An in-host model of acute infection: measles as a case study

Measles Infection Dose Responses: Insights from Mathematical Modeling

How viral infections develop can change based on the number of viruses initially entering the body. The understanding of the impacts of infection doses remains incomplete, in part due to challenging constraints, and a lack of research. Gaining more insights is crucial regarding the measles virus (MV). The higher the MV infection dose, the earlier the peak of acute viremia, but the magnitude of the peak viremia remains almost constant. Measles is highly contagious, causes immunosuppression such as lymphopenia, and contributes substantially to childhood morbidity and mortality. This work investigated mechanisms underlying the observed wild-type measles infection dose responses in cynomolgus monkeys. We fitted longitudinal data on viremia using maximum likelihood estimation, and used the Akaike Information Criterion (AIC) to evaluate relevant biological hypotheses and their respective model parameterizations. The lowest AIC indicates a linear relationship between the infection dose, the initial viral load, and the initial number of activated MV-specific T cells. Early peak viremia is associated with high initial number of activated MV-specific T cells. Thus, when MV infection dose increases, the initial viremia and associated immune cell stimulation increase, and reduce the time it takes for T cell killing to be sufficient, thereby allowing dose-independent peaks for viremia, MV-specific T cells, and lymphocyte depletion. Together, these results suggest that the development of measles depends on virus-host interactions at the start and the efficiency of viral control by cellular immunity. These relationships are additional motivations for prevention, vaccination, and early treatment for measles.

Modelling Immune Memory Development

The cellular adaptive immune response to influenza has been analyzed through several recent mathematical models. In particular, Zarnitsyna et al. (Front Immunol 7:1-9, 2016) show how central memory CD8+ T cells reach a plateau after repeated infections, and analyze their role in the immune response to further challenges. In this paper, we further investigate the theoretical features of that model by extracting from the infection dynamics a discrete map that describes the build-up of memory cells. Furthermore, we show how the model by Zarnitsyna et al. (Front Immunol 7:1-9, 2016) can be viewed as a fast-scale approximation of a model allowing for recruitment of target epithelial cells. Finally, we analyze which components of the model are essential to understand the progressive build-up of immune memory. This is performed through the analysis of simplified versions of the model that include some components only of immune response. The analysis performed may also provide a theoretical framework for understanding the conditions under which two-dose vaccination strategies can be helpful.

Immune amnesia induced by measles and its effects on concurrent epidemics

It has been recently discovered that the measles virus can damage pre-existing immunological memory, destroying B lymphocytes and reducing the diversity of non-specific B cells of the infected host. In particular, this implies that previously acquired immunization from vaccination or direct exposition to other pathogens could be partially erased in a phenomenon named ‘immune amnesia’, whose effects can become particularly worrisome given the actual rise of anti-vaccination movements. Here, we present the first attempt to incorporate immune amnesia into standard models of epidemic spreading by proposing a simple model for the spreading of two concurrent pathogens causing measles and another generic disease. Different analyses confirm that immune amnesia can have important consequences for epidemic spreading, significantly altering the vaccination coverage required to reach herd immunity. We also uncover the existence of novel propagating and endemic phases induced by immune amnesia. Finally, we discuss the meaning and consequences of our results and their relation with, e.g. immunization strategies, together with the possibility that explosive types of transitions may emerge, making immune-amnesia effects particularly dramatic. This work opens the door to further developments and analyses of immune-amnesia effects, contributing also to the theory of interacting epidemics on complex networks.

What Is the Evidence to Support a Correlate of Protection for Measles? A Systematic Review

BACKGROUND

Many studies assume that the serologic correlate of protection from measles disease is 120 mIU/mL. We systematically reviewed the literature to examine the evidence supporting this correlate of protection.

METHODS

We searched peer-reviewed and gray literature for articles reporting a measles correlate of protection. We excluded studies focusing on special populations, infants aged <9 months, and those using animal models or nonstandard vaccines or administration routes. We extracted and synthesized data from full-text articles that met inclusion criteria.

RESULTS

We screened 14 778 articles and included 5 studies in our review. The studies reported either preexposure antibody concentrations of individuals along with a description of symptoms postexposure, or the proportion of measles cases that had preexposure antibody concentrations above a threshold of immunity specified by the authors. Some studies also described secondary antibody responses upon exposure. The variation in laboratory methods between studies made comparisons difficult. Some of the studies that assumed 120 mIU/mL as a correlate of protection identified symptomatic individuals with preexposure titers exceeding this threshold.

CONCLUSIONS

Our findings underscore the scant data upon which the commonly used 120 mIU/mL measles threshold of protection is based, suggesting that further work is required to characterize the measles immunity threshold.

Integrating mathematical models with experimental data to investigate the within-host dynamics of bacterial infections

Bacterial infections still constitute a major cause of mortality and morbidity worldwide. The unavailability of therapeutics, antimicrobial resistance and the chronicity of infections due to incomplete clearance contribute to this phenomenon. Despite the progress in antimicrobial and vaccine development, knowledge about the effect that therapeutics have on the host–bacteria interactions remains incomplete. Insights into the characteristics of bacterial colonization and migration between tissues and the relationship between replication and host- or therapeutically induced killing can enable efficient design of treatment approaches. Recently, innovative experimental techniques have generated data enabling the qualitative characterization of aspects of bacterial dynamics. Here, we argue that mathematical modeling as an adjunct to experimental data can enrich the biological insight that these data provide. However, due to limited interdisciplinary training, efforts to combine the two remain limited. To promote this dialogue, we provide a categorization of modeling approaches highlighting their relationship to data generated by a range of experimental techniques in the area of in vivo bacterial dynamics. We outline common biological themes explored using mathematical models with case studies across all pathogen classes. Finally, this review advocates multidisciplinary integration to improve our mechanistic understanding of bacterial infections and guide the use of existing or new therapies.

Within-host infectious disease models accommodating cellular coinfection, with an application to influenza

Within-host models are useful tools for understanding the processes regulating viral load dynamics. While existing models have considered a wide range of within-host processes, at their core these models have shown remarkable structural similarity. Specifically, the structure of these models generally consider target cells to be either uninfected or infected, with the possibility of accommodating further resolution (e.g. cells that are in an eclipse phase). Recent findings, however, indicate that cellular coinfection is the norm rather than the exception for many viral infectious diseases, and that cells with high multiplicity of infection are present over at least some duration of an infection. The reality of these cellular coinfection dynamics is not accommodated in current within-host models although it may be critical for understanding within-host dynamics. This is particularly the case if multiplicity of infection impacts infected cell phenotypes such as their death rate and their viral production rates. Here, we present a new class of within-host disease models that allow for cellular coinfection in a scalable manner by retaining the low-dimensionality that is a desirable feature of many current within-host models. The models we propose adopt the general structure of epidemiological ‘macroparasite’ models that allow hosts to be variably infected by parasites such as nematodes and host phenotypes to flexibly depend on parasite burden. Specifically, our within-host models consider target cells as ‘hosts’ and viral particles as ‘macroparasites’, and allow viral output and infected cell lifespans, among other phenotypes, to depend on a cell’s multiplicity of infection. We show with an application to influenza that these models can be statistically fit to viral load and other within-host data, and demonstrate using model selection approaches that they have the ability to outperform traditional within-host viral dynamic models. Important in vivo quantities such as the mean multiplicity of cellular infection and time-evolving reassortant frequencies can also be quantified in a straightforward manner once these macroparasite models have been parameterized. The within-host model structure we develop here provides a mathematical way forward to address questions related to the roles of cellular coinfection, collective viral interactions, and viral complementation in within-host viral dynamics and evolution.

Modeling the measles paradox reveals the importance of cellular immunity in regulating viral clearance

Measles virus (MV) is a highly contagious member of the Morbillivirus genus that remains a major cause of childhood mortality worldwide. Although infection induces a strong MV-specific immune response that clears viral load and confers lifelong immunity, transient immunosuppression can also occur, leaving the host vulnerable to colonization from secondary pathogens. This apparent contradiction of viral clearance in the face of immunosuppression underlies what is often referred to as the 'measles paradox', and remains poorly understood. To explore the mechanistic basis underlying the measles paradox, and identify key factors driving viral clearance, we return to a previously published dataset of MV infection in rhesus macaques. These data include virological and immunological information that enable us to fit a mathematical model describing how the virus interacts with the host immune system. In particular, our model incorporates target cell depletion through infection of host immune cells-a hallmark of MV pathology that has been neglected from previous models. We find the model captures the data well, and that both target cell depletion and immune activation are required to explain the overall dynamics. Furthermore, by simulating conditions of increased target cell availability and suppressed cellular immunity, we show that the latter causes greater increases in viral load and delays to MV clearance. Overall, this signals a more dominant role for cellular immunity in resolving acute MV infection. Interestingly, we find contrasting dynamics dominated by target cell depletion when viral fitness is increased. This may have wider implications for animal morbilliviruses, such as canine distemper virus (CDV), that cause fatal target cell depletion in their natural hosts. To our knowledge this work represents the first fully calibrated within-host model of MV dynamics and, more broadly, provides a new platform from which to explore the complex mechanisms underlying Morbillivirus infection.

Infection-acquired versus vaccine-acquired immunity in an SIRWS model

In some disease systems, the process of waning immunity can be subtle, involving a complex relationship between the duration of immunity-acquired either through natural infection or vaccination-and subsequent boosting of immunity through asymptomatic re-exposure. We present and analyse a model of infectious disease transmission where primary and secondary infections are distinguished to examine the interplay between infection and immunity. Additionally we allow the duration of infection-acquired immunity to differ from that of vaccine-acquired immunity to explore the impact on long-term disease patterns and prevalence of infection in the presence of immune boosting. Our model demonstrates that vaccination may induce cyclic behaviour, and the ability of vaccinations to reduce primary infections may not lead to decreased transmission. Where the boosting of vaccine-acquired immunity delays a primary infection, the driver of transmission largely remains primary infections. In contrast, if the immune boosting bypasses a primary infection, secondary infections become the main driver of transmission under a sufficiently long duration of immunity. Our results show that the epidemiological patterns of an infectious disease may change considerably when the duration of vaccine-acquired immunity differs from that of infection-acquired immunity. Our study highlights that for any particular disease and associated vaccine, a detailed understanding of the waning and boosting of immunity and how the duration of protection is influenced by infection prevalence are important as we seek to optimise vaccination strategies.

On the Role of CD8+ T Cells in Determining Recovery Time from Influenza Virus Infection

Myriad experiments have identified an important role for CD8⁺ T cell response mechanisms in determining recovery from influenza A virus infection. Animal models of influenza infection further implicate multiple elements of the immune response in defining the dynamical characteristics of viral infection. To date, influenza virus models, while capturing particular aspects of the natural infection history, have been unable to reproduce the full gamut of observed viral kinetic behavior in a single coherent framework. Here, we introduce a mathematical model of influenza viral dynamics incorporating innate, humoral, and cellular immune components and explore its properties with a particular emphasis on the role of cellular immunity. Calibrated against a range of murine data, our model is capable of recapitulating observed viral kinetics from a multitude of experiments. Importantly, the model predicts a robust exponential relationship between the level of effector CD8⁺ T cells and recovery time, whereby recovery time rapidly decreases to a fixed minimum recovery time with an increasing level of effector CD8⁺ T cells. We find support for this relationship in recent clinical data from influenza A (H7N9) hospitalized patients. The exponential relationship implies that people with a lower level of naive CD8⁺ T cells may receive significantly more benefit from induction of additional effector CD8⁺ T cells arising from immunological memory, itself established through either previous viral infection or T cell-based vaccines.

Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis

The devastation caused by periodic measles outbreaks motivated efforts over more than a century to mathematically model measles disease and transmission. Following the identification of rubella, which similarly presents with fever and rash and causes congenital rubella syndrome (CRS) in infants born to women first infected with rubella early in pregnancy, modelers also began to characterize rubella disease and transmission. Despite the relatively large literature, no comprehensive review to date provides an overview of dynamic transmission models for measles and rubella developed to support risk and policy analysis. This systematic review of the literature identifies quantitative measles and/or rubella dynamic transmission models and characterizes key insights relevant for prospective modeling efforts. Overall, measles and rubella represent some of the relatively simplest viruses to model due to their ability to impact only humans and the apparent life-long immunity that follows survival of infection and/or protection by vaccination, although complexities arise due to maternal antibodies and heterogeneity in mixing and some models considered potential waning immunity and reinfection. This review finds significant underreporting of measles and rubella infections and widespread recognition of the importance of achieving and maintaining high population immunity to stop and prevent measles and rubella transmission. The significantly lower transmissibility of rubella compared to measles implies that all countries could eliminate rubella and CRS by using combination of measles- and rubella-containing vaccines (MRCVs) as they strive to meet regional measles elimination goals, which leads to the recommendation of changing the formulation of national measles-containing vaccines from measles only to MRCV as the standard of care.

Immuno-epidemiology of a population structured by immune status: a mathematical study of waning immunity and immune system boosting

When the body gets infected by a pathogen the immune system develops pathogen-specific immunity. Induced immunity decays in time and years after recovery the host might become susceptible again. Exposure to the pathogen in the environment boosts the immune system thus prolonging the time in which a recovered individual is immune. Such an interplay of within host processes and population dynamics poses significant challenges in rigorous mathematical modeling of immuno-epidemiology. We propose a framework to model SIRS dynamics, monitoring the immune status of individuals and including both waning immunity and immune system boosting. Our model is formulated as a system of two ordinary differential equations (ODEs) coupled with a PDE. After showing existence and uniqueness of a classical solution, we investigate the local and the global asymptotic stability of the unique disease-free stationary solution. Under particular assumptions on the general model, we can recover known examples such as large systems of ODEs for SIRWS dynamics, as well as SIRS with constant delay.

Within-host viral dynamics of dengue serotype 1 infection

Dengue, the most common mosquito-borne viral infection of humans, is endemic across much of the world, including much of tropical Asia and is increasing in its geographical range. Here, we present a mathematical model of dengue virus dynamics within infected individuals, detailing the interaction between virus and a simple immune response. We fit this model to measurements of plasma viral titre from cases of primary and secondary DENV 1 infection in Vietnam. We show that variation in model parameters governing the immune response is sufficient to create the observed variation in virus dynamics between individuals. Estimating model parameter values, we find parameter differences between primary and secondary cases consistent with the theory of antibody-dependent enhancement (namely enhanced rates of viral entry to target cells in secondary cases). Finally, we use our model to examine the potential impact of an antiviral drug on the within-host dynamics of dengue. We conclude that the impact of antiviral therapy on virus dynamics is likely to be limited if therapy is only started at the onset of symptoms, owing to the typically late stage of viral pathogenesis reached by the time symptoms are manifested and thus treatment is started.

A large-scale immuno-epidemiological simulation of influenza A epidemics

Background

Agent based models (ABM) are useful to explore population-level scenarios of disease spread and containment, but typically characterize infected individuals using simplified models of infection and symptoms dynamics. Adding more realistic models of individual infections and symptoms may help to create more realistic population level epidemic dynamics.

Methods

Using an equation-based, host-level mathematical model of influenza A virus infection, we develop a function that expresses the dependence of infectivity and symptoms of an infected individual on initial viral load, age, and viral strain phenotype. We incorporate this response function in a population-scale agent-based model of influenza A epidemic to create a hybrid multiscale modeling framework that reflects both population dynamics and individualized host response to infection.

Results

At the host level, we estimate parameter ranges using experimental data of H1N1 viral titers and symptoms measured in humans. By linearization of symptoms responses of the host-level model we obtain a map of the parameters of the model that characterizes clinical phenotypes of influenza infection and immune response variability over the population. At the population-level model, we analyze the effect of individualizing viral response in agent-based model by simulating epidemics across Allegheny County, Pennsylvania under both age-specific and age-independent severity assumptions.

Conclusions

We present a framework for multi-scale simulations of influenza epidemics that enables the study of population-level effects of individual differences in infections and symptoms, with minimal additional computational cost compared to the existing population-level simulations.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2458-14-1019) contains supplementary material, which is available to authorized users.

The dynamical consequences of seasonal forcing, immune boosting and demographic change in a model of disease transmission

The impact of seasonal effects on the time course of an infectious disease can be dramatic. Seasonal fluctuations in the transmission rate for an infectious disease are known mathematically to induce cyclical behaviour and drive the onset of multistable and chaotic dynamics. These properties of forced dynamical systems have previously been used to explain observed changes in the period of outbreaks of infections such as measles, varicella (chickenpox), rubella and pertussis (whooping cough). Here, we examine in detail the dynamical properties of a seasonally forced extension of a model of infection previously used to study pertussis. The model is novel in that it includes a non-linear feedback term capturing the interaction between exposure and the duration of protection against re-infection. We show that the presence of limit cycles and multistability in the unforced system give rise to complex and intricate behaviour as seasonal forcing is introduced. Through a mixture of numerical simulation and bifurcation analysis, we identify and explain the origins of chaotic regions of parameter space. Furthermore, we identify regions where saddle node lines and period-doubling cascades of different orbital periods overlap, suggesting that the system is particularly sensitive to small perturbations in its parameters and prone to multistable behaviour. From a public health point of view - framed through the 'demographic transition' whereby a population׳s birth rate drops over time (and life-expectancy commensurately increases) - we argue that even weak levels of seasonal-forcing and immune boosting may contribute to the myriad of complex and unexpected epidemiological behaviours observed for diseases such as pertussis. Our approach helps to contextualise these epidemiological observations and provides guidance on how to consider the potential impact of vaccination programs.

Viral kinetic modeling: state of the art

Viral kinetic (VK) modeling has led to increased understanding of the within host dynamics of viral infections and the effects of therapy. Here we review recent developments in the modeling of viral infection kinetics with emphasis on two infectious diseases: hepatitis C and influenza. We review how VK modeling has evolved from simple models of viral infections treated with a drug or drug cocktail with an assumed constant effectiveness to models that incorporate drug pharmacokinetics and pharmacodynamics, as well as phenomenological models that simply assume drugs have time varying-effectiveness. We also discuss multiscale models that include intracellular events in viral replication, models of drug-resistance, models that include innate and adaptive immune responses and models that incorporate cell-to-cell spread of infection. Overall, VK modeling has provided new insights into the understanding of the disease progression and the modes of action of several drugs. We expect that VK modeling will be increasingly used in the coming years to optimize drug regimens in order to improve therapeutic outcomes and treatment tolerability for infectious diseases.

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.

Modeling inoculum dose dependent patterns of acute virus infections

Inoculum dose, i.e. the number of pathogens at the beginning of an infection, often affects key aspects of pathogen and immune response dynamics. These in turn determine clinically relevant outcomes, such as morbidity and mortality. Despite the general recognition that inoculum dose is an important component of infection outcomes, we currently do not understand its impact in much detail. This study is intended to start filling this knowledge gap by analyzing inoculum dependent patterns of viral load dynamics in acute infections. Using experimental data for adenovirus and infectious bronchitis virus infections as examples, we demonstrate inoculum dose dependent patterns of virus dynamics. We analyze the data with the help of mathematical models to investigate what mechanisms can reproduce the patterns observed in experimental data. We find that models including components of both the innate and adaptive immune response are needed to reproduce the patterns found in the data. We further analyze which types of innate or adaptive immune response models agree with observed data. One interesting finding is that only models for the adaptive immune response that contain growth terms partially independent of viral load can properly reproduce observed patterns. This agrees with the idea that an antigen-independent, programmed response is part of the adaptive response. Our analysis provides useful insights into the types of model structures that are required to properly reproduce observed virus dynamics for varying inoculum doses. We suggest that such models should be taken as basis for future models of acute viral infections.

Prolonged persistence of measles virus RNA is characteristic of primary infection dynamics

Measles virus (MeV) is the poster child for acute infection followed by lifelong immunity. However, recent work shows the presence of MeV RNA in multiple sites for up to 3 mo after infection in a proportion of infected children. Here, we use experimental infection of rhesus macaques to show that prolonged RNA presence is characteristic of primary infection. We found that viral RNA persisted in the blood, respiratory tract, or lymph nodes four to five times longer than the infectious virus and that the clearance of MeV RNA from blood happened in three phases: rapid decline coincident with clearance of infectious virus, a rebound phase with increases up to 10-fold, and a phase of slow decrease to undetectable levels. To examine the effect of individual host immune factors on MeV load dynamics further, we developed a mathematical model that expressed viral replication and elimination in terms of the strength of MeV-specific T-cell responses, antibody responses, target cell limitations, and immunosuppressive activity of regulatory T cells. Based on the model, we demonstrate that viral dynamics, although initially regulated by T cells, require antibody to eliminate viral RNA. These results have profound consequences for our view of acute viral infections, the development of prolonged immunity, and, potentially, viral evolution.

Influenza pandemic waves under various mitigation strategies with 2009 H1N1 as a case study

A significant feature of influenza pandemics is multiple waves of morbidity and mortality over a few months or years. The size of these successive waves depends on intervention strategies including antivirals and vaccination, as well as the effects of immunity gained from previous infection. However, the global vaccine manufacturing capacity is limited. Also, antiviral stockpiles are costly and thus, are limited to very few countries. The combined effect of antivirals and vaccination in successive waves of a pandemic has not been quantified. The effect of acquired immunity from vaccination and previous infection has also not been characterized. In times of a pandemic threat countries must consider the effects of a limited vaccine, limited antiviral use and the effects of prior immunity so as to adopt a pandemic strategy that will best aid the population. We developed a mathematical model describing the first and second waves of an influenza pandemic including drug therapy, vaccination and acquired immunity. The first wave model includes the use of antiviral drugs under different treatment profiles. In the second wave model the effects of antivirals, vaccination and immunity gained from the first wave are considered. The models are used to characterize the severity of infection in a population under different drug therapy and vaccination strategies, as well as school closure, so that public health policies regarding future influenza pandemics are better informed.

Immunobiological outcomes of repeated chlamydial infection from two models of within-host population dynamics

Background

Chlamydia trachomatis is a common human pathogen that mediates disease processes capable of inflicting serious complications on reproduction. Aggressive inflammatory immune responses are thought to not only direct a person's level of immunity but also the potential for immunopathology. With human immunobiology being debated as a cause of prevailing epidemiological trends, we examined some fundamental issues regarding susceptibility to multiple chlamydial infections that could have implications for infection spread. We argue that, compared to less-frequent exposure, frequent exposure to chlamydia may well produce unique immunobiological characteristics that likely to have important clinical and epidemiological implications.

Methods and Results

As a novel tool for studying chlamydia, we applied principles of modeling within-host pathogen dynamics to enable an understanding of some fundamental characteristics of an individual's immunobiology during multiple chlamydial infections. While the models were able to reproduce shorter-term infection kinetics of primary and secondary infections previously observed in animal models, it was also observed that longer periods between initial and second infection may increase an individual's chlamydial load and lengthen their duration of infectiousness. The cessation of short-term repeated exposure did not allow for the formation of long-lasting immunity. However, frequent re-exposure non-intuitively linked the formation of protective immunity, persistent infection, and the potential for immunopathology.

Conclusions

Overall, these results provide interesting insights that should be verified with continued study. Nevertheless, these results appear to raise challenges for current evidence of the development of long-lasting immunity against chlamydia, and suggest the existence of a previously unidentified mechanism for the formation of persistent infection. The obvious next goal is to investigate the qualitative impact of these results on the spread of chlamydia.

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.

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.