcome of infection at the individual level determines if, when and how much the individual host will further transmit the infectious agent into the environment, eventually affecting the spread of the infection in the host population. We expect the conceptual modelling framework developed here to be applicable to many infectious disease with free-living pathogens in the environment beyond the specific disease system of human schistosomiasis considered here.

Identifying selection in the within-host evolution of influenza using viral sequence data

The within-host evolution of influenza is a vital component of its epidemiology. A question of particular interest is the role that selection plays in shaping the viral population over the course of a single infection. We here describe a method to measure selection acting upon the influenza virus within an individual host, based upon time-resolved genome sequence data from an infection. Analysing sequence data from a transmission study conducted in pigs, describing part of the haemagglutinin gene (HA1) of an influenza virus, we find signatures of non-neutrality in six of a total of sixteen infections. We find evidence for both positive and negative selection acting upon specific alleles, while in three cases, the data suggest the presence of time-dependent selection. In one infection we observe what is potentially a specific immune response against the virus; a non-synonymous mutation in an epitope region of the virus is found to be under initially positive, then strongly negative selection. Crucially, given the lack of homologous recombination in influenza, our method accounts for linkage disequilibrium between nucleotides at different positions in the haemagglutinin gene, allowing for the analysis of populations in which multiple mutations are present at any given time. Our approach offers a new insight into the dynamics of influenza infection, providing a detailed characterisation of the forces that underlie viral evolution.

The evolution of the influenza virus is of great importance for human health. Through evolution, current influenza viruses develop the ability to infect people who have been vaccinated against earlier strains. New strains of influenza that infect birds and pigs could evolve to infect and spread between people, causing a global pandemic. The influenza virus lives within a human or animal host, so that viral evolution happens within, or in the spread between, individuals. As such, what happens to the virus during the course of an infection is a question of great interest. We here describe a statistical method that uses viral genome sequence data to measure how evolution affects the influenza virus within a single host. Studying data from infections transmitted between pigs, we find evidence for evolutionary adaptation in six of sixteen animals for which data were available. In one case, an immune response mounted by a pig against the virus is apparent. Our method provides a statistical framework for using sequence data to study viral evolution on very short timescales, enabling new research into within-host viral evolution.

Co-infection and super-infection models in evolutionary epidemiology

Multiple infections are intensively studied because of their consequences for the health of the host but also because they can radically alter the selective pressures acting on parasites. I discuss how multiple infections have been modelled in evolutionary epidemiology. First, I briefly mention within-host models, which are at the root of these epidemiological models. Then, I present the super-infection framework, with an original focus on how the definition of the super-infection function can lead to evolutionary branching. There are several co-infection models and, for each of them, I briefly go through the underlying mathematics (especially the invasion fitness of a mutant strain) and I discuss the biological assumptions they make and the questions they consequently may ask. In particular, I show that a widely used co-infection model should not be invoked for invasion analyses because it confers a frequency-dependent advantage to rare neutral mutants. Finally, I present more recent frameworks, such as the Price equation framework in epidemiology, that can account for increased parasite diversity. To conclude, I discuss some perspectives for the study of multiple infections in evolutionary epidemiology.

Evolution of acuteness in pathogen metapopulations: conflicts between "classical" and invasion-persistence trade-offs

Classical life-history theory predicts that acute, immunizing pathogens should maximize between-host transmission. When such pathogens induce violent epidemic outbreaks, however, a pathogen's short-term advantage at invasion may come at the expense of its ability to persist in the population over the long term. Here, we seek to understand how the classical and invasion-persistence trade-offs interact to shape pathogen life-history evolution as a function of the size and structure of the host population. We develop an individual-based infection model at three distinct levels of organization: within an individual host, among hosts within a local population, and among local populations within a metapopulation. We find a continuum of evolutionarily stable pathogen strategies. At one end of the spectrum-in large well-mixed populations-pathogens evolve to greater acuteness to maximize between-host transmission: the classical trade-off theory applies in this regime. At the other end of the spectrum-when the host population is broken into many small patches-selection favors less acute pathogens, which persist longer within a patch and thereby achieve enhanced between-patch transmission: the invasion-persistence tradeoff dominates in this regime. Between these extremes, we explore the effects of the size and structure of the host population in determining pathogen strategy. In general, pathogen strategies respond to evolutionary pressures arising at both scales.

The arrested immunity hypothesis in an immunoepidemiological model of Chlamydia transmission

For curable infectious diseases, public health strategies such as treatment can effectively shorten an individual's infectious period, and thus limit their role in transmission. However, because treatment effectively eliminates antigen impingement, these types of control strategies may also paradoxically impair the development of adaptive immune responses. For sexually transmitted Chlamydia trachomatis infections, this latter effect has been coined the arrested immunity hypothesis, and is discussed to carry significant epidemiological implications for those individuals who return to similar sexual networks with similar sexual behavior. Here, we examine the effect of antibiotic treatment on the spread of Chlamydia infection through a simple immunoepidemiological framework that characterizes the population as a collection of dynamically evolving individuals in small, paradigmatic networks. Within each individual there is an explicit representation of pathogen replication, accumulation and persistence of an immune response, followed by a gradual waning of that response once the infection is cleared. Individuals are then nested in networks, allowing the variability in the life history of their infection to be functions of both individual immune dynamics as well as their position in the network. Model results suggest that the timing and coverage of treatment are important contributors to the development of immunity and reinfection. In particular, the impact of treatment on the spread of infection between individuals can be beneficial, have no effect, or be deleterious depending on who is treated and when. Although we use sexually transmitted Chlamydia infection as an example, the observed results arise endogenously from a basic model structure, and thus warrant consideration to understanding the interaction of infection, treatment, and spread of other infectious diseases.

Is HIV short-sighted? Insights from a multistrain nested model

An important component of pathogen evolution at the population level is evolution within hosts. Unless evolution within hosts is very slow compared to the duration of infection, the composition of pathogen genotypes within a host is likely to change during the course of an infection, thus altering the composition of genotypes available for transmission as infection progresses. We develop a nested modeling approach that allows us to follow the evolution of pathogens at the epidemiological level by explicitly considering within-host evolutionary dynamics of multiple competing strains and the timing of transmission. We use the framework to investigate the impact of short-sighted within-host evolution on the evolution of virulence of human immunodeficiency virus (HIV), and find that the topology of the within-host adaptive landscape determines how virulence evolves at the epidemiological level. If viral reproduction rates increase significantly during the course of infection, the viral population will evolve a high level of virulence even though this will reduce the transmission potential of the virus. However, if reproduction rates increase more modestly, as data suggest, our model predicts that HIV virulence will be only marginally higher than the level that maximizes the transmission potential of the virus.

Viral substitution rate variation can arise from the interplay between within-host and epidemiological dynamics

The evolutionary rates of RNA viruses can differ from one another by several orders of magnitude. Much of this variation has been explained by differences in viral mutation rates and selective environments. However, substitution rates also vary considerably across viral populations belonging to the same species. In particular, viral lineages from epidemic regions tend to have higher substitution rates than those from endemic regions, and lineages from populations with higher contact rates tend to have higher substitution rates than those from populations with lower contact rates. We address the mechanism behind these patterns by using a nested modeling approach, whereby we integrate within-host viral replication dynamics with a population-level epidemiological model. Through numerical simulations and analytical approximations, we show that variation in viral substitution rates over the course of an infection, coupled with differences in age of infection of transmitting hosts under different epidemiological scenarios, can explain these evolutionary patterns. We further derive analytical estimates of expected substitution rate differences under epidemic versus endemic epidemiological conditions. By comparing these estimates to empirical data for four viral species, we show that these factors are sufficient to explain observed variation in substitution rates in three of four cases. This work shows that even in neutrally evolving viral populations, epidemiological dynamics can alter substitution rates via the interplay between within-host replication dynamics and population-level disease dynamics.

Towards multiscale modeling of influenza infection

Aided by recent advances in computational power, algorithms, and higher fidelity data, increasingly detailed theoretical models of infection with influenza A virus are being developed. We review single scale models as they describe influenza infection from intracellular to global scales, and, in particular, we consider those models that capture details specific to influenza and can be used to link different scales. We discuss the few multiscale models of influenza infection that have been developed in this emerging field. In addition to discussing modeling approaches, we also survey biological data on influenza infection and transmission that is relevant for constructing influenza infection models. We envision that, in the future, multiscale models that capitalize on technical advances in experimental biology and high performance computing could be used to describe the large spatial scale epidemiology of influenza infection, evolution of the virus, and transmission between hosts more accurately.

A multi-scale analysis of influenza A virus fitness trade-offs due to temperature-dependent virus persistence

Successful replication within an infected host and successful transmission between hosts are key to the continued spread of most pathogens. Competing selection pressures exerted at these different scales can lead to evolutionary trade-offs between the determinants of fitness within and between hosts. Here, we examine such a trade-off in the context of influenza A viruses and the differential pressures exerted by temperature-dependent virus persistence. For a panel of avian influenza A virus strains, we find evidence for a trade-off between the persistence at high versus low temperatures. Combining a within-host model of influenza infection dynamics with a between-host transmission model, we study how such a trade-off affects virus fitness on the host population level. We show that conclusions regarding overall fitness are affected by the type of link assumed between the within- and between-host levels and the main route of transmission (direct or environmental). The relative importance of virulence and immune response mediated virus clearance are also found to influence the fitness impacts of virus persistence at low versus high temperatures. Based on our results, we predict that if transmission occurs mainly directly and scales linearly with virus load, and virulence or immune responses are negligible, the evolutionary pressure for influenza viruses to evolve toward good persistence at high within-host temperatures dominates. For all other scenarios, influenza viruses with good environmental persistence at low temperatures seem to be favored.

It has recently been suggested that for avian influenza viruses, prolonged persistence in the environment plays an important role in the transmission between birds. In such situations, influenza virus strains may face a trade-off: they need to persist well in the environment at low temperatures, but they also need to do well inside an infected bird at higher temperatures. Here, we analyze how potential trade-offs on these two scales interact to determine overall fitness of the virus. We find that the link between infection dynamics within a host and virus shedding and transmission is crucial in determining the relative advantage of good low-temperature versus high-temperature persistence. We also find that the role of virus-induced mortality, the immune response and the route of transmission affect the balance between optimal low-temperature and high-temperature persistence.

Multiple scales of selection influence the evolutionary emergence of novel pathogens

When pathogens encounter a novel environment, such as a new host species or treatment with an antimicrobial drug, their fitness may be reduced so that adaptation is necessary to avoid extinction. Evolutionary emergence is the process by which new pathogen strains arise in response to such selective pressures. Theoretical studies over the last decade have clarified some determinants of emergence risk, but have neglected the influence of fitness on evolutionary rates and have not accounted for the multiple scales at which pathogens must compete successfully. We present a cross-scale theory for evolutionary emergence, which embeds a mechanistic model of within-host selection into a stochastic model for emergence at the population scale. We explore how fitness landscapes at within-host and between-host scales can interact to influence the probability that a pathogen lineage will emerge successfully. Results show that positive correlations between fitnesses across scales can greatly facilitate emergence, while cross-scale conflicts in selection can lead to evolutionary dead ends. The local genotype space of the initial strain of a pathogen can have disproportionate influence on emergence probability. Our cross-scale model represents a step towards integrating laboratory experiments with field surveillance data to create a rational framework to assess emergence risk.

Multiple infections and the evolution of virulence

Infections that consist of multiple parasite strains or species are common in the wild and are a major public health concern. Theory suggests that these infections have a key influence on the evolution of infectious diseases and, more specifically, on virulence evolution. However, we still lack an overall vision of the empirical support for these predictions. We argue that within-host interactions between parasites largely determine how virulence evolves and that experimental data support model predictions. Then, we explore the main limitation of the experimental study of such 'mixed infections', which is that it draws conclusions on evolutionary outcomes from studies conducted at the individual level. We also discuss differences between coinfections caused by different strains of the same species or by different species. Overall, we argue that it is possible to make sense out of the complexity inherent to multiple infections and that experimental evolution settings may provide the best opportunity to further our understanding of virulence evolution.

Immunity and the emergence of virulent pathogens

The emergence/re-emergence of infectious diseases has been one of the major concerns for human and wildlife health. In spite of the medical and veterinary progresses as to prevent and cure infectious diseases, during the last decades we have witnessed the emergence/re-emergence of virulent pathogens that pose a threat to humans and wildlife. Many factors that might drive the emergence of these novel pathogens have been identified and several reviews have been published on this topic in the last years. Among the most cited and recognized drivers of pathogen emergence are climate change, habitat destruction, increased contact with reservoirs, etc. These factors mostly refer to environmental determinants of emergence. However, the immune system of the host is probably the most important environmental trait parasites have to cope with. Here, we wish to discuss how immune-mediated selection might affect the emergence/re-emergence of infectious diseases and drive the evolution of disease severity. Vaccination, natural (age-associated) and acquired immunodeficiencies, organ transplantation, environmental contamination with chemicals that disrupt immune functions form populations of hosts that might exert specific immune-mediated selection on a range of pathogens, shaping their virulence and evolution, and favoring their spread to other populations of hosts.

Linking immunological and epidemiological dynamics of HIV: the case of super-infection

In this paper, a two-strain model that links immunological and epidemiological dynamics across scales is formulated. On the within-host scale, the two strains eliminate each other with the strain with the larger immunological reproduction persisting. However, on the population scale superinfection is possible, with the strain with larger immunological reproduction number super-infecting the strain with the smaller immunological reproduction number. The two models are linked through the age-since-infection structure of the epidemiological variables. In addition, the between-host transmission and the disease-induced death rate depend on the within-host viral load. The immunological reproduction numbers, the epidemiological reproduction numbers and invasion reproduction numbers are computed. Besides the disease-free equilibrium, there are two population-level strain one and strain two isolated equilibria, as well as a population-level coexistence equilibrium when both invasion reproduction numbers are greater than one. The single-strain population-level equilibria are locally asymptotically stable suggesting that in the absence of superinfection oscillations do not occur, a result contrasting previous studies of HIV age-since-infection structured models. Simulations suggest that the epidemiological reproduction number and HIV population prevalence are monotone functions of the within-host parameters with reciprocal trends. In particular, HIV medications that decrease within-host viral load also increase overall population prevalence. The effect of the immunological parameters on the population reproduction number and prevalence is more pronounced when the initial viral load is lower.

A modeller's perspective on infection dynamics within and between hosts

The goal of this case-series was to increase our understanding of some complex within and between-host infection dynamics through the creation of mathematical and computational models that are able to capture the existing host and/or parasite heterogeneity. This goal was reached through a series of research projects (regarding experimental autoimmune encephalomyelitis (EAE) in mice, Mycobacterium avium subspecies paratuberculosis infection in cattle, Eimeria acervulina infection in chicken and human malaria) that gradually build up in complexity of both the system modelled and the modelling techniques used. In this case-series, the vast majority of model components have a direct link with reality. The results have shown some detailed examples of the valuable contribution that models have in understanding infection processes. The most satisfying achievements have come from those models that were able to, in hindsight, make complicated experimental results seem obvious and logical, and where the process of building the model was as insightful as the final results. The models created in these projects help to explain a wide range of sometimes contradictory experimental results and are used to predict the effect of control measures. In addition, they generate ideas for the development of new methods of control.

A mathematical model for coupling within-host and between-host dynamics in an environmentally-driven infectious disease

This work presents a new model for the linking of within- and between-host dynamics. We use this as a conceptual model for the dynamics of Toxoplasma gondii, in which the parasite's life cycle includes interactions with the environment. We postulate the infection process to depend on the size of the infective inoculum that susceptible hosts may acquire by interacting with a contaminated environment. Because the dynamical processes associated with the within- and between-host occur on different time scales, the model behaviors can be analyzed by using a singular perturbation argument, which allows us to decouple the full model by separating the fast- and slow-systems. We define new reproductive numbers for the within-host and between host dynamics for both the isolated systems and the coupled system. Particularly, the reproduction number for the between-host (slow) system dependent on the parameters associated with the within-host (fast) system in a very natural way. We show that these reproduction numbers determine the stability of the infection-free and the endemic equilibrium points. Our model may present a so-called backward bifurcation.

Evolution of viral life-cycle in response to cytotoxic T lymphocyte-mediated immunity

Viruses in mammals are constantly faced with the problem of elimination by the host immunity. Cytotoxic T lymphocyte (CTL) responses are thought to play a major role in the control and clearance of several viral infections in mice and humans. It is therefore expected that over evolutionary time, viruses would be forced to evolve to avoid recognition by CTLs. Indeed, a number of studies have documented the accumulation of viral variants with escape mutations. These mutations allow viruses to hide from CTL responses common in the host population. CTLs recognize viruses by short protein sequences, named epitopes, derived from viral proteins. The efficiency of viral recognition by epitope-specific CTL responses depends on the expression pattern of the proteins carrying these epitopes, and the total amount of that protein (and thus epitopes) in the cell. When a virus replicates in a cell, some viral genes are expressed early in the life cycle of the virus, while other proteins are expressed late. For example, HIV infected cells first express Rev and Tat proteins, and the Gag proteins are expressed late. Here we propose a dynamical model of the viral life cycle to study how expression level of early vs. late genes may affect viral dynamics within the host and virus transmission over the course of infection. We find that for acute and chronic viral infections lower expression of early genes than that of the late genes is expected to give selective advantage and higher transmission to viruses.

Bridging scales in the evolution of infectious disease life histories: application

Within- and between-host disease processes occur on the same timescales, therefore changes in the within-host dynamics of parasites, resources, and immunity can interact with changes in the epidemiological dynamics to affect evolutionary outcomes. Consequently, studies of the evolution of disease life histories, that is, infection-age-specific patterns of transmission and virulence, have been constrained by the need for a mechanistic understanding of within-host disease dynamics. In a companion paper (Day et al. 2011), we develop a novel approach that quantifies the relevant within-host aspects of disease through genetic covariance functions. Here, we demonstrate how to apply this theory to data. Using two previously published datasets from rodent malaria infections, we show how to translate experimental measures into disease life-history traits, and how to quantify the covariance in these traits. Our results show how patterns of covariance can interact with epidemiological dynamics to affect evolutionary predictions for disease life history. We also find that the selective constraints on disease life-history evolution can vary qualitatively, and that "simple" virulence-transmission trade-offs that are often the subject of experimental investigation can be obscured by trade-offs within one trait alone. Finally, we highlight the type and quality of data required for future applications.

Within-host parasite cooperation and the evolution of virulence

Infections by multiple genotypes are common in nature and are known to select for higher levels of virulence for some parasites. When parasites produce public goods (PGs) within the host, such co-infections have been predicted to select for lower levels of virulence. However, this prediction is based on simplifying assumptions regarding epidemiological feedbacks on the multiplicity of infections (MOI). Here, we analyse the case of parasites producing a PG (for example, siderophore-producing bacteria) using a nested model that ties together within-host and epidemiological processes. We find that the prediction that co-infection should select for less virulent strains for PG-producing parasites is only valid if both parasite transmission and virulence are linear functions of parasite density. If there is a trade-off relationship such that virulence increases more rapidly than transmission, or if virulence also depends on the total amount of PGs produced, then more complex relationships between virulence and the MOI are predicted. Our results reveal that explicitly taking into account the distribution of parasite strains among hosts could help better understand the selective pressures faced by parasites at the population level.

A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead

Most mathematical models used to study the dynamics of influenza A have thus far focused on the between-host population level, with the aim to inform public health decisions regarding issues such as drug and social distancing intervention strategies, antiviral stockpiling or vaccine distribution. Here, we investigate mathematical modeling of influenza infection spread at a different scale; namely that occurring within an individual host or a cell culture. We review the models that have been developed in the last decades and discuss their contributions to our understanding of the dynamics of influenza infections. We review kinetic parameters (e.g., viral clearance rate, lifespan of infected cells) and values obtained through fitting mathematical models, and contrast them with values obtained directly from experiments. We explore the symbiotic role of mathematical models and experimental assays in improving our quantitative understanding of influenza infection dynamics. We also discuss the challenges in developing better, more comprehensive models for the course of influenza infections within a host or cell culture. Finally, we explain the contributions of such modeling efforts to important public health issues, and suggest future modeling studies that can help to address additional questions relevant to public health.

Two optimal mutation rates in obligate pathogens subject to deleterious mutation

Pathogen species with high mutation rates are likely to accumulate deleterious mutations that reduce their reproductive potential within the host. By altering the within-host growth rate of the pathogen, the deleterious mutation load has the potential to affect epidemiological properties such as prevalence, mean pathogen load, and the mean duration of infections. Here, I examine an epidemiological model that allows for multiple segregating mutations that affect within-host replication efficiency. The model demonstrates a complex range of outcomes depending on pathogen mutation rate, including two distinct, widely separated mutation rates associated with high pathogen prevalence. The low mutation rate prevalence peak is associated with small amounts of genetic diversity within the pathogen population, relatively stable prevalence and infection dynamics, and genetic variation partitioned between hosts. The high mutation rate peak is characterized by considerable genetic diversity both within and between hosts, relatively frequent invasions by more virulent types, and is qualitatively similar to an RNA virus quasispecies. The two prevalence peaks are separated by a valley where natural selection favors evolution toward the optimal within-host state, which is associated with high virulence and relatively rapid host mortality. Both chronic and acute infections are examined using stochastic forward simulations.

Epidemiological and clinical consequences of within-host evolution

Many viruses and bacteria are known to evolve rapidly over the course of an infection. However, epidemiological studies generally assume that within-host evolution is an instantaneous process. We argue that the dynamics of within-host evolution has implications at the within-host and at the between-host levels. We first show that epidemiologists should consider within-host evolution, notably because it affects the genotype of the pathogen that is transmitted. We then present studies that investigate evolution at the within-host level and examine the extent to which these studies can help to understand infection traits involved in the epidemiology (e.g. transmission rate, virulence, recovery rate). Finally, we discuss how new techniques for data acquisition can open new perspectives for empirical and theoretical research.

Identifying genetic markers of adaptation for surveillance of viral host jumps

Adaptation is often thought to affect the likelihood that a virus will be able to successfully emerge in a new host species. If so, surveillance for genetic markers of adaptation could help to predict the risk of disease emergence. However, adaptation is difficult to distinguish conclusively from the other processes that generate genetic change. In this Review we survey the research on the host jumps of influenza A, severe acute respiratory syndrome-coronavirus, canine parvovirus and Venezuelan equine encephalitis virus to illustrate the insights that can arise from combining genetic surveillance with microbiological experimentation in the context of epidemiological data. We argue that using a multidisciplinary approach for surveillance will provide a better understanding of when adaptations are required for host jumps and thus when predictive genetic markers may be present.

Trade-offs in resource allocation in the intracellular life-cycle of hepatitis C virus

Positive sense single-stranded RNA viruses undergo three mutually exclusive processes to replicate within a cell. These are translation to produce proteins, replication to produce RNA viral genomes, and packaging to form virions. The allocation of newly synthesised viral genomes to these processes, which can be regarded as life-history traits, may be subject to natural selection for efficient reproduction. Here, we develop a mathematical model of the process of intracellular viral replication to study alternative strategies for the allocation and reallocation of viral genomes to these processes. We explore four cases of the model: (1) Free Movement, in which viral genomes can freely be allocated and reallocated among translation, replication and packaging; (2) Unidirectional Reallocation, in which allocation occurs freely but reallocation can only proceed from translation to replication to packaging; (3) Conveyor Belt, in which viral genomes are first allocated to translation, then passed on to replication and finally to packaging; and (4) Permanent Allocation in which new genomes are allocated to the three processes but not reallocated between them. We apply this model to hepatitis C virus and study changes in the production of virus as the rates of allocation and reallocation are varied. We find that high viral production occurs when allocation and reallocation of the genome are weighted towards the translation and replication processes. The replication process in particular is favoured. The most productive strategy is a form of the Free Movement model in which genomes are allocated entirely to the replication-translation cycle while allowing some genomes to be packaged through reallocation.

Intensive Farming: Evolutionary Implications for Parasites and Pathogens

An increasing number of scientists have recently raised concerns about the threat posed by human intervention on the evolution of parasites and disease agents. New parasites (including pathogens) keep emerging and parasites which previously were considered to be ‘under control’ are re-emerging, sometimes in highly virulent forms. This re-emergence may be parasite evolution, driven by human activity, including ecological changes related to modern agricultural practices. Intensive farming creates conditions for parasite growth and transmission drastically different from what parasites experience in wild host populations and may therefore alter selection on various traits, such as life-history traits and virulence. Although recent epidemic outbreaks highlight the risks associated with intensive farming practices, most work has focused on reducing the short-term economic losses imposed by parasites, such as application of chemotherapy. Most of the research on parasite evolution has been conducted using laboratory model systems, often unrelated to economically important systems. Here, we review the possible evolutionary consequences of intensive farming by relating current knowledge of the evolution of parasite life-history and virulence with specific conditions experienced by parasites on farms. We show that intensive farming practices are likely to select for fast-growing, early-transmitted, and hence probably more virulent parasites. As an illustration, we consider the case of the fish farming industry, a branch of intensive farming which has dramatically expanded recently and present evidence that supports the idea that intensive farming conditions increase parasite virulence. We suggest that more studies should focus on the impact of intensive farming on parasite evolution in order to build currently lacking, but necessary bridges between academia and decision-makers.

Phenotypic differences in viral immune escape explained by linking within-host dynamics to host-population immunity

Viruses that do not cause life-long immunity persist by evolving rapidly in response to prevailing host immunity. The immune-escape mutants emerge frequently, displacing or co-circulating with native strains even though mutations conferring immune evasion are often detrimental to viral replication. The epidemiological dynamics of immune-escape in acute-infection viruses with high transmissibility have been interpreted mainly through immunity dynamics at the host population level, despite the fact that immune-escape evolution involves dynamical processes that feedback across the within- and between-host scales. To address this gap, we use a nested model of within- and between-host infection dynamics to examine how the interaction of viral replication rate and cross-immunity imprint host population immunity, which in turn determines viral immune escape. Our explicit consideration of direct and immune-mediated competitive interactions between strains within-hosts revealed three insights pertaining to risk and control of viral immune-escape: (1) replication rate and immune-stimulation deficiencies (i.e., original antigenic sin) act synergistically to increase immune escape, (2) immune-escape mutants with replication deficiencies relative to their wildtype progenitor are most successful under moderate cross-immunity and frequent re-infections, and (3) the immunity profile along short host-transmission chains (local host-network structure) is a key determinant of immune escape.

Risk factors for the evolutionary emergence of pathogens

Recent outbreaks of novel infectious diseases (e.g. SARS, influenza H1N1) have highlighted the threat of cross-species pathogen transmission. When first introduced to a population, a pathogen is often poorly adapted to its new host and must evolve in order to escape extinction. Theoretical arguments and empirical studies have suggested various factors to explain why some pathogens emerge and others do not, including host contact structure, pathogen adaptive pathways and mutation rates. Using a multi-type branching process, we model the spread of an introduced pathogen evolving through several strains. Extending previous models, we use a network-based approach to separate host contact patterns from pathogen transmissibility. We also allow for arbitrary adaptive pathways. These generalizations lead to novel predictions regarding the impact of hypothesized risk factors. Pathogen fitness depends on the host population in which it circulates, and the ‘riskiest’ contact distribution and adaptive pathway depend on initial transmissibility. Emergence probability is sensitive to mutation probabilities and number of adaptive steps required, with the possibility of large adaptive steps (e.g. simultaneous point mutations or recombination) having a dramatic effect. In most situations, increasing overall mutation probability increases the risk of emergence; however, notable exceptions arise when deleterious mutations are available.

Risk-based probabilistic approach to assess the impact of false mussel invasions on farmed hard clams

The purpose of this article is to provide a risk-based predictive model to assess the impact of false mussel Mytilopsis sallei invasions on hard clam Meretrix lusoria farms in the southwestern region of Taiwan. The actual spread of invasive false mussel was predicted by using analytical models based on advection-diffusion and gravity models. The proportion of hard clam colonized and infestation by false mussel were used to characterize risk estimates. A mortality model was parameterized to assess hard clam mortality risk characterized by false mussel density and infestation intensity. The published data were reanalyzed to parameterize a predictive threshold model described by a cumulative Weibull distribution function that can be used to estimate the exceeding thresholds of proportion of hard clam colonized and infestation. Results indicated that the infestation thresholds were 2-17 ind clam(-1) for adult hard clams, whereas 4 ind clam(-1) for nursery hard clams. The average colonization thresholds were estimated to be 81-89% for cultivated and nursery hard clam farms, respectively. Our results indicated that false mussel density and infestation, which caused 50% hard clam mortality, were estimated to be 2,812 ind m(-2) and 31 ind clam(-1), respectively. This study further indicated that hard clam farms that are close to the coastal area have at least 50% probability for 43% mortality caused by infestation. This study highlighted that a probabilistic risk-based framework characterized by probability distributions and risk curves is an effective representation of scientific assessments for farmed hard clam in response to the nonnative false mussel invasion.

Modeling the dynamics of viral evolution considering competition within individual hosts and at population level: the effects of treatment

We consider two viral strains competing against each other within individual hosts (at cellular level) and at population level (for infecting hosts) by studying two cases. In the first case, the strains do not mutate into each other. In this case, we found that each individual in the population can be infected by only one strain and that co-existence in the population is possible only when the strain that has the greater basic intracellular reproduction number, R (0c ), has the smaller population number R (0p ). Treatment against the one strain shifts the population equilibrium toward the other strain in a complicated way (see Appendix B). In the second case, we assume that the strain that has the greater intracellular number R (0c ) can mutate into the other strain. In this case, individual hosts can be simultaneously infected by both strains (co-existence within the host). Treatment shifts the prevalence of the two strains within the hosts, depending on the mortality induced by the treatment, which is, in turn, dependent upon the doses given to each individual. The relative proportions of the strains at the population level, under treatment, depend both on the relative proportions within the hosts (which is determined by the dosage of treatment) and on the number of individuals treated per unit time, that is, the rate of treatment. Implications for cases of real diseases are briefly discussed.

The evolutionary dynamics of a rapidly mutating virus within and between hosts: the case of hepatitis C virus

Many pathogens associated with chronic infections evolve so rapidly that strains found late in an infection have little in common with the initial strain. This raises questions at different levels of analysis because rapid within-host evolution affects the course of an infection, but it can also affect the possibility for natural selection to act at the between-host level. We present a nested approach that incorporates within-host evolutionary dynamics of a rapidly mutating virus (hepatitis C virus) targeted by a cellular cross-reactive immune response, into an epidemiological perspective. The viral trait we follow is the replication rate of the strain initiating the infection. We find that, even for rapidly evolving viruses, the replication rate of the initial strain has a strong effect on the fitness of an infection. Moreover, infections caused by slowly replicating viruses have the highest infection fitness (i.e., lead to more secondary infections), but strains with higher replication rates tend to dominate within a host in the long-term. We also study the effect of cross-reactive immunity and viral mutation rate on infection life history traits. For instance, because of the stochastic nature of our approach, we can identify factors affecting the outcome of the infection (acute or chronic infections). Finally, we show that anti-viral treatments modify the value of the optimal initial replication rate and that the timing of the treatment administration can have public health consequences due to within-host evolution. Our results support the idea that natural selection can act on the replication rate of rapidly evolving viruses at the between-host level. It also provides a mechanistic description of within-host constraints, such as cross-reactive immunity, and shows how these constraints affect the infection fitness. This model raises questions that can be tested experimentally and underlines the necessity to consider the evolution of quantitative traits to understand the outcome and the fitness of an infection.

Rapidly mutating viruses, such as hepatitis C virus, can escape host immunity by generating new strains that avoid the immune system. Existing data support the idea that such within-host evolution affects the outcome of the infection. Few theoretical models address this question and most follow viral diversity or qualitative traits, such as drug resistance. Here, we study the evolution of two virus quantitative traits—the replication rate and the ability to be recognised by the immune response—during an infection. We develop an epidemiological framework where transmission events are driven by within-host dynamics. We find that the replication rate of the virus that initially infects the host has a strong influence on the epidemiological success of the disease. Furthermore, we show that the cross-reactive immune response is key to determining the outcome of the infection (acute or chronic). Finally, we show that the timing of the start of an anti-viral treatment has a strong effect on viral evolution, which impacts the efficiency of the treatment. Our analysis suggests a new mechanism to explain infection outcomes and proposes testable predictions that can drive future experimental approaches.

RT-SHIV subpopulation dynamics in infected macaques during anti-HIV therapy

BACKGROUND

To study the dynamics of wild-type and drug-resistant HIV-1 RT variants, we developed a methodology that follows the fates of individual genomes over time within the viral quasispecies. Single genome sequences were obtained from 3 pigtail macaques infected with a recombinant simian immunodeficiency virus containing the RT coding region from HIV-1 (RT-SHIV) and treated with short-course efavirenz monotherapy 13 weeks post-infection followed by daily combination antiretroviral therapy (ART) beginning at week 17. Bioinformatics tools were constructed to trace individual genomes from the beginning of infection to the end of the treatment.

RESULTS

A well characterized challenge RT-SHIV inoculum was used to infect three monkeys. The RT-SHIV inoculum had 9 variant subpopulations and the dominant subpopulation accounted for 80% of the total genomes. In two of the three monkeys, the inoculated wild-type virus was rapidly replaced by new wild type variants. By week 13, the original dominant subpopulation in the inoculum was replaced by new dominant subpopulations, followed by emergence of variants carrying known NNRTI resistance mutations. However, during ART, virus subpopulations containing resistance mutations did not outgrow the wide-type subpopulations until a minor subpopulation carrying linked drug resistance mutations (K103N/M184I) emerged. We observed that persistent viremia during ART is primarily made up of wild type subpopulations. We also found that subpopulations carrying the V75L mutation, not known to be associated with NNRTI resistance, emerged initially in week 13 in two macaques. Eventually, all subpopulations from these two macaques carried the V75L mutation.

CONCLUSION

This study quantitatively describes virus evolution and population dynamics patterns in an animal model. The fact that wild type subpopulations remained as dominant subpopulations during ART treatment suggests that the presence or absence of at least some known drug resistant mutations may not greatly affect virus replication capacity in vivo. Additionally, the emergence and prevalence of V75L indicates that this mutation may provide the virus a selective advantage, perhaps escaping the host immure system surveillance. Our new method to quantitatively analyze viral population dynamics enabled us to observe the relative competitiveness and adaption of different viral variants and provided a valuable tool for studying HIV subpopulation emergence, persistence, and decline during ART.

Antigenic diversity, transmission mechanisms, and the evolution of pathogens

Pathogens have evolved diverse strategies to maximize their transmission fitness. Here we investigate these strategies for directly transmitted pathogens using mathematical models of disease pathogenesis and transmission, modeling fitness as a function of within- and between-host pathogen dynamics. The within-host model includes realistic constraints on pathogen replication via resource depletion and cross-immunity between pathogen strains. We find three distinct types of infection emerge as maxima in the fitness landscape, each characterized by particular within-host dynamics, host population contact network structure, and transmission mode. These three infection types are associated with distinct non-overlapping ranges of levels of antigenic diversity, and well-defined patterns of within-host dynamics and between-host transmissibility. Fitness, quantified by the basic reproduction number, also falls within distinct ranges for each infection type. Every type is optimal for certain contact structures over a range of contact rates. Sexually transmitted infections and childhood diseases are identified as exemplar types for low and high contact rates, respectively. This work generates a plausible mechanistic hypothesis for the observed tradeoff between pathogen transmissibility and antigenic diversity, and shows how different classes of pathogens arise evolutionarily as fitness optima for different contact network structures and host contact rates.

Infectious diseases vary widely in how they affect those who get infected and how they are transmitted. As an example, the duration of a single infection can range from days to years, while transmission can occur via the respiratory route, water or sexual contact. Measles and HIV are contrasting examples—both are caused by RNA viruses, but one is a genetically diverse, lethal sexually transmitted infection (STI) while the other is a relatively mild respiratory childhood disease with low antigenic diversity. We investigate why the most transmissible respiratory diseases such as measles and rubella are antigenically static, meaning immunity is lifelong, while other diseases—such as influenza, or the sexually transmitted diseases—seem to trade transmissibility for the ability to generate multiple diverse strains so as to evade host immunity. We use mathematical models of disease progression and evolution within the infected host coupled with models of transmission between hosts to explore how transmission modes, host contact rates and network structure determine antigenic diversity, infectiousness and duration of infection. In doing so, we classify infections into three types—measles-like (high transmissibility, but antigenically static), flu-like (lower transmissibility, but more antigenically diverse), and STI-like (very antigenically diverse, long lived infection, but low overall transmissibility).

Exploring the impact of target cell heterogeneity on HIV loads in a within-host model

HIV can be transmitted from blood plasma or semen of an infected male. Viral loads in blood plasma are routinely measured, but the same is not true of semen. Even before drug treatment, viral loads have been shown to be different in the two body compartments (blood and genital tract), and this heterogeneity may be exacerbated by treatments using those antiretroviral drugs which have different efficacies in the two compartments. In addition to this heterogeneity, and despite highly effective drugs (in the blood) low-level viral replication is commonly reported for HIV patients as are differences in drug resistant mutation patterns in the two compartments. In this paper we investigate the effect of target cell heterogeneity between compartments on HIV viral loads using a within-host model that includes wildtype and drug resistant strains of HIV. We find that modelling target cell heterogeneity in the blood and male genital tract gives different viral loads in the two compartments prior to treatment and allows low-level viral loads to persist during therapy even if drug penetration is good. The model also allows coexistence of the two viral strains (in the absence of a mutation mechanism) with different dominance patterns in each body compartment. Our results suggest that monitoring of blood plasma viral strains may not give an accurate picture of the strains of HIV being transmitted between individuals and that continued research into the nature of HIV target cells in the male genital tract would be beneficial.

Hierarchical demography: a general approach with an application to honey bees

Hierarchical population structure, where individuals are aggregated into colonies or similar groups that themselves grow, survive or perish, and potentially produce offspring groups, is an important feature of many biological systems, most notably eusocial organisms such as the honey bee, Apis mellifera. Despite this hierarchical structure, there is a paucity of analytical models and theory linking the dynamics of individuals within colonies to the dynamics of a population of colonies. We present an analytical framework that provides a simple, robust, and predictive theory for the population dynamics of hierarchical organisms. Our framework explicitly describes and links demographic dynamics for the different levels in the hierarchy (individuals, groups, population). We illustrate the application of the framework by developing a model for honey bees and analyzing the effects of life history traits such as worker life span and size at swarming on the growth rate of populations. We conclude by discussing possible extensions of the model that increase its realism and expand its usefulness beyond swarm-founding, monogynous, eusocial insects.

Competition favours reduced cost of plasmids to host bacteria

Conjugative plasmids of Gram-negative bacteria have both vertical and horizontal modes of transmission: they are segregated to daughter cells during division, and transferred between hosts by plasmid-encoded conjugative machinery. Despite maintaining horizontal mobility, many plasmids carry fertility inhibition (fin) systems that repress their own conjugative transfer. To assess the ecological basis of self-transfer repression, we compared the invasion of bacterial populations by fin(+) and fin(-) variants of the plasmid R1 using a computational model and co-culture competitions. We observed that the fin(+) variant had a modest cost to the host (measured by reduction in growth rate), while the fin(-) variant incurred a larger cost. In simulations and empirical competitions the fin(-) plasmid invaded cultures quickly, but was subsequently displaced by the fin(+) plasmid. This indicated a competitive advantage to reducing horizontal transmission and allowing increased host replication. Computational simulations predicted that the advantage associated with reduced cost to the host would be maintained over a wide range of environmental conditions and plasmid costs. We infer that vertical transmission in concert with competitive exclusion favour decreased horizontal mobility of plasmids. Similar dynamics may exert evolutionary pressure on parasites, such as temperate bacteriophages and vertically transmitted animal viruses, to limit their rates of horizontal transfer.

Implications of vaccination and waning immunity

For infectious diseases where immunization can offer lifelong protection, a variety of simple models can be used to explain the utility of vaccination as a control method. However, for many diseases, immunity wanes over time and is subsequently enhanced (boosted) by asymptomatic encounters with the infection. The study of this type of epidemiological process requires a model formulation that can capture both the within-host dynamics of the pathogen and immune system as well as the associated population-level transmission dynamics. Here, we parametrize such a model for measles and show how vaccination can have a range of unexpected consequences as it reduces the natural boosting of immunity as well as reducing the number of naive susceptibles. In particular, we show that moderate waning times (40-80 years) and high levels of vaccination (greater than 70%) can induce large-scale oscillations with substantial numbers of symptomatic cases being generated at the peak. In addition, we predict that, after a long disease-free period, the introduction of infection will lead to far larger epidemics than that predicted by standard models. These results have clear implications for the long-term success of any vaccination campaign and highlight the need for a sound understanding of the immunological mechanisms of immunity and vaccination.

Virulence evolution and the trade-off hypothesis: history, current state of affairs and the future

It has been more than two decades since the formulation of the so-called 'trade-off' hypothesis as an alternative to the then commonly accepted idea that parasites should always evolve towards avirulence (the 'avirulence hypothesis'). The trade-off hypothesis states that virulence is an unavoidable consequence of parasite transmission; however, since the 1990s, this hypothesis has been increasingly challenged. We discuss the history of the study of virulence evolution and the development of theories towards the trade-off hypothesis in order to illustrate the context of the debate. We investigate the arguments raised against the trade-off hypothesis and argue that trade-offs exist, but may not be of the simple form that is usually assumed, involving other mechanisms (and life-history traits) than those originally considered. Many processes such as pathogen adaptation to within-host competition, interactions with the immune system and shifting transmission routes, will all be interrelated making sweeping evolutionary predictions harder to obtain. We argue that this is the heart of the current debate in the field and while species-specific models may be better predictive tools, the trade-off hypothesis and its basic extensions are necessary to assess the qualitative impacts of virulence management strategies.

Acute or chronic? Within-host models with immune dynamics, infection outcome, and parasite evolution

There is ample theoretical and experimental evidence that virulence evolution depends on the immune response of the host. In this article, we review a number of recent studies that attempt to explicitly incorporate the dynamics of the immune system (instead of merely representing it by a single black box parameter) in models for the evolution of parasite virulence. A striking observation is that the type of infection (acute or chronic) is invariably considered to be a constraint that model assumptions have to satisfy rather than as a potential outcome of the interaction of the parasite with its host's immune system. We argue that avoiding making assumptions about the type of infection will lead to a better understanding of infectious diseases, even though a number of fundamental and technical problems remain. Dynamical modeling of the immune system opens a wide range of perspectives: for understanding how the immune system eradicates a parasite (which it does for most pathogens but not for all, HIV being a notorious example of a virus that is not completely eliminated), for studying multiple infections through concomitant immunity, for understanding the emergence and evolution of the immune system in animals, and for evolutionary epidemiology in general (e.g., predicting evolutionary consequences of new therapies and public health policies). We conclude by discussing new approaches based on embedded (or nested) models and identify future perspectives for the modeling of infectious diseases.