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

Quantifying the relationship between within-host dynamics and transmission for viral diseases of livestock

Understanding the population dynamics of an infectious disease requires linking within-host dynamics and between-host transmission in a quantitative manner, but this is seldom done in practice. Here a simple phenomenological model for viral dynamics within a host is linked to between-host transmission by assuming that the probability of transmission is related to log viral titre. Data from transmission experiments for two viral diseases of livestock, foot-and-mouth disease virus in cattle and swine influenza virus in pigs, are used to parametrize the model and, importantly, test the underlying assumptions. The model allows the relationship between within-host parameters and transmission to be determined explicitly through their influence on the reproduction number and generation time. Furthermore, these critical within-host parameters (time and level of peak titre, viral growth and clearance rates) can be computed from more complex within-host models, raising the possibility of assessing the impact of within-host processes on between-host transmission in a more detailed quantitative manner.

Within-Host Mathematical Models of Antibiotic Resistance

Mathematical models have been used to study the spread of infectious diseases from person to person. More recently studies are developing within-host modeling which provides an understanding of how pathogens-bacteria, fungi, parasites, or viruses-develop, spread, and evolve inside a single individual and their interaction with the host's immune system.Such models have the potential to provide a more detailed and complete description of the pathogenesis of diseases within-host and identify other influencing factors that may not be detected otherwise. Mathematical models can be used to aid understanding of the global antibiotic resistance (ABR) crisis and identify new ways of combating this threat.ABR occurs when bacteria respond to random or selective pressures and adapt to new environments through the acquisition of new genetic traits. This is usually through the acquisition of a piece of DNA from other bacteria, a process called horizontal gene transfer (HGT), the modification of a piece of DNA within a bacterium, or through. Bacteria have evolved mechanisms that enable them to respond to environmental threats by mutation, and horizontal gene transfer (HGT): conjugation; transduction; and transformation. A frequent mechanism of HGT responsible for spreading antibiotic resistance on the global scale is conjugation, as it allows the direct transfer of mobile genetic elements (MGEs). Although there are several MGEs, the most important MGEs which promote the development and rapid spread of antimicrobial resistance genes in bacterial populations are plasmids and transposons. Each of the resistance-spread-mechanisms mentioned above can be modeled allowing us to understand the process better and to define strategies to reduce resistance.

Linking within- and between-host scales for understanding the evolutionary dynamics of quantitative antimicrobial resistance

Understanding both the epidemiological and evolutionary dynamics of antimicrobial resistance is a major public health concern. In this paper, we propose a nested model, explicitly linking the within- and between-host scales, in which the level of resistance of the bacterial population is viewed as a continuous quantitative trait. The within-host dynamics is based on integro-differential equations structured by the resistance level, while the between-host scale is additionally structured by the time since infection. This model simultaneously captures the dynamics of the bacteria population, the evolutionary transient dynamics which lead to the emergence of resistance, and the epidemic dynamics of the host population. Moreover, we precisely analyze the model proposed by particularly performing the uniform persistence and global asymptotic results. Finally, we discuss the impact of the treatment rate of the host population in controlling both the epidemic outbreak and the average level of resistance, either if the within-host scale therapy is a success or failure. We also explore how transitions between infected populations (treated and untreated) can impact the average level of resistance, particularly in a scenario where the treatment is successful at the within-host scale.

Within- and between-host dynamics of producer and non-producer pathogens

For infections to be maintained in a population, pathogens must compete to colonize hosts and transmit between them. We use an experimental approach to investigate within-and-between host dynamics using the pathogen Pseudomonas aeruginosa and the animal host Caenorhabditis elegans. Within-host interactions can involve the production of goods that are beneficial to all pathogens in the local environment but susceptible to exploitation by non-producers. We exposed the nematode host to ‘producer’ and two ‘non-producer’ bacterial strains (specifically for siderophore production and quorum sensing), in single infections and coinfections, to investigate within-host colonization. Subsequently, we introduced infected nematodes to pathogen-naive populations to allow natural transmission between hosts. We find that producer pathogens are consistently better at colonizing hosts and transmitting between them than non-producers during coinfection and single infection. Non-producers were poor at colonizing hosts and between-host transmission, even when coinfecting with producers. Understanding pathogen dynamics across these multiple levels will ultimately help us predict and control the spread of infections, as well as contribute to explanations for the persistence of cooperative genotypes in natural populations.

Eco-evolutionary trade-offs in the dynamics of prion strain competition

Prion and prion-like molecules are a type of self-replicating aggregate protein that have been implicated in a variety of neurodegenerative diseases. Over recent decades, the molecular dynamics of prions have been characterized both empirically and through mathematical models, providing insights into the epidemiology of prion diseases and the impact of prions on the evolution of cellular processes. At the same time, a variety of evidence indicates that prions are themselves capable of a form of evolution, in which changes to their structure that impact their rate of growth or fragmentation are replicated, making such changes subject to natural selection. Here we study the role of such selection in shaping the characteristics of prions under the nucleated polymerization model (NPM). We show that fragmentation rates evolve to an evolutionary stable value which balances rapid reproduction of PrPSc aggregates with the need to produce stable polymers. We further show that this evolved fragmentation rate differs in general from the rate that optimizes transmission between cells. We find that under the NPM, prions that are both evolutionary stable and optimized for transmission have a characteristic length of three times the critical length below which they become unstable. Finally, we study the dynamics of inter-cellular competition between strains, and show that the eco-evolutionary trade-off between intra- and inter-cellular competition favours coexistence.

Evolutionary dynamics within and among competing groups

Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible for profound transitions in evolutionary history, including the origin of cellular life, multicellular life, and even societies. Here, we synthesize a growing literature that extends evolutionary game theory to describe multilevel evolutionary dynamics, using nested birth-death processes and partial differential equations to model natural selection acting on competition within and among groups of individuals. We analyze how mechanisms known to promote cooperation within a single group-including assortment, reciprocity, and population structure-alter evolutionary outcomes in the presence of competition among groups. We find that population structures most conducive to cooperation in multiscale systems can differ from those most conducive within a single group. Likewise, for competitive interactions with a continuous range of strategies we find that among-group selection may fail to produce socially optimal outcomes, but it can nonetheless produce second-best solutions that balance individual incentives to defect with the collective incentives for cooperation. We conclude by describing the broad applicability of multiscale evolutionary models to problems ranging from the production of diffusible metabolites in microbes to the management of common-pool resources in human societies.

The effect of bottleneck size on evolution in nested Darwinian populations

Previous work has shown how a minimal ecological structure consisting of patchily distributed resources and recurrent dispersal between patches can scaffold Darwinian properties onto collections of cells. When the timescale of dispersal is long compared with the time to consume resources, patch fitness increases but comes at a cost to cell growth rates. This creates conditions that initiate evolutionary transitions in individuality. A key feature of the scaffold is a bottleneck created during dispersal, causing patches to be founded by single cells. The bottleneck decreases competition within patches and, hence, creates a strong hereditary link at the level of patches. Here, we construct a fully stochastic model to investigate the effect of bottleneck size on the evolutionary dynamics of both cells and collectives. We show that larger bottlenecks simply slow the dynamics, but, at some point, which depends on the parameters of the within-patch model, the direction of evolution towards the equilibrium reverses. Introduction of random fluctuations in bottleneck sizes with some positive probability of smaller sizes counteracts this, even when the probability of smaller bottlenecks is minimal.

The mechanism shaping the logistic growth of mutation proportion in epidemics at population scale

Virus evolution is a common process of pathogen adaption to host population and environment. Frequently, a small but important fraction of virus mutations are reported to contribute to higher risks of host infection, which is one of the major determinants of infectious diseases outbreaks at population scale. The key mutations contributing to transmission advantage of a genetic variant often grow and reach fixation rapidly. Based on classic epidemiology theories of disease transmission, we proposed a mechanistic explanation of the process that between-host transmission advantage may shape the observed logistic curve of the mutation proportion in population. The logistic growth of mutation is further generalized by incorporating time-varying selective pressure to account for impacts of external factors on pathogen adaptiveness. The proposed model is implemented in real-world data of COVID-19 to capture the emerging trends and changing dynamics of the B.1.1.7 strains of SARS-CoV-2 in England. The model characterizes and establishes the underlying theoretical mechanism that shapes the logistic growth of mutation in population.

Asexual reproductive potential trumps virulence as a predictor of competitive ability in mixed infections

Natural infections frequently involve several co-infecting pathogen strains. These mixed infections can affect the extent of the infection, the transmission success of the pathogen and the eventual epidemic outcome. To date, few studies have investigated how mixed infections affect transmission between hosts. Zymoseptoria tritici is a highly diverse wheat pathogen in which multiple strains often coexist in the same lesion. Here we demonstrate that the most competitive strains often exclude their competitors during serial passages of mixed infections. The outcome of the competition depended on both the host genotype and the genotypes of the competing pathogen strains. Differences in virulence among the strains were not associated with competitive advantages during transmission, while differences in reproductive potential had a strong effect on strain competitive ability. Overall, our findings suggest that host specialization is determined mainly by the ability to successfully transmit offspring to new hosts during mixed infections.

The source of individual heterogeneity shapes infectious disease outbreaks

There is known heterogeneity between individuals in infectious disease transmission patterns. The source of this heterogeneity is thought to affect epidemiological dynamics but studies tend not to control for the overall heterogeneity in the number of secondary cases caused by an infection. To explore the role of individual variation in infection duration and transmission rate in parasite emergence and spread, while controlling for this potential bias, we simulate stochastic outbreaks with and without parasite evolution. As expected, heterogeneity in the number of secondary cases decreases the probability of outbreak emergence. Furthermore, for epidemics that do emerge, assuming more realistic infection duration distributions leads to faster outbreaks and higher epidemic peaks. When parasites require adaptive mutations to cause large epidemics, the impact of heterogeneity depends on the underlying evolutionary model. If emergence relies on within-host evolution, decreasing the infection duration variance decreases the probability of emergence. These results underline the importance of accounting for realistic distributions of transmission rates to anticipate the effect of individual heterogeneity on epidemiological dynamics.

Dynamics in a disease transmission model coupled virus infection in host with incubation delay and environmental effects

In this paper, a disease transmission model coupled virus infection in host with incubation delay and environmental effects is studied. For the virus infection model in host with immune, latent delay and environmental virus invading, the threshold criteria on the global stability of antibody-free and antibody response infection equilibria are established. For the disease transmission model with incubation delay and immune response in host, basic reproduction number R 0 is defined, and the local stability of equilibria are established, i.e., the disease-free equilibrium is locally asymptotically stable if R 0 < 1 , and the endemic equilibrium is locally asymptotically stable if R 0 > 1 . Furthermore, the uniform persistence of positive solutions is studied while there is not the direct transmission of disease by the infected individuals. Finally, the numerical examples are presented to verify the main results.

The role of a programmatic immune response on the evolution of pathogen traits

In modelling pathogen evolution during epidemics, it is important to understand the interactions between within-host infection dynamics and between-host pathogen transmission. Multiscale models often assume an immune response that is highly responsive to pathogen dynamics. Empirical evidence, however, suggests that the immune response in acute infections is triggered and programmatic. This leads to somewhat more predictable infection trajectories where transition times and, consequently, the infectious window are non-exponentially distributed. Here, we develop a within-host model where the immune response is triggered by pathogen growth but otherwise develops independently, and use this to obtain analytic expressions for the infectious period and peak pathogen load. This allows us to model the basic reproductive number in terms of explicit functional relationships among within-host traits including the growth rate of the pathogen. We find that the dependence of pathogen load and the infectious window on within-host parameters constrains the evolution of the pathogen growth rate. At low growth rate, selection favours a higher pathogen load and therefore increasing pathogen growth rate. At high growth rates, selection for a longer infectious window trades off against selection against the effects of virulence. At intermediate growth rates the basic reproductive number is relatively insensitive to changes in the growth rate. The resulting "flat" region of the pathogen fitness landscape is due to the stability of the programmatic immune response in clearing the infection.

A time-since-infection model for populations with two pathogens

The pioneering work of Kermack and McKendrick (1927, 1932, 1933) is now most known for introducing the SIR model, which divides a population into discrete compartments for susceptible, infected and removed individuals. The SIR model is the archetype of widely used compartmental models for epidemics. It is sometimes forgotten, that Kermack and McKendrick introduced the SIR model as a special case of a more general framework. This general framework distinguishes individuals not only by whether they are susceptible, infected or removed, but additionally tracks the time passed since they got infected. Such time-since-infection models can mechanistically link within-host dynamics to the population level. This allows the models to account for more details of the disease dynamics, such as delays of infectiousness and symptoms during the onset of an infection. Details like this can be vital for interpreting epidemiological data. The time-since-infection framework was originally formulated for a host population with a single pathogen. However, the interactions of multiple pathogens within hosts and within a population can be crucial for understanding the severity and spread of diseases. Current models for multiple pathogens mostly rely on compartmental models. While such models are relatively easy to set up, they do not have the same mechanistic underpinning as time-since-infection models. To approach this gap of connecting within-host dynamics of multiple pathogens to the population level, we here extend the time-since-infection framework of Kermack and McKendrick for two pathogens. We derive formulas for the basic reproduction numbers in the system. Those numbers determine whether a pathogen can invade a population, potentially depending on whether the other pathogen is present or not. We then demonstrate use of the framework by setting up a simple within-host model that we connect to the population model. The example illustrates the context-specific information required for this type of model, and shows how the system can be simulated numerically. We verify that the formulas for the basic reproduction numbers correctly specify the invasibility conditions.

An Embedded Multiscale Modelling to Guide Control and Elimination of Paratuberculosis in Ruminants

In recent years, multiscale modelling approach has begun to receive an overwhelming appreciation as an appropriate technique to characterize the complexity of infectious disease systems. In this study, we develop an embedded multiscale model of paratuberculosis in ruminants at host level that integrates the within-host scale and the between-host. A key feature of embedded multiscale models developed at host level of organization of an infectious disease system is that the within-host scale and the between-host scale influence each other in a reciprocal (i.e., both) way through superinfection, that is, through repeated infection before the host recovers from the initial infectious episode. This key feature is demonstrated in this study through a multiscale model of paratuberculosis in ruminants. The results of this study, through numerical analysis of the multiscale model, show that superinfection influences the dynamics of paratuberculosis only at the start of the infection, while the MAP bacteria replication continuously influences paratuberculosis dynamics throughout the infection until the host recovers from the initial infectious episode. This is largely because the replication of MAP bacteria at the within-host scale sustains the dynamics of paratuberculosis at this scale domain. We further use the embedded multiscale model developed in this study to evaluate the comparative effectiveness of paratuberculosis health interventions that influence the disease dynamics at different scales from efficacy data.

Modeling and Research on an Immuno-Epidemiological Coupled System with Coinfection

In this paper, a two-strain model with coinfection that links immunological and epidemiological dynamics across scales is formulated. On the with-in host scale, the two strains eliminate each other with the strain having the larger immunological reproduction number persisting. However, on the population scale coinfection is a common occurrence. Individuals infected with strain one can become coinfected with strain two and similarly for individuals originally infected with strain two. The immunological reproduction numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{j}$$\end{document}Rj, the epidemiological reproduction numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{j}$$\end{document}Rj and invasion reproduction numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{j}^{i}$$\end{document}Rji are computed. Besides the disease-free equilibrium, there are strain one and strain two dominance equilibria. The disease-free equilibrium is locally asymptotically stable when the epidemiological reproduction numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{j}$$\end{document}Rj are smaller than one. In addition, each strain dominance equilibrium is locally asymptotically stable if the corresponding epidemiological reproduction number is larger than one and the invasion reproduction number of the other strain is smaller than one. The coexistence equilibrium exists when all the reproduction numbers are greater than one. Simulations suggest that when both invasion reproduction numbers are smaller than one, bistability occurs with one of the strains persisting or the other, depending on initial conditions.

Cross-scale dynamics and the evolutionary emergence of infectious diseases

When emerging pathogens encounter new host species for which they are poorly adapted, they must evolve to escape extinction. Pathogens experience selection on traits at multiple scales, including replication rates within host individuals and transmissibility between hosts. We analyze a stochastic model linking pathogen growth and competition within individuals to transmission between individuals. Our analysis reveals a new factor, the cross-scale reproductive number of a mutant virion, that quantifies how quickly mutant strains increase in frequency when they initially appear in the infected host population. This cross-scale reproductive number combines with viral mutation rates, single-strain reproductive numbers, and transmission bottleneck width to determine the likelihood of evolutionary emergence, and whether evolution occurs swiftly or gradually within chains of transmission. We find that wider transmission bottlenecks facilitate emergence of pathogens with short-term infections, but hinder emergence of pathogens exhibiting cross-scale selective conflict and long-term infections. Our results provide a framework to advance the integration of laboratory, clinical, and field data in the context of evolutionary theory, laying the foundation for a new generation of evidence-based risk assessment of emergence threats.

Patch dynamics modeling framework from pathogens' perspective: Unified and standardized approach for complicated epidemic systems

Mathematical models are powerful tools to investigate, simulate, and evaluate potential interventions for infectious diseases dynamics. Much effort has focused on the Susceptible-Infected-Recovered (SIR)-type compartment models. These models consider host populations and measure change of each compartment. In this study, we propose an alternative patch dynamic modeling framework from pathogens' perspective. Each patch, the basic module of this modeling framework, has four standard mechanisms of pathogen population size change: birth (replication), death, inflow, and outflow. This framework naturally distinguishes between-host transmission process (inflow and outflow) and within-host infection process (replication) during the entire transmission-infection cycle. We demonstrate that the SIR-type model is actually a special cross-sectional and discretized case of our patch dynamics model in pathogens' viewpoint. In addition, this patch dynamics modeling framework is also an agent-based model from hosts' perspective by incorporating individual host's specific traits. We provide an operational standard to formulate this modular-designed patch dynamics model. Model parameterization is feasible with a wide range of sources, including genomics data, surveillance data, electronic health record, and from other emerging technologies such as multiomics. We then provide two proof-of-concept case studies to tackle some of the existing challenges of SIR-type models: sexually transmitted disease and healthcare acquired infections. This patch dynamics modeling framework not only provides theoretical explanations to known phenomena, but also generates novel insights of disease dynamics from a more holistic viewpoint. It is also able to simulate and handle more complicated scenarios across biological scales such as the current COVID-19 pandemic.

An age-structured model for coupling within-host and between-host dynamics in environmentally-driven infectious diseases

In this paper, an age-structured epidemic model for coupling within-host and between-host dynamics in environmentally-driven infectious diseases is investigated. The model is described by a mixed system of ordinary and partial differential equations which is constituted by the within-host virus infectious fast time ordinary system and the between-host disease transmission slow time age-structured system. The isolated fast system has been investigated in previous literatures, and the main results are introduced. For the isolated slow system, the basic reproduction number R _b0, the positivity and ultimate boundedness of solutions are obtained, the existence of equilibria, the local stability of equilibria, and the global stability of disease-free equilibrium are established. We see that when R _b0 ≤ 1 the system only has the disease-free equilibrium which is globally asymptotically stable, and when R _b0 > 1 the system has a unique endemic equilibrium which is local asymptotically stable. With regard to the coupled slow system, the basic reproduction number R_b , the positivity and boundedness of solutions and the existence of equilibria are firstly obtained. Particularly, the coupled slow system can exist two positive equilibria when R_b  < 1 and a unique endemic equilibrium when R_b  > 1. When R_b  < 1 the disease-free equilibrium is local asymptotically stable, and when R_b  > 1 and an additional condition is satisfied the unique endemic equilibrium is local asymptotically stable. When there exist two positive equilibria, under an additional condition the local asymptotic stability of a positive equilibrium and the instability of other positive equilibrium also are established. The numerical examples show that the additional condition may be removed. The research shows that the coupled slow age-structured system has more complex dynamical behavior than the corresponding isolated slow system.

Declining trend in HIV new infections in Guangxi, China: insights from linking reported HIV/AIDS cases with CD4-at-diagnosis data

Background

The Guangxi Zhuang Autonomous Region bears a relatively high burden of HIV/AIDS infection. The number of accumulatively reported HIV/AIDS cases in Guangxi is the third highest among 31 provinces or Autonomous Region from 2004 to 2007, changed to the second highest between 2011 and 2013, then returned to the third highest again after 2014. We aim to estimate the new infections and evaluate the real-time HIV epidemic in Guangxi, China, in order to reveal the rule of HIV transmission.

Methods

Firstly, the number of annually reported HIV and AIDS cases, as well as the number of cases linked with CD4 data are extracted from the HIV/AIDS information system in China. Secondly, two CD4-staged models are formulated by linking the with-host information on CD4 level to between-host transmission and surveillance data. Thirdly, new HIV infections, diagnosis rates and undiagnosed infections over time are estimated by using Bayesian method and Maximum Likelihood Estimation method.

Results

The data reveal that the newly reported cases have been decreasing since 2011, while lots of cases are identified at late CD4 stage. The data fitted results indicate that both models can describe the trend of the epidemic well. The estimation results show that the new and undiagnosed infections began to decrease from the period2006 - 2008. However, the diagnosis probabilities/rates keep at a very low level, and there are still a large number of infections undiagnosed, most of which have a large probability to be identified at late CD4 stage.

Conclusions

Our findings suggest that HIV/AIDS epidemic in Guangxi has been controlled to a certain extent, while the diagnosis rate still needs to be improved. More attentions should be paid to identify infections at their early CD4 stages. Meanwhile, comprehensive intervention measures should be continually strengthened in avoid of the rebound of new infections.

Analysis of Multilevel Replicator Dynamics for General Two-Strategy Social Dilemma

Here, we consider a game-theoretic model of multilevel selection in which individuals compete based on their payoff and groups also compete based on the average payoff of group members. Our focus is on multilevel social dilemmas: games in which individuals are best off cheating, while groups of individuals do best when composed of many cooperators. We analyze the dynamics of the two-level replicator dynamics, a nonlocal hyperbolic PDE describing deterministic birth-death dynamics for both individuals and groups. While past work on such multilevel dynamics has restricted attention to scenarios with exactly solvable within-group dynamics, we use comparison principles and an invariant property of the tail of the population distribution to extend our analysis to all possible two-player, two-strategy social dilemmas. In the Stag-Hunt and similar games with coordination thresholds, we show that any amount of between-group competition allows for fixation of cooperation in the population. For the prisoners' dilemma and Hawk-Dove game, we characterize the threshold level of between-group selection dividing a regime in which the population converges to a delta function at the equilibrium of the within-group dynamics from a regime in which between-group competition facilitates the existence of steady-state densities supporting greater levels of cooperation. In particular, we see that the threshold selection strength and average payoff at steady state depend on a tug-of-war between the individual-level incentive to be a defector in a many-cooperator group and the group-level incentive to have many cooperators over many defectors. We also find that lower-level selection casts a long shadow: If groups are best off with a mix of cooperators and defectors, then there will always be fewer cooperators than optimal at steady state, even in the limit of infinitely strong competition between groups.

A theoretical framework for transitioning from patient-level to population-scale epidemiological dynamics: influenza A as a case study

Multi-scale epidemic forecasting models have been used to inform population-scale predictions with within-host models and/or infection data collected in longitudinal cohort studies. However, most multi-scale models are complex and require significant modelling expertise to run. We formulate an alternative multi-scale modelling framework using a compartmental model with multiple infected stages. In the large-compartment limit, our easy-to-use framework generates identical results compared to previous more complicated approaches. We apply our framework to the case study of influenza A in humans. By using a viral dynamics model to generate synthetic patient-level data, we explore the effects of limited and inaccurate patient data on the accuracy of population-scale forecasts. If infection data are collected daily, we find that a cohort of at least 40 patients is required for a mean population-scale forecasting error below 10%. Forecasting errors may be reduced by including more patients in future cohort studies or by increasing the frequency of observations for each patient. Our work, therefore, provides not only an accessible epidemiological modelling framework but also an insight into the data required for accurate forecasting using multi-scale models.

A Mathematical Framework for Predicting Lifestyles of Viral Pathogens

Despite being similar in structure, functioning, and size, viral pathogens enjoy very different, usually well-defined ways of life. They occupy their hosts for a few days (influenza), for a few weeks (measles), or even lifelong (HCV), which manifests in acute or chronic infections. The various transmission routes (airborne, via direct physical contact, etc.), degrees of infectiousness (referring to the viral load required for transmission), antigenic variation/immune escape and virulence define further aspects of pathogenic lifestyles. To survive, pathogens must infect new hosts; the success determines their fitness. Infection happens with a certain likelihood during contact of hosts, where contact can also be mediated by vectors. Besides structural aspects of the host-contact network, three parameters appear to be key: the contact rate and the infectiousness during contact, which encode the mode of transmission, and third the immunity of susceptible hosts. On these grounds, what can be said about the reproductive success of viral pathogens? This is the biological question addressed in this paper. The answer extends earlier results of the author and makes explicit connection to another basic work on the evolution of pathogens. A mathematical framework is presented that models intra- and inter-host dynamics in a minimalistic but unified fashion covering a broad spectrum of viral pathogens, including those that cause flu-like infections, childhood diseases, and sexually transmitted infections. These pathogens turn out as local maxima of numerically simulated fitness landscapes. The models involve differential and integral equations, agent-based simulation, networks, and probability.

Linking sex differences to the evolution of infectious disease life-histories

Sex differences in the prevalence, course and severity of infection are widespread, yet the evolutionary consequences of these differences remain unclear. Understanding how male-female differences affect the trajectory of infectious disease requires connecting the contrasting dynamics that pathogens might experience within each sex to the number of susceptible and infected individuals that are circulating in a population. In this study, we build on theory using genetic covariance functions to link the growth of a pathogen within a host to the evolution and spread of disease between individuals. Using the Daphnia-Pasteuria system as a test case, we show that on the basis of within-host dynamics alone, females seem to be more evolutionarily liable for the pathogen, with higher spore loads and greater divergence among pathogen genotypes as infection progresses. Between-host transmission, however, appears to offset the lower performance of a pathogen within a male host, making even subtle differences between the sexes evolutionarily relevant, as long as the selection generated by the between-host dynamics is sufficiently strong. Our model suggests that relatively simple differences in within-host processes occurring in males and females can lead to complex patterns of genetic constraint on pathogen evolution, particularly during an expanding epidemic.This article is part of the theme issue 'Linking local adaptation with the evolution of sex differences'.

On the diverse and opposing effects of nutrition on pathogen virulence

Climate change and anthropogenic activity are currently driving large changes in nutritional availability across ecosystems, with consequences for infectious disease. An increase in host nutrition could lead to more resources for hosts to expend on the immune system or for pathogens to exploit. In this paper, we report a meta-analysis of studies on host-pathogen systems across the tree of life, to examine the impact of host nutritional quality and quantity on pathogen virulence. We did not find broad support across studies for a one-way effect of nutrient availability on pathogen virulence. We thus discuss a hypothesis that there is a balance between the effect of host nutrition on the immune system and on pathogen resources, with the pivot point of the balance differing for vertebrate and invertebrate hosts. Our results suggest that variation in nutrition, caused by natural or anthropogenic factors, can have diverse effects on infectious disease outcomes across species.

A general framework for modelling the impact of co-infections on pathogen evolution

Theoretical models suggest that mixed-strain infections, or co-infections, are an important driver of pathogen evolution. However, the within-host dynamics of co-infections vary enormously, which complicates efforts to develop a general understanding of how co-infections affect evolution. Here, we develop a general framework which condenses the within-host dynamics of co-infections into a few key outcomes, the most important of which is the overall R0 of the co-infection. Similar to how fitness is determined by two different alleles in a heterozygote, the R0 of a co-infection is a product of the R0 values of the co-infecting strains, shaped by the interaction of those strains at the within-host level. Extending the analogy, we propose that the overall R0 reflects the dominance of the co-infecting strains, and that the ability of a mutant strain to invade a population is a function of its dominance in co-infections. To illustrate the utility of these concepts, we use a within-host model to show how dominance arises from the within-host dynamics of a co-infection, and then use an epidemiological model to demonstrate that dominance is a robust predictor of the ability of a mutant strain to save a maladapted wild-type strain from extinction (evolutionary emergence).

The replicator dynamics for multilevel selection in evolutionary games

We consider a stochastic model for evolution of group-structured populations in which interactions between group members correspond to the Prisoner's Dilemma or the Hawk-Dove game. Selection operates at two organization levels: individuals compete with peer group members based on individual payoff, while groups also compete with other groups based on average payoff of group members. In the Prisoner's Dilemma, this creates a tension between the two levels of selection, as defectors are favored at the individual level, whereas groups with at least some cooperators outperform groups of defectors at the between-group level. In the limit of infinite group size and infinite number of groups, we derive a non-local PDE that describes the probability distribution of group compositions in the population. For special families of payoff matrices, we characterize the long-time behavior of solutions of our equation, finding a threshold intensity of between-group selection required to sustain density steady states and the survival of cooperation. When all-cooperator groups are most fit, the average and most abundant group compositions at steady state range from featuring all-defector groups when individual-level selection dominates to featuring all-cooperator groups when group-level selection dominates. When the most fit groups have a mix of cooperators and defectors, then the average and most abundant group compositions always feature a smaller fraction of cooperators than required for the optimal mix, even in the limit where group-level selection is infinitely stronger than individual-level selection. In such cases, the conflict between the two levels of selection cannot be decoupled, and cooperation cannot be sustained at all in the case where between-group competition favors an even mix of cooperators and defectors.

The effect of the infection within the individual host on its propagation in the population

We consider nested or multiscale models to study the effect of the temporal evolution of the disease within the host in the population dynamics of the disease, for one and two infectious agents. We assumed a coupling between the within-host infection rate and the between-host transmission rate. The age of infection within each individual in a population affects the probability of transmission of the disease to a susceptible host and this will affect the temporal evolution of the disease in the host population. To analyze the infection within the host, we consider bacterial-like and viral-like infections. In the model for two infectious agents, we found that, when strain 2 has a basic reproduction number R 02 greater than the basic reproduction number R 01 of strain 1, strain 2 replaces strain 1 in the population. However, if R 02 > R 01 but the values are closer, the replacement does not occur immediately and both strains can coexist for a long time. We applied the model to a scenario in which patients infected with the hepatitis C virus (HCV) are cleared of HCV when super-infected with the hepatitis A virus (HAV). We compared the time for the replacement of HCV by HAV in the population considering instantaneous and non-instantaneous replacement within the individuals. The model developed can be generalized for more than two infectious agents.

Conflict and accord of optimal treatment strategies for HIV infection within and between hosts

Most of previous studies investigated the optimal control of HIV infection at either within-host or between-host level. However, the optimal treatment strategy for the individual may not be optimal for the population and vice versa. To determine when the two-level optimal controls are in accord or conflict, we develop a multi-scale model using various functions that link the viral load within host and the transmission rate between hosts, calibrated by cohort data. We obtain the within-host optimal treatment scheme that minimizes the viral load and maximizes the count of healthy cells at the individual level, and the coupled optimal scheme that minimizes the basic reproduction number at the population level. Mathematical analysis shows that whether the two-level optimal controls coincide depends on the sign of the product of their switching functions. Numerical results suggest that they are in accord for a high maximal drug efficacy but may conflict for a low drug efficacy. Using the multi-scale model, we also identify a threshold of the treatment effectiveness that determines how early treatment initiation can affect the disease dynamics among population. These results may help develop a synergistic treatment protocol beneficial to both HIV-infected individuals and the whole population.

Resource-driven changes to host population stability alter the evolution of virulence and transmission

What drives the evolution of parasite life-history traits? Recent studies suggest that linking within- and between-host processes can provide key insight into both disease dynamics and parasite evolution. Still, it remains difficult to understand how to pinpoint the critical factors connecting these cross-scale feedbacks, particularly under non-equilibrium conditions; many natural host populations inherently fluctuate and parasites themselves can strongly alter the stability of host populations. Here, we develop a general model framework that mechanistically links resources to parasite evolution across a gradient of stable and unstable conditions. First, we dynamically link resources and between-host processes (host density, stability, transmission) to virulence evolution, using a 'non-nested' model. Then, we consider a 'nested' model where population-level processes (transmission and virulence) depend on resource-driven changes to individual-level (within-host) processes (energetics, immune function, parasite production). Contrary to 'non-nested' model predictions, the 'nested' model reveals complex effects of host population dynamics on parasite evolution, including regions of evolutionary bistability; evolution can push parasites towards strongly or weakly stabilizing strategies. This bistability results from dynamic feedbacks between resource-driven changes to host density, host immune function and parasite production. Together, these results highlight how cross-scale feedbacks can provide key insights into the structuring role of parasites and parasite evolution.This article is part of the theme issue 'Anthropogenic resource subsidies and host-parasite dynamics in wildlife'.

Symbiont evolution during the free-living phase can improve host colonization

For micro-organisms cycling between free-living and host-associated stages, where reproduction occurs in both of these lifestyles, an interesting inquiry is whether evolution during the free-living stage can be positively pleiotropic to microbial fitness in a host environment. To address this topic, the squid host Euprymna tasmanica and the marine bioluminescent bacterium Vibrio fischeri were utilized. Microbial ecological diversification in static liquid microcosms was used to simulate symbiont evolution during the free-living stage. Thirteen genetically distinct V. fischeri strains from a broad diversity of ecological sources (e.g. squid light organs, fish light organs and seawater) were examined to see if the results were reproducible in many different genetic settings. Genetic backgrounds that are closely related can be predisposed to considerable differences in how they respond to similar selection pressures. For all strains examined, new mutations with striking and facilitating effects on host colonization arose quickly during microbial evolution in the free-living stage, regardless of the ecological context under consideration for a strain’s genetic background. Microbial evolution outside a host environment promoted host range expansion, improved host colonization for a micro-organism, and diminished the negative correlation between biofilm formation and motility.

A novel framework for inferring parameters of transmission from viral sequence data

Transmission between hosts is a critical part of the viral lifecycle. Recent studies of viral transmission have used genome sequence data to evaluate the number of particles transmitted between hosts, and the role of selection as it operates during the transmission process. However, the interpretation of sequence data describing transmission events is a challenging task. We here present a novel and comprehensive framework for using short-read sequence data to understand viral transmission events, designed for influenza virus, but adaptable to other viral species. Our approach solves multiple shortcomings of previous methods for this purpose; for example, we consider transmission as an event involving whole viruses, rather than sets of independent alleles. We demonstrate how selection during transmission and noisy sequence data may each affect naive inferences of the population bottleneck, accounting for these in our framework so as to achieve a correct inference. We identify circumstances in which selection for increased viral transmission may or may not be identified from data. Applying our method to experimental data in which transmission occurs in the presence of strong selection, we show that our framework grants a more quantitative insight into transmission events than previous approaches, inferring the bottleneck in a manner that accounts for selection, both for within-host virulence, and for inherent viral transmissibility. Our work provides new opportunities for studying transmission processes in influenza, and by extension, in other infectious diseases.

Effects of Transmission Bottlenecks on the Diversity of Influenza A Virus

We investigate the fate of de novo mutations that occur during the in-host replication of a pathogenic virus, predicting the probability that such mutations are passed on during disease transmission to a new host. Using influenza A virus as a model organism, we develop a life-history model of the within-host dynamics of the infection, deriving a multitype branching process with a coupled deterministic model to capture the population of available target cells. We quantify the fate of neutral mutations and mutations affecting five life-history traits: clearance, attachment, budding, cell death, and eclipse phase timing. Despite the severity of disease transmission bottlenecks, our results suggest that in a single transmission event, several mutations that appeared de novo in the donor are likely to be transmitted to the recipient. Even in the absence of a selective advantage for these mutations, the sustained growth phase inherent in each disease transmission cycle generates genetic diversity that is not eliminated during the transmission bottleneck.

Within-host dynamics and random duration of pathogen infection: Implications for between-host transmission

Taking an ecological perspective, this paper reports theoretical and empirical results concerning fatal bacterial infections of adult insects. Two models, each combining deterministic and stochastic elements, characterize how the pathogen's dynamics might govern an infected host's mortality rate. We analyze the models in detail for exponential pathogen growth, and apply them to observed insect mortality when the pathogen's growth is unregulated. We then allow bacteriophage to generate fluctuations in the within-host pathogen density; we demonstrate that only one of our models matches host mortality rates when pathogen growth is regulated by phage. We generalize our results on mortality hazard of individual hosts to analyze how random duration of the infectious period can combine with probabilistic transmission events to affect between-host transmission.

A discrete-time analog for coupled within-host and between-host dynamics in environmentally driven infectious disease

In this paper, we establish a discrete-time analog for coupled within-host and between-host systems for an environmentally driven infectious disease with fast and slow two time scales by using the non-standard finite difference scheme. The system is divided into a fast time system and a slow time system by using the idea of limit equations. For the fast system, the positivity and boundedness of the solutions, the basic reproduction number and the existence for infection-free and unique virus infectious equilibria are obtained, and the threshold conditions on the local stability of equilibria are established. In the slow system, except for the positivity and boundedness of the solutions, the existence for disease-free, unique endemic and two endemic equilibria are obtained, and the sufficient conditions on the local stability for disease-free and unique endemic equilibria are established. To return to the coupling system, the local stability for the virus- and disease-free equilibrium, and virus infectious but disease-free equilibrium is established. The numerical examples show that an endemic equilibrium is locally asymptotically stable and the other one is unstable when there are two endemic equilibria.

Variability in fitness effects can preclude selection of the fittest

Evolutionary biologists often predict the outcome of natural selection on an allele by measuring its effects on lifetime survival and reproduction of individual carriers. However, alleles affecting traits like sex, evolvability, and cooperation can cause fitness effects that depend heavily on differences in the environmental, social, and genetic context of individuals carrying the allele. This variability makes it difficult to summarize the evolutionary fate of an allele based solely on its effects on any one individual. Attempts to average over this variability can sometimes salvage the concept of fitness. In other cases evolutionary outcomes can only be predicted by considering the entire genealogy of an allele, thus limiting the utility of individual fitness altogether. We describe a number of intriguing new evolutionary phenomena that have emerged in studies that explicitly model long-term lineage dynamics and discuss implications for the evolution of infectious diseases.

Predicting HIV-1 transmission and antibody neutralization efficacy in vivo from stoichiometric parameters

The potential of broadly neutralizing antibodies targeting the HIV-1 envelope trimer to prevent HIV-1 transmission has opened new avenues for therapies and vaccines. However, their implementation remains challenging and would profit from a deepened mechanistic understanding of HIV-antibody interactions and the mucosal transmission process. In this study we experimentally determined stoichiometric parameters of the HIV-1 trimer-antibody interaction, confirming that binding of one antibody is sufficient for trimer neutralization. This defines numerical requirements for HIV-1 virion neutralization and thereby enables mathematical modelling of in vitro and in vivo antibody neutralization efficacy. The model we developed accurately predicts antibody efficacy in animal passive immunization studies and provides estimates for protective mucosal antibody concentrations. Furthermore, we derive estimates of the probability for a single virion to start host infection and the risks of male-to-female HIV-1 transmission per sexual intercourse. Our work thereby delivers comprehensive quantitative insights into both the molecular principles governing HIV-antibody interactions and the initial steps of mucosal HIV-1 transmission. These insights, alongside the underlying, adaptable modelling framework presented here, will be valuable for supporting in silico pre-trial planning and post-hoc evaluation of HIV-1 vaccination or antibody treatment trials.

On the principle of host evolution in host-pathogen interactions

In this paper, we use a two-host one pathogen immuno-epidemiological model to argue that the principle for host evolution, when the host is subjected to a fatal disease, is minimization of the case fatality proportion [Formula: see text]. This principle is valid whether the disease is chronic or leads to recovery. In the case of continuum of hosts, stratified by their immune response stimulation rate a, we suggest that [Formula: see text] has a minimum because a trade-off exists between virulence to the host induced by the pathogen and virulence induced by the immune response. We find that the minimization of the case fatality proportion is an evolutionary stable strategy for the host.

Disease dynamics in a coupled cholera model linking within-host and between-host interactions

A new modelling framework is proposed to study the within-host and between-host dynamics of cholera, a severe intestinal infection caused by the bacterium Vibrio cholerae. The within-host dynamics are characterized by the growth of highly infectious vibrios inside the human body. These vibrios shed from humans contribute to the environmental bacterial growth and the transmission of the disease among humans, providing a link from the within-host dynamics at the individual level to the between-host dynamics at the population and environmental level. A fast-slow analysis is conducted based on the two different time scales in our model. In particular, a bifurcation study is performed, and sufficient and necessary conditions are derived that lead to a backward bifurcation in cholera epidemics. Our result regarding the backward bifurcation highlights the challenges in the prevention and control of cholera.

Exposing the diversity of multiple infection patterns

Natural populations often have to cope with genetically distinct parasites that can coexist, or not, within the same hosts. Theoretical models addressing the evolution of virulence have considered two within host infection outcomes, namely superinfection and coinfection. The field somehow became limited by this dichotomy that does not correspond to an empirical reality as other infection patterns, namely sets of within-host infection outcomes, are possible. We indeed formally prove there are over one hundred different infection patterns solely for recoverable chronic infections caused by two genetically distinct horizontally-transmitted microparasites. We afterwards highlight eight infection patterns using an explicit modelling of within-host dynamics that captures a large range of ecological interactions, five of which have been neglected so far. To clarify the terminology related to multiple infections, we introduce terms describing these new relevant patterns and illustrate them with existing biological systems. These infection patterns constitute a new framework for linking within-host and between-host dynamics, which is a requirement to forward our understanding of the epidemiology and the evolution of parasites.

Models of Viral Population Dynamics

Models of viral population dynamics have contributed enormously to our understanding of the pathogenesis and transmission of several infectious diseases, the coevolutionary dynamics of viruses and their hosts, the mechanisms of action of drugs, and the effectiveness of interventions. In this chapter, we review major advances in the modeling of the population dynamics of the human immunodeficiency virus (HIV) and briefly discuss adaptations to other viruses.

Crossing the scale from within-host infection dynamics to between-host transmission fitness: a discussion of current assumptions and knowledge

The progression of an infection within a host determines the ability of a pathogen to transmit to new hosts and to maintain itself in the population. While the general connection between the infection dynamics within a host and the population-level transmission dynamics of pathogens is widely acknowledged, a comprehensive and quantitative understanding that would allow full integration of the two scales is still lacking. Here, we provide a brief discussion of both models and data that have attempted to provide quantitative mappings from within-host infection dynamics to transmission fitness. We present a conceptual framework and provide examples of studies that have taken first steps towards development of a quantitative framework that scales from within-host infections to population-level fitness of different pathogens. We hope to illustrate some general themes, summarize some of the recent advances and-maybe most importantly-discuss gaps in our ability to bridge these scales, and to stimulate future research on this important topic.

Early HAART Initiation May Not Reduce Actual Reproduction Number and Prevalence of MSM Infection: Perspectives from Coupled within- and between-Host Modelling Studies of Chinese MSM Populations

Having a thorough understanding of the infectivity of HIV, time of initiating treatment and emergence of drug resistant virus variants is crucial in mitigating HIV infection. There are many challenges to evaluating the long-term effect of the Highly Active Antiretroviral Therapy (HAART) on disease transmission at the population level. We proposed an individual based model by coupling within-host dynamics and between-host dynamics and conduct stochastic simulation in the group of men who have sex with men (MSM). The mean actual reproduction number is estimated to be 3.6320 (95% confidence interval: [3.46, 3.80]) for MSM group without treatment. Stochastic simulations show that given relatively high (low) level of drug efficacy after emergence of drug resistant variants, early initiation of treatment leads to a less (greater) actual reproduction number, lower (higher) prevalence and less (more) incidences, compared to late initiation of treatment. This implies early initiation of HAART may not always lower the actual reproduction number and prevalence of infection, depending on the level of treatment efficacy after emergence of drug resistant virus variants, frequency of high-risk behaviors and etc. This finding strongly suggests early initiation of HAART should be implemented with great care especially in the settings where the effective drugs are limited. Coupling within-host dynamics with between-host dynamics can provide critical information about impact of HAART on disease transmission and thus help to assist treatment strategy design and HIV/AIDS prevention and control.

An immuno-eco-epidemiological model of competition

This paper introduces a novel immuno-eco-epidemiological model of competition in which one of the species is affected by a pathogen. The infected individuals from species one are structured by time-since-infection and the within-host dynamics of the pathogen and the immune response is also modelled. A novel feature of the model is the impact of the species two numbers on the ability of species one to mount an immune response. The within-host model has three equilibria: an extinction equilibrium, pathogen-only equilibrium and pathogen and immune response equilibrium which exists if the immune response reproduction number R0 > 1. The extinction equilibrium is always unstable, the pathogen-only equilibrium is stable if R0 < 1, and the coexistence equilibrium is stable whenever it exists. The between-host competition model has six equilibria: an extinction equilibrium, three disease-free equilibria: species one-only equilibrium, species two-only equilibrium and a disease-free species coexistence equilibrium. There are also two disease-present equilibria: species one-only disease equilibrium and disease coexistence equilibrium. The existence and stability of these equilibria are governed by six reproduction numbers. Results show that for a non-fatal disease, the disease coexistence equilibrium is stable whenever it exists.

The role of pathogen shedding in linking within- and between-host pathogen dynamics

A model linking within- and between-host pathogen dynamics via pathogen shedding (emission of pathogens throughout the course of infection) is developed, and several aspects of host availability and co-infection are considered. In this model, the rate of pathogen shedding affects both the pathogen population size within a host (also affecting host mortality) and the rate of infection of new hosts. Our goal is to ascertain how the rate of shedding is likely to evolve, and what factors permit coexistence of alternative shedding rates in a pathogen population. For a constant host population size (where an increase in infected hosts necessarily decreases susceptible hosts), important differences arise depending on whether pathogens compete only for susceptible (uninfected) hosts, or whether co-infection allows for competition for infected hosts. With no co-infection, the pathogen type that can persist with the lowest number of susceptible hosts will outcompete any other, which under the assumptions of the model is the pathogen with the highest basic reproduction number. This is often a pathogen with a relatively high shedding rate (s). If within-host competition is allowed, a trade-off develops due to the conflicting effects of shedding on within- and between-host pathogen dynamics, with within-host competition favoring clones with low shedding rates while between-host competition benefits clones with higher shedding rates. With within-host competition for the same host cells, low shedding rate clones should eliminate high-s clones in a co-infected host, if equilibrium is reached. With co-infection, but no within-host competition, pathogen clones still interact by affecting the mortality of co-infected hosts; here, coexistence is more likely. With co-infection, two clones can coexist if one is the superior competitor for uninfected hosts and the other for co-infected hosts.

The adaptive evolution of virulence: a review of theoretical predictions and empirical tests

Why is it that some parasites cause high levels of host damage (i.e. virulence) whereas others are relatively benign? There are now numerous reviews of virulence evolution in the literature but it is nevertheless still difficult to find a comprehensive treatment of the theory and data on the subject that is easily accessible to non-specialists. Here we attempt to do so by distilling the vast theoretical literature on the topic into a set of relatively few robust predictions. We then provide a comprehensive assessment of the available empirical literature that tests these predictions. Our results show that there have been some notable successes in integrating theory and data but also that theory and empiricism in this field do not ‘speak’ to each other very well. We offer a few suggestions for how the connection between the two might be improved.

Fitness Inference from Short-Read Data: Within-Host Evolution of a Reassortant H5N1 Influenza Virus

We present a method to infer the role of selection acting during the within-host evolution of the influenza virus from short-read genome sequence data. Linkage disequilibrium between loci is accounted for by treating short-read sequences as noisy multilocus emissions from an underlying model of haplotype evolution. A hierarchical model-selection procedure is used to infer the underlying fitness landscape of the virus insofar as that landscape is explored by the viral population. In a first application of our method, we analyze data from an evolutionary experiment describing the growth of a reassortant H5N1 virus in ferrets. Across two sets of replica experiments we infer multiple alleles to be under selection, including variants associated with receptor binding specificity, glycosylation, and with the increased transmissibility of the virus. We identify epistasis as an important component of the within-host fitness landscape, and show that adaptation can proceed through multiple genetic pathways.

Could the human papillomavirus vaccines drive virulence evolution?

The human papillomavirus (HPV) vaccines hold great promise for preventing several cancers caused by HPV infections. Yet little attention has been given to whether HPV could respond evolutionarily to the new selection pressures imposed on it by the novel immunity response created by the vaccine. Here, we present and theoretically validate a mechanism by which the vaccine alters the transmission-recovery trade-off that constrains HPV's virulence such that higher oncogene expression is favoured. With a high oncogene expression strategy, the virus is able to increase its viral load and infected cell population before clearance by the vaccine, thus improving its chances of transmission. This new rapid cell-proliferation strategy is able to circulate between hosts with medium to high turnover rates of sexual partners. We also discuss the importance of better quantifying the duration of challenge infections and the degree to which a vaccinated host can shed virus. The generality of the models presented here suggests a wider applicability of this mechanism, and thus highlights the need to investigate viral oncogenicity from an evolutionary perspective.