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

Open questions in the social lives of viruses

Social interactions among viruses occur whenever multiple viral genomes infect the same cells, hosts, or populations of hosts. Viral social interactions range from cooperation to conflict, occur throughout the viral world, and affect every stage of the viral lifecycle. The ubiquity of these social interactions means that they can determine the population dynamics, evolutionary trajectory, and clinical progression of viral infections. At the same time, social interactions in viruses raise new questions for evolutionary theory, providing opportunities to test and extend existing frameworks within social evolution. Many opportunities exist at this interface: Insights into the evolution of viral social interactions have immediate implications for our understanding of the fundamental biology and clinical manifestation of viral diseases. However, these opportunities are currently limited because evolutionary biologists only rarely study social evolution in viruses. Here, we bridge this gap by (1) summarizing the ways in which viruses can interact socially, including consequences for social evolution and evolvability; (2) outlining some open questions raised by viruses that could challenge concepts within social evolution theory; and (3) providing some illustrative examples, data sources, and conceptual questions, for studying the natural history of social viruses.

Machine learning aided multiscale modelling of the HIV-1 infection in the presence of NRTI therapy

Human Immunodeficiency Virus (HIV) is one of the most common chronic infectious diseases in humans. Extending the expected lifetime of patients depends on the use of optimal antiretroviral therapies. Emergence of the drug-resistant strains can reduce the effectiveness of treatments and lead to Acquired Immunodeficiency Syndrome (AIDS), even with antiretroviral therapy. Investigating the genotype-phenotype relationship is a crucial process for optimizing the therapy protocols of the patients. Here, a mathematical modelling framework is proposed to address the impact of existing mutations, timing of initiation, and adherence levels of nucleotide reverse transcriptase inhibitors (NRTIs) on the evolutionary dynamics of the virus strains. For the first time, the existing Stanford HIV drug resistance data have been combined with a multi-strain within-host ordinary differential equation (ODE) model to track the dynamics of the most common NRTI-resistant strains. Overall, the D4T-3TC, D4T-AZT and TDF-D4T drug combinations have been shown to provide higher success rates in preventing treatment failure and further drug resistance. The results are in line with the genotype-phenotype data and pharmacokinetic parameters of the NRTI inhibitors. Moreover, we show that the undetectable mutant strains at the diagnosis have a significant effect on the success/failure rates of the NRTI treatments. Predictions on undetectable strains through our multi-strain within-host model yielded the possible role of viral evolution on the treatment outcomes. It has been recognized that the improvement of multi-scale models can contribute to the understanding of the evolutionary dynamics, and treatment options, and potentially increase the reliability of genotype-phenotype models.

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.

Stability and Hopf bifurcation of an HIV infection model with two time delays

This work focuses on an HIV infection model with intracellular delay and immune response delay, in which the former delay refers to the time it takes for healthy cells to become infectious after infection, and the latter delay refers to the time when immune cells are activated and induced by infected cells. By investigating the properties of the associated characteristic equation, we derive sufficient criteria for the asymptotic stability of the equilibria and the existence of Hopf bifurcation to the delayed model. Based on normal form theory and center manifold theorem, the stability and the direction of the Hopf bifurcating periodic solutions are studied. The results reveal that the intracellular delay cannot affect the stability of the immunity-present equilibrium, but the immune response delay can destabilize the stable immunity-present equilibrium through the Hopf bifurcation. Numerical simulations are provided to support the theoretical results.

Modelling: Understanding pandemics and how to control them

New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.

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.

Transmitted HIV-1 is more virulent in heterosexual individuals than men-who-have-sex-with-men

Transmission bottlenecks introduce selection pressures on HIV-1 that vary with the mode of transmission. Recent studies on small cohorts have suggested that stronger selection pressures lead to fitter transmitted/founder (T/F) strains. Manifestations of this selection bias at the population level have remained elusive. Here, we analysed early CD4 cell count measurements reported from ∼340,000 infected heterosexual individuals (HET) and men-who-have-sex-with-men (MSM), across geographies, ethnicities and calendar years. The reduction in CD4 counts early in infection is reflective of the virulence of T/F strains. MSM and HET use predominant modes of transmission, namely, anal and penile-vaginal, with among the largest differences in the selection pressures at transmission across modes. Further, in most geographies, the groups show little inter-mixing, allowing for the differential selection bias to be sustained and amplified. We found that the early reduction in CD4 counts was consistently greater in HET than MSM (P<0.05). To account for inherent variations in baseline CD4 counts, we constructed a metric to quantify the extent of progression to AIDS as the ratio of the reduction in measured CD4 counts from baseline and the reduction associated with AIDS. We found that this progression corresponding to the early CD4 measurements was ∼68% for MSM and ∼87% for HET on average (P<10⁻⁴; Cohen’s d, d_s = 0.36), reflecting the more severe disease caused by T/F strains in HET than MSM at the population level. Interestingly, the set-point viral load was not different between the groups (d_s<0.12), suggesting that MSM were more tolerant and not more resistant to their T/F strains than HET. This difference remained when we controlled for confounding factors using multivariable regression. We concluded that the different selection pressures at transmission have resulted in more virulent T/F strains in HET than MSM. These findings have implications for our understanding of HIV-1 pathogenesis, evolution, and epidemiology.

HIV-1 encounters a key bottleneck at the time of its transmission from one individual to another. This transmission bottleneck can differ between modes of transmission. The stronger this bottleneck is, the more fit the virus has to be to be successfully transmitted. Accordingly, the transmitted/founder (T/F) strains of HIV-1 may have different fitness in risk groups that use different modes of transmission. While studies on small cohorts do support this notion, observations of the manifestations of this differential selection bias at the population level have been lacking. Here, we examined reported early CD4 count measurements from ∼340,000 HET and MSM, across geographies, ethnicities, and calendar years. Early CD4 counts are a measure of the severity of the infection due to T/F strains. HET and MSM transmit predominantly via penile-vaginal and anal modes, respectively, and do not inter-mix significantly. Remarkably, we found that HET consistently had lower early CD4 counts than MSM. This difference could not be attributed to potential confounding factors, such as set-point viral load. The difference thus provided evidence that T/F strains had evolved to be more virulent in HET than MSM at the population level. Intervention strategies may benefit from accounting for this difference between risk groups.

Backward bifurcation in within-host HIV models

The activation and proliferation of naive CD4 T cells produce helper T cells, and increase the susceptible population in the presence of HIV. This may cause backward bifurcation. To verify this, we construct a simple within-host HIV model that includes the key variables, namely healthy naive CD4 T cells, helper T cells, infected CD4 T cells and virus. When the viral basic reproduction number R₀ is less than unity, we show theoretically and numerically that bistability for R_C<R₀<1 can be caused by a backward bifurcation due to a new susceptible population produced by activation of healthy naive CD4 T cells that become helper T cells. An extended model including the CTL dynamics may also show this backward bifurcation. In the case that the homeostatic source of healthy naive CD4 T cells is large, R_C is approximately the threshold for HIV to persist independent of initial conditions. The backward bifurcation may still occur even when we consider latent infections of naive CD4 T cells. Thus to control the spread of within-host HIV, it may be necessary for treatment to reduce the reproduction number below R_C.

A Network Immuno-Epidemiological HIV Model

In this paper we formulate a multi-scale nested immuno-epidemiological model of HIV on complex networks. The system is described by ordinary differential equations coupled with a partial differential equation. First, we prove the existence and uniqueness of the immunological model and then establish the well-posedness of the multi-scale model. We derive an explicit expression of the basic reproduction number [Formula: see text] of the immuno-epidemiological model. The system has a disease-free equilibrium and an endemic equilibrium. The disease-free equilibrium is globally stable when [Formula: see text] and unstable when [Formula: see text]. Numerical simulations suggest that [Formula: see text] increases as the number of nodes in the network increases. Further, we find that for a scale-free network the number of infected individuals at equilibrium is a hump-like function of the within-host reproduction number; however, the dependence becomes monotone if the network has predominantly low connectivity nodes or high connectivity nodes.

Superinfection and the evolution of an initial asymptomatic stage

Pathogens have evolved a variety of life-history strategies. An important strategy consists of successful transmission by an infected host before the appearance of symptoms, that is, while the host is still partially or fully asymptomatic. During this initial stage of infection, it is possible for another pathogen to superinfect an already infected host and replace the previously infecting pathogen. Here, we study the effect of superinfection during the first stage of an infection on the evolutionary dynamics of the degree to which the host is asymptomatic (host latency) in that same stage. We find that superinfection can lead to major differences in evolutionary behaviour. Most strikingly, the duration of immunity following infection can significantly influence pathogen evolutionary dynamics, whereas without superinfection the outcomes are independent of host immunity. For example, changes in host immunity can drive evolutionary transitions from a fully symptomatic to a fully asymptomatic first infection stage. Additionally, if superinfection relative to susceptible infection is strong enough, evolution can lead to a unique strategy of latency that corresponds to a local fitness minimum, and is therefore invasible by nearby mutants. Thus, this strategy is a branching point, and can lead to coexistence of pathogens with different latencies. Furthermore, in this new framework with superinfection, we also find that there can exist two interior singular strategies. Overall, new evolutionary outcomes can cascade from superinfection.

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.

Within-Host Phenotypic Evolution and the Population-Level Control of Chronic Viral Infections by Treatment and Prophylaxis

Chronic viral infections can persist for decades spanning thousands of viral generations, leading to a highly diverse population of viruses with its own complex evolutionary history. We propose an expandable mathematical framework for understanding how the emergence of genetic and phenotypic diversity affects the population-level control of those infections by both non-curative treatment and chemo-prophylactic measures. Our frameworks allows both neutral and phenotypic evolution, and we consider the specific evolution of contagiousness, resistance to therapy, and efficacy of prophylaxis. We compute both the controlled and uncontrolled, population-level basic reproduction number accounting for the within-host evolutionary process where new phenotypes emerge and are lost in infected persons, which we also extend to include both treatment and prophylactic control efforts. We used these results to discuss the conditions under which the relative efficacy of prophylactic versus therapeutic methods of control are superior. Finally, we give expressions for the endemic equilibrium of these models for certain constrained versions of the within-host evolutionary model providing a potential method for estimating within-host evolutionary parameters from population-level genetic sequence data.

How mechanistic modelling supports decision making for the control of enzootic infectious diseases

Controlling enzootic diseases, which generate a large cumulative burden and are often unregulated, is needed for sustainable farming, competitive agri-food chains, and veterinary public health. We discuss the benefits and challenges of mechanistic epidemiological modelling for livestock enzootics, with particular emphasis on the need for interdisciplinary approaches. We focus on issues arising when modelling pathogen spread at various scales (from farm to the region) to better assess disease control and propose targeted options. We discuss in particular the inclusion of farmers' strategic decision-making, the integration of within-host scale to refine intervention targeting, and the need to ground models on data.

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.

Ecological scaffolding and the evolution of individuality

Evolutionary transitions in individuality are central to the emergence of biological complexity. Recent experiments provide glimpses of processes underpinning the transition from single cells to multicellular life and draw attention to the critical role of ecology. Here, we emphasize this ecological dimension and argue that its current absence from theoretical frameworks hampers development of general explanatory solutions. Using mechanistic mathematical models, we show how a minimal ecological structure comprising patchily distributed resources and between-patch dispersal can scaffold Darwinian-like properties on collectives of cells. This scaffolding causes cells to participate directly in the process of evolution by natural selection as if they were members of multicellular collectives, with collectives participating in a death-birth process arising from the interplay between the timing of dispersal events and the rate of resource use by cells. When this timescale is sufficiently long and new collectives are founded by single cells, collectives experience conditions that favour evolution of a reproductive division of labour. Together our simple model makes explicit key events in the major evolutionary transition to multicellularity. It also makes predictions concerning the life history of certain pathogens and serves as an ecological recipe for experimental realization of evolutionary transitions.

Prisoners of war - host adaptation and its constraints on virus evolution

Recent discoveries of contemporary genotypes of hepatitis B virus and parvovirus B19 in ancient human remains demonstrate that little genetic change has occurred in these viruses over 4,500-6,000 years. Endogenous viral elements in host genomes provide separate evidence that viruses similar to many major contemporary groups circulated 100 million years ago or earlier. In this Opinion article, we argue that the extraordinary conservation of virus genome sequences is best explained by a niche-filling model in which fitness optimization is rapidly achieved in their specific hosts. Whereas short-term substitution rates reflect the accumulation of tolerated sequence changes within adapted genomes, longer-term rates increasingly resemble those of their hosts as the evolving niche moulds and effectively imprisons the virus in co-adapted virus-host relationships. Contrastingly, viruses that jump hosts undergo strong and stringent adaptive selection as they maximize their fit to their new niche. This adaptive capability may paradoxically create evolutionary stasis in long-term host relationships. While viruses can evolve and adapt rapidly, their hosts may ultimately shape their longer-term evolution.

A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment

In the present paper we propose a simple time-varying ODE model to describe the evolution of HIV epidemic in Italy. The model considers a single population of susceptibles, without distinction of high-risk groups within the general population, and accounts for the presence of immigration and emigration, modelling their effects on both the general demography and the dynamics of the infected subpopulations. To represent the intra-host disease progression, the untreated infected population is distributed over four compartments in cascade according to the CD4 counts. A further compartment is added to represent infected people under antiretroviral therapy. The per capita exit rate from treatment, due to voluntary interruption or failure of therapy, is assumed variable with time. The values of the model parameters not reported in the literature are assessed by fitting available epidemiological data over the decade 2003÷2012. Predictions until year 2025 are computed, enlightening the impact on the public health of the early initiation of the antiretroviral therapy. The benefits of this change in the treatment eligibility consist in reducing the HIV incidence rate, the rate of new AIDS cases, and the rate of death from AIDS. Analytical results about properties of the model in its time-invariant form are provided, in particular the global stability of the equilibrium points is established either in the absence and in the presence of infected among immigrants.

Multi-scale immunoepidemiological modeling of within-host and between-host HIV dynamics: systematic review of mathematical models

OBJECTIVE

The objective of this study is to conduct a systematic review of multi-scale HIV immunoepidemiological models to improve our understanding of the synergistic impact between the HIV viral-immune dynamics at the individual level and HIV transmission dynamics at the population level.

BACKGROUND

While within-host and between-host models of HIV dynamics have been well studied at a single scale, connecting the immunological and epidemiological scales through multi-scale models is an emerging method to infer the synergistic dynamics of HIV at the individual and population levels.

METHODS

We reviewed nine articles using the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) framework that focused on the synergistic dynamics of HIV immunoepidemiological models at the individual and population levels.

RESULTS

HIV immunoepidemiological models simulate viral immune dynamics at the within-host scale and the epidemiological transmission dynamics at the between-host scale. They account for longitudinal changes in the immune viral dynamics of HIV+ individuals, and their corresponding impact on the transmission dynamics in the population. They are useful to analyze the dynamics of HIV super-infection, co-infection, drug resistance, evolution, and treatment in HIV+ individuals, and their impact on the epidemic pathways in the population. We illustrate the coupling mechanisms of the within-host and between-host scales, their mathematical implementation, and the clinical and public health problems that are appropriate for analysis using HIV immunoepidemiological models.

CONCLUSION

HIV immunoepidemiological models connect the within-host immune dynamics at the individual level and the epidemiological transmission dynamics at the population level. While multi-scale models add complexity over a single-scale model, they account for the time varying immune viral response of HIV+ individuals, and the corresponding impact on the time-varying risk of transmission of HIV+ individuals to other susceptibles in the population.

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.

Short-Sighted Virus Evolution and a Germline Hypothesis for Chronic Viral Infections

With extremely short generation times and high mutability, many viruses can rapidly evolve and adapt to changing environments. This ability is generally beneficial to viruses as it allows them to evade host immune responses, evolve new behaviours, and exploit ecological niches. However, natural selection typically generates adaptation in response to the immediate selection pressures that a virus experiences in its current host. Consequently, we argue that some viruses, particularly those characterised by long durations of infection and ongoing replication, may be susceptible to short-sighted evolution, whereby a virus' adaptation to its current host will be detrimental to its onward transmission within the host population. Here we outline the concept of short-sighted viral evolution and provide examples of how it may negatively impact viral transmission among hosts. We also propose that viruses that are vulnerable to short-sighted evolution may exhibit strategies that minimise its effects. We speculate on the various mechanisms by which this may be achieved, including viral life history strategies that result in low rates of within-host evolution, or the establishment of a 'germline' lineage of viruses that avoids short-sighted evolution. These concepts provide a new perspective on the way in which some viruses have been able to establish and maintain global pandemics.

Modelling the evolution of HIV-1 virulence in response to imperfect therapy and prophylaxis

Average HIV-1 virulence appears to have evolved in different directions in different host populations since antiretroviral therapy first became available, and models predict that HIV drugs can select for either higher or lower virulence, depending on how treatment is administered. However, HIV virulence evolution in response to "leaky" therapy (treatment that imperfectly suppresses viral replication) and the use of preventive drugs (pre-exposure prophylaxis) has not been explored. Using adaptive dynamics, we show that higher virulence can evolve when antiretroviral therapy is imperfectly effective and that this evolution erodes some of the long-term clinical and epidemiological benefits of HIV treatment. The introduction of pre-exposure prophylaxis greatly reduces infection prevalence, but can further amplify virulence evolution when it, too, is leaky. Increasing the uptake rate of these imperfect interventions increases selection for higher virulence and can lead to counterintuitive increases in infection prevalence in some scenarios. Although populations almost always fare better with access to interventions than without, untreated individuals could experience particularly poor clinical outcomes when virulence evolves. These findings predict that antiretroviral drugs may have underappreciated evolutionary consequences, but that maximizing drug efficacy can prevent this evolutionary response. We suggest that HIV virulence evolution should be closely monitored as access to interventions continues to improve.

Effect of the Latent Reservoir on the Evolution of HIV at the Within- and Between-Host Levels

The existence of long-lived reservoirs of latently infected CD4+ T cells is the major barrier to curing HIV, and has been extensively studied in this light. However, the effect of these reservoirs on the evolutionary dynamics of the virus has received little attention. Here, we present a within-host quasispecies model that incorporates a long-lived reservoir, which we then nest into an epidemiological model of HIV dynamics. For biologically plausible parameter values, we find that the presence of a latent reservoir can severely delay evolutionary dynamics within a single host, with longer delays associated with larger relative reservoir sizes and/or homeostatic proliferation of cells within the reservoir. These delays can fundamentally change the dynamics of the virus at the epidemiological scale. In particular, the delay in within-host evolutionary dynamics can be sufficient for the virus to evolve intermediate viral loads consistent with maximising transmission, as is observed, and not the very high viral loads that previous models have predicted, an effect that can be further enhanced if viruses similar to those that initiate infection are preferentially transmitted. These results depend strongly on within-host characteristics such as the relative reservoir size, with the evolution of intermediate viral loads observed only when the within-host dynamics are sufficiently delayed. In conclusion, we argue that the latent reservoir has important, and hitherto under-appreciated, roles in both within- and between-host viral evolution.

Large Variations in HIV-1 Viral Load Explained by Shifting-Mosaic Metapopulation Dynamics

The viral population of HIV-1, like many pathogens that cause systemic infection, is structured and differentiated within the body. The dynamics of cellular immune trafficking through the blood and within compartments of the body has also received wide attention. Despite these advances, mathematical models, which are widely used to interpret and predict viral and immune dynamics in infection, typically treat the infected host as a well-mixed homogeneous environment. Here, we present mathematical, analytical, and computational results that demonstrate that consideration of the spatial structure of the viral population within the host radically alters predictions of previous models. We study the dynamics of virus replication and cytotoxic T lymphocytes (CTLs) within a metapopulation of spatially segregated patches, representing T cell areas connected by circulating blood and lymph. The dynamics of the system depend critically on the interaction between CTLs and infected cells at the within-patch level. We show that for a wide range of parameters, the system admits an unexpected outcome called the shifting-mosaic steady state. In this state, the whole body’s viral population is stable over time, but the equilibrium results from an underlying, highly dynamic process of local infection and clearance within T-cell centers. Notably, and in contrast to previous models, this new model can explain the large differences in set-point viral load (SPVL) observed between patients and their distribution, as well as the relatively low proportion of cells infected at any one time, and alters the predicted determinants of viral load variation.

A novel metapopulation model of HIV suggests that within-host infections are characterized by a highly dynamic process of localized infection followed by clearance within T cell centers.

When a person is infected with HIV, the initial peak level of virus in the blood is usually very high before a lower, relatively stable level is reached and maintained for the duration of the chronic infection. This stable level is known as the set-point viral load (SPVL) and is associated with severity of infection. SPVL is also highly variable among patients, ranging from 100 to a million copies of the virus per mL of blood. The replicative capacity of the infecting virus and the strength of the immune response both influence SPVL. However, standard mathematical models show that variation in these two factors cannot easily reproduce the observed distribution of SPVL among patients. Standard models typically treat infected individuals as well-mixed systems, but in reality viral replication is localised in T-cell centres, or patches, found in secondary lymphoid tissue. To account for this population structure, we developed a carefully parameterised metapopulation model. We find the system can reach a steady state at which the viral load in the blood is relatively stable, representing SPVL, but surprisingly, the patches are highly dynamic, characterised by bursts of infection followed by elimination of virus due to localised host immune responses. Significantly, this model can reproduce the wide distribution of SPVLs found among infected individuals for realistic distributions of viral replicative capacity and strength of immune response. Our model can also be used in the future to understand other aspects of chronic HIV infection.

Prognostic Value of HIV-1 RNA on CD4 Trajectories and Disease Progression Among Antiretroviral-Naive HIV-Infected Adults in Botswana: A Joint Modeling Analysis

Although HIV-1 RNA levels are measured at the time of initial diagnosis, the results are not used for the clinical follow-up of the patients. This study evaluates the prognostic value of the baseline HIV-1 RNA levels (above or below 10,000 copies/ml) on rate of disease progression, among antiretroviral therapy (ART)-naive patients in Botswana. A prospective cohort of 436 HIV-infected ART-naive adults with baseline CD4 > 400 cells/mm(3) were followed quarterly for 5 years in an urban clinic in Botswana. Baseline HIV-1 RNA levels and longitudinal CD4(+) T-cell count data were analyzed, using mixed-effects regression jointly modeled with the times to a composite endpoint defined by AIDS-defining clinical conditions or death. During 1,547 person-years (PYs) follow-up time, 106 individuals became eligible for ART initiation (incidence rate: 0.07 PYs) and 6 participants died of AIDS-related illness. There were 203 (47%) individuals with baseline HIV-1 RNA <10,000 copies/ml and 233 (53%) individuals with baseline RNA >10,000 copies/ml. The slope of the predicted CD4 trajectory for individuals with baseline HIV-1 RNA >10,000 copies/ml is 30% steeper than that for those with baseline RNA <10,000. The hazard of reaching the composite endpoint for the individuals with baseline HIV-1 RNA >10,000 copies/ml was 2.3 (95% confidence interval: 1.5-3.0) times higher than that for those with baseline HIV-1 RNA <10,000 copies/ml. CD4 decline in individuals with HIV-1 RNA >10,000 copies/ml is much faster than that in those with RNA <10,000. The elevated HIV-1 RNA can be used as a marker to identify individuals at risk of faster disease progression.

Connecting within-host dynamics to the rate of viral molecular evolution

Viruses evolve rapidly, providing a unique system for understanding the processes that influence rates of molecular evolution. Neutral theory posits that the evolutionary rate increases linearly with the mutation rate. The occurrence of deleterious mutations causes this relationship to break down at high mutation rates. Previous studies have identified this as an important phenomenon, particularly for RNA viruses which can mutate at rates near the extinction threshold. We propose that in addition to mutation dynamics, viral within-host dynamics can also affect the between-host evolutionary rate. We present an analytical model that predicts the neutral evolution rate for viruses as a function of both within-host parameters and deleterious mutations. To examine the effect of more detailed aspects of the virus life cycle, we also present a computational model that simulates acute virus evolution using target cell-limited dynamics. Using influenza A virus as a case study, we find that our simulation model can predict empirical rates of evolution better than a model lacking within-host details. The analytical model does not perform as well as the simulation model but shows how the within-host basic reproductive number influences evolutionary rates. These findings lend support to the idea that the mutation rate alone is not sufficient to predict the evolutionary rate in viruses, instead calling for improved models that account for viral within-host dynamics.

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.

Disentangling the impact of within-host evolution and transmission dynamics on the tempo of HIV-1 evolution

OBJECTIVE

To determine how HIV-1 risk groups impact transmitted diversity and the tempo of viral evolution at a population scale.

METHODS

We investigated a set of previously described transmission chains (n = 70) using a population genetic approach, and tested whether the expected differences in proportions of multivariant transmissions are reflected by varying proportions of transmitted diversity between men having sex with men (MSM) and heterosexual (HET) subpopulations - the largest contributors to HIV spread. To assess evolutionary rate differences among the different risk groups, we compiled risk group datasets for subtypes A1, B and CRF01_AE, and directly compared the absolute substitution rate and its synonymous and non-synonymous components.

RESULTS

There was sufficient demographic signal to inform the transmission model in Bayesian evolutionary analysis by sampling trees using env data to compare the transmission bottleneck size between the MSM and HET risk groups. We found no indications for a different proportion of transmitted genetic diversity at the population level between these groups. In the direct rate comparisons between the risk groups, however, we consistently recovered a higher evolutionary rate in the male-dominated risk group compared to the HET datasets.

CONCLUSION

We find that the risk group composition affects the viral evolutionary rate and therefore potentially also the adaptation rate. In particular, risk group-specific sex ratios, and the variation in within-host evolutionary rates between men and women, impose evolutionary rate differences at the epidemic level, but we cannot exclude a role of varying transmission rates.

Adaptive virulence evolution: the good old fitness-based approach

Infectious diseases could be expected to evolve towards complete avirulence to their hosts if given enough time. However, this is not the case. Often, virulence is maintained because it is linked to adaptive advantages to the parasite, a situation that is often associated with the hypothesis known as the transmission-virulence trade-off hypothesis. Here, we argue that this hypothesis has three limitations, which are related to how virulence is defined, the possibility of multiple trade-offs, and the difficulty of testing the hypothesis empirically. By adopting a fitness-based approach, where the relation between virulence and the fitness of the parasite throughout its life cycle is directly assessed, it is possible to address these limitations and to determine directly whether virulence is adaptive.

High heritability is compatible with the broad distribution of set point viral load in HIV carriers

Set point viral load in HIV patients ranges over several orders of magnitude and is a key determinant of disease progression in HIV. A number of recent studies have reported high heritability of set point viral load implying that viral genetic factors contribute substantially to the overall variation in viral load. The high heritability is surprising given the diversity of host factors associated with controlling viral infection. Here we develop an analytical model that describes the temporal changes of the distribution of set point viral load as a function of heritability. This model shows that high heritability is the most parsimonious explanation for the observed variance of set point viral load. Our results thus not only reinforce the credibility of previous estimates of heritability but also shed new light onto mechanisms of viral pathogenesis.

Following an initial peak in viremia, the viral load in HIV infected patients settles down to a set point which remains more or less stable during chronic HIV infection. This set point viral load is one of the key factors determining the rate of disease progression. The extent to which it is determined by the virus versus host genetics is thus central to developing a better understanding of disease progression. Here we develop an analytical model that describes the changes of the distribution of set point viral load in the HIV carrier population over a full cycle of transmission. Applying this model to patient data we find that the most parsimonious explanation for the observed large variation of set point viral load across HIV patients is that set point viral load is highly heritable from donors to recipients. This implies that set point viral load is to a considerable extent under the genetic control of the virus.

Immuno-epidemiological modeling of HIV-1 predicts high heritability of the set-point virus load, while selection for CTL escape dominates virulence evolution

It has been suggested that HIV-1 has evolved its set-point virus load to be optimized for transmission. Previous epidemiological models and studies into the heritability of set-point virus load confirm that this mode of adaptation within the human population is feasible. However, during the many cycles of replication between infection of a host and transmission to the next host, HIV-1 is under selection for escape from immune responses, and not transmission. Here we investigate with computational and mathematical models how these two levels of selection, within-host and between-host, are intertwined. We find that when the rate of immune escape is comparable to what has been observed in patients, immune selection within hosts is dominant over selection for transmission. Surprisingly, we do find high values for set-point virus load heritability, and argue that high heritability estimates can be caused by the 'footprints' left by differing hosts' immune systems on the virus.

Seven challenges in modeling pathogen dynamics within-host and across scales

The population dynamics of infectious disease is a mature field in terms of theory and to some extent, application. However for microparasites, the theory and application of models of the dynamics within a single infected host is still an open field. Further, connecting across the scales--from cellular to host level, to population level--has potential to vastly improve our understanding of pathogen dynamics and evolution. Here, we highlight seven challenges in the following areas: transmission bottlenecks, heterogeneity within host, dynamic fitness landscapes within hosts, making use of next-generation sequencing data, capturing superinfection and when and how to model more than two scales.

Seven challenges for metapopulation models of epidemics, including households models

This paper considers metapopulation models in the general sense, i.e. where the population is partitioned into sub-populations (groups, patches,...), irrespective of the biological interpretation they have, e.g. spatially segregated large sub-populations, small households or hosts themselves modelled as populations of pathogens. This framework has traditionally provided an attractive approach to incorporating more realistic contact structure into epidemic models, since it often preserves analytic tractability (in stochastic as well as deterministic models) but also captures the most salient structural inhomogeneity in contact patterns in many applied contexts. Despite the progress that has been made in both the theory and application of such metapopulation models, we present here several major challenges that remain for future work, focusing on models that, in contrast to agent-based ones, are amenable to mathematical analysis. The challenges range from clarifying the usefulness of systems of weakly-coupled large sub-populations in modelling the spread of specific diseases to developing a theory for endemic models with household structure. They include also developing inferential methods for data on the emerging phase of epidemics, extending metapopulation models to more complex forms of human social structure, developing metapopulation models to reflect spatial population structure, developing computationally efficient methods for calculating key epidemiological model quantities, and integrating within- and between-host dynamics in models.

An HIV epidemic model based on viral load dynamics: value in assessing empirical trends in HIV virulence and community viral load

Trends in HIV virulence have been monitored since the start of the AIDS pandemic, as studying HIV virulence informs our understanding of HIV epidemiology and pathogenesis. Here, we model changes in HIV virulence as a strictly evolutionary process, using set point viral load (SPVL) as a proxy, to make inferences about empirical SPVL trends from longitudinal HIV cohorts. We develop an agent-based epidemic model based on HIV viral load dynamics. The model contains functions for viral load and transmission, SPVL and disease progression, viral load trajectories in multiple stages of infection, and the heritability of SPVL across transmissions. We find that HIV virulence evolves to an intermediate level that balances infectiousness with longer infected lifespans, resulting in an optimal SPVL∼4.75 log10 viral RNA copies/mL. Adaptive viral evolution may explain observed HIV virulence trends: our model produces SPVL trends with magnitudes that are broadly similar to empirical trends. With regard to variation among studies in empirical SPVL trends, results from our model suggest that variation may be explained by the specific epidemic context, e.g. the mean SPVL of the founding lineage or the age of the epidemic; or improvements in HIV screening and diagnosis that results in sampling biases. We also use our model to examine trends in community viral load, a population-level measure of HIV viral load that is thought to reflect a population's overall transmission potential. We find that community viral load evolves in association with SPVL, in the absence of prevention programs such as antiretroviral therapy, and that the mean community viral load is not necessarily a strong predictor of HIV incidence.

The genealogical population dynamics of HIV-1 in a large transmission chain: bridging within and among host evolutionary rates

Transmission lies at the interface of human immunodeficiency virus type 1 (HIV-1) evolution within and among hosts and separates distinct selective pressures that impose differences in both the mode of diversification and the tempo of evolution. In the absence of comprehensive direct comparative analyses of the evolutionary processes at different biological scales, our understanding of how fast within-host HIV-1 evolutionary rates translate to lower rates at the between host level remains incomplete. Here, we address this by analyzing pol and env data from a large HIV-1 subtype C transmission chain for which both the timing and the direction is known for most transmission events. To this purpose, we develop a new transmission model in a Bayesian genealogical inference framework and demonstrate how to constrain the viral evolutionary history to be compatible with the transmission history while simultaneously inferring the within-host evolutionary and population dynamics. We show that accommodating a transmission bottleneck affords the best fit our data, but the sparse within-host HIV-1 sampling prevents accurate quantification of the concomitant loss in genetic diversity. We draw inference under the transmission model to estimate HIV-1 evolutionary rates among epidemiologically-related patients and demonstrate that they lie in between fast intra-host rates and lower rates among epidemiologically unrelated individuals infected with HIV subtype C. Using a new molecular clock approach, we quantify and find support for a lower evolutionary rate along branches that accommodate a transmission event or branches that represent the entire backbone of transmitted lineages in our transmission history. Finally, we recover the rate differences at the different biological scales for both synonymous and non-synonymous substitution rates, which is only compatible with the ‘store and retrieve’ hypothesis positing that viruses stored early in latently infected cells preferentially transmit or establish new infections upon reactivation.

Since its discovery three decades ago, the HIV epidemic has unfolded into one of the most devastating pandemics in human history. When HIV replication cannot be completely inhibited, the fast-evolving retrovirus continuously evades intra-host immune and drug selective pressure, but diversifies according to more neutral epidemiological dynamics at the interhost level. Limited evidence suggests that the virus may evolve faster in a single host than in a population of hosts, and various hypotheses have been put forward to explain this phenomenon. Here, we develop a new computational approach aimed at integrating host transmission information with pathogen genealogical reconstructions. We apply this approach to comprehensive sequence data sets sampled from a large HIV-1 subtype C transmission chain, and in addition to providing several insights into the reconstruction of HIV-1 transmissions histories and its associated population dynamics, we find that transmission decreases the HIV-1 evolutionary rate. The fact that we also identify this decline for substitutions that do not alter amino acid substitutions provides evidence against hypotheses that invoke selection forces. Instead, our findings support earlier reports that new infections start preferentially with less evolved variants, which may be stored in latently infected cells, and this may vary among different HIV-1 subtypes.

Virulence and pathogenesis of HIV-1 infection: an evolutionary perspective

Why some individuals develop AIDS rapidly whereas others remain healthy without treatment for many years remains a central question of HIV research. An evolutionary perspective reveals an apparent conflict between two levels of selection on the virus. On the one hand, there is rapid evolution of the virus in the host, and on the other, new observations indicate the existence of virus factors that affect the virulence of infection whose influence persists over years in infected individuals and across transmission events. Here, we review recent evidence that shows that viral genetic factors play a larger role in modulating disease severity than anticipated. We propose conceptual models that reconcile adaptive evolution at both levels of selection. Evolutionary analysis provides new insight into HIV pathogenesis.