Modeling Within-Host Evolution of HIV: Mutation, Competition and Strain Replacement

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.

Evolution during primary HIV infection does not require adaptive immune selection

Modern HIV research depends crucially on both viral sequencing and population measurements. To directly link mechanistic biological processes and evolutionary dynamics during HIV infection, we developed multiple within-host phylodynamic models of HIV primary infection for comparative validation against viral load and evolutionary dynamics data. The optimal model of primary infection required no positive selection, suggesting that the host adaptive immune system reduces viral load but surprisingly does not drive observed viral evolution. Rather, the fitness (infectivity) of mutant variants is drawn from an exponential distribution in which most variants are slightly less infectious than their parents (nearly neutral evolution). This distribution was not largely different from either in vivo fitness distributions recorded beyond primary infection or in vitro distributions that are observed without adaptive immunity, suggesting the intrinsic viral fitness distribution may drive evolution. Simulated phylogenetic trees also agree with independent data and illuminate how phylogenetic inference must consider viral and immune-cell population dynamics to gain accurate mechanistic insights.

Real-Time Infectious Disease Modeling to Inform Emergency Public Health Decision Making

Infectious disease transmission is a nonlinear process with complex, sometimes unintuitive dynamics. Modeling can transform information about a disease process and its parameters into quantitative projections that help decision makers compare public health response options. However, modelers face methodologic challenges, data challenges, and communication challenges, which are exacerbated under the time constraints of a public health emergency. We review methods, applications, challenges and opportunities for real-time infectious disease modeling during public health emergencies, with examples drawn from the two deadliest pandemics in recent history: HIV/AIDS and coronavirus disease 2019 (COVID-19).

Expected final online publication date for the Annual Review of Public Health, Volume 43 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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.

Combination anti-coronavirus therapies based on nonlinear mathematical models

Using nonlinear mathematical models and experimental data from laboratory and clinical studies, we have designed new combination therapies against COVID-19.

Variable Effect of HIV Superinfection on Clinical Status: Insights From Mathematical Modeling

HIV superinfection (infection of an HIV positive individual with another strain of the virus) has been shown to result in a deterioration of clinical status in multiple case studies. However, superinfection with no (or positive) clinical outcome might easily go unnoticed, and the typical effect of superinfection is unknown. We analyzed mathematical models of HIV dynamics to assess the effect of superinfection under various assumptions. We extended the basic model of virus dynamics to explore systematically a set of model variants incorporating various details of HIV infection (homeostatic target cell dynamics, bystander killing, interference competition between viral clones, multiple target cell types, virus-induced activation of target cells). In each model, we identified the conditions for superinfection, and investigated whether and how successful invasion by a second viral strain affects the level of uninfected target cells. In the basic model, and in some of its extensions, the criteria for invasion necessarily entail a decrease in the equilibrium abundance of uninfected target cells. However, we identified three novel scenarios where superinfection can substantially increase the uninfected cell count: (i) if the rate of new infections saturates at high infectious titers (due to interference competition or cell-autonomous innate immunity); or when the invading strain is more efficient at infecting activated target cells, but less efficient at (ii) activating quiescent cells or (iii) inducing bystander killing of these cells. In addition, multiple target cell types also allow for modest increases in the total target cell count. We thus conclude that the effect of HIV superinfection on clinical status might be variable, complicated by factors that are independent of the invasion fitness of the second viral strain.

Mathematical Analysis of Viral Replication Dynamics and Antiviral Treatment Strategies: From Basic Models to Age-Based Multi-Scale Modeling

Viral infectious diseases are a global health concern, as is evident by recent outbreaks of the middle east respiratory syndrome, Ebola virus disease, and re-emerging zika, dengue, and chikungunya fevers. Viral epidemics are a socio-economic burden that causes short- and long-term costs for disease diagnosis and treatment as well as a loss in productivity by absenteeism. These outbreaks and their socio-economic costs underline the necessity for a precise analysis of virus-host interactions, which would help to understand disease mechanisms and to develop therapeutic interventions. The combination of quantitative measurements and dynamic mathematical modeling has increased our understanding of the within-host infection dynamics and has led to important insights into viral pathogenesis, transmission, and disease progression. Furthermore, virus-host models helped to identify drug targets, to predict the treatment duration to achieve cure, and to reduce treatment costs. In this article, we review important achievements made by mathematical modeling of viral kinetics on the extracellular, intracellular, and multi-scale level for Human Immunodeficiency Virus, Hepatitis C Virus, Influenza A Virus, Ebola Virus, Dengue Virus, and Zika Virus. Herein, we focus on basic mathematical models on the population scale (so-called target cell-limited models), detailed models regarding the most important steps in the viral life cycle, and the combination of both. For this purpose, we review how mathematical modeling of viral dynamics helped to understand the virus-host interactions and disease progression or clearance. Additionally, we review different types and effects of therapeutic strategies and how mathematical modeling has been used to predict new treatment regimens.

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.

Within-host evolution decreases virulence in an opportunistic bacterial pathogen

Background

Pathogens evolve in a close antagonistic relationship with their hosts. The conventional theory proposes that evolution of virulence is highly dependent on the efficiency of direct host-to-host transmission. Many opportunistic pathogens, however, are not strictly dependent on the hosts due to their ability to reproduce in the free-living environment. Therefore it is likely that conflicting selection pressures for growth and survival outside versus within the host, rather than transmission potential, shape the evolution of virulence in opportunists. We tested the role of within-host selection in evolution of virulence by letting a pathogen Serratia marcescens db11 sequentially infect Drosophila melanogaster hosts and then compared the virulence to strains that evolved only in the outside-host environment.

Results

We found that the pathogen adapted to both Drosophila melanogaster host and novel outside-host environment, leading to rapid evolutionary changes in the bacterial life-history traits including motility, in vitro growth rate, biomass yield, and secretion of extracellular proteases. Most significantly, selection within the host led to decreased virulence without decreased bacterial load while the selection lines in the outside-host environment maintained the same level of virulence with ancestral bacteria.

Conclusions

This experimental evidence supports the idea that increased virulence is not an inevitable consequence of within-host adaptation even when the epidemiological restrictions are removed. Evolution of attenuated virulence could occur because of immune evasion within the host. Alternatively, rapid fluctuation between outside-host and within-host environments, which is typical for the life cycle of opportunistic bacterial pathogens, could lead to trade-offs that lower pathogen virulence.

Modeling multiple infection of cells by viruses: Challenges and insights

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

Cladograms with Path to Event (ClaPTE): a novel algorithm to detect associations between genotypes or phenotypes using phylogenies

BACKGROUND

Associations between genotype and phenotype provide insight into the evolution of pathogenesis, drug resistance, and the spread of pathogens between hosts. However, common ancestry can lead to apparent associations between biologically unrelated features. The novel method Cladograms with Path to Event (ClaPTE) detects associations between character-pairs (either a pair of mutations or a mutation paired with a phenotype) while adjusting for common ancestry, using phylogenetic trees.

METHODS

ClaPTE tests for character-pairs changing close together on the phylogenetic tree, consistent with an associated character-pair. ClaPTE is compared to three existing methods (independent contrasts, mixed model, and likelihood ratio) to detect character-pair associations adjusted for common ancestry. Comparisons utilize simulations on gene trees for: HIV Env, HIV promoter, and bacterial DnaJ and GuaB; and case studies for Oseltamavir resistance in Influenza, and for DnaJ and GuaB. Simulated data include both true-positive/associated character-pairs, and true-negative/not-associated character-pairs, used to assess type I (frequency of p-values in true-negatives) and type II (sensitivity to true-positives) error control.

RESULTS AND CONCLUSIONS

ClaPTE has competitive sensitivity and better type I error control than existing methods. In the Influenza/Oseltamavir case study, ClaPTE reports no new permissive mutations but detects associations between adjacent (in primary sequence) amino acid positions which other methods miss. In the DnaJ and GuaB case study, ClaPTE reports more frequent associations between positions both from the same protein family than between positions from different families, in contrast to other methods. In both case studies, the results from ClaPTE are biologically plausible.

Complex dynamic behavior in a viral model with state feedback control strategies

With the consideration of mechanism of prevention and control for the spread of viral diseases, in this paper, we propose two novel virus dynamics models where state feedback control strategies are introduced. The first model incorporates the density of infected cells (or free virus) as control threshold value; we analytically show the existence and orbit stability of positive periodic solution. Theoretical results imply that the density of infected cells (or free virus) can be controlled within an adequate level. The other model determines the control strategies by monitoring the density of uninfected cells when it reaches a risk threshold value. We analytically prove the existence and orbit stability of semi-trivial periodic solution, which show that the viral disease dies out. Numerical simulations are carried out to illustrate the main results.

Understanding virus-host dynamics following EIAV infection in SCID horses

We develop a mathematical model for the interaction between two competing equine infectious anemia virus strains and neutralizing antibodies. We predict that elimination of one or both virus strains depends on the initial antibody levels, the strength of antibody mediated neutralization, and the persistence of antibody over time. We further show that the ability of a subdominant, neutralization resistant virus to dominate the infection transiently or permanently is dependent on the antibody-mediated neutralization effect. Finally, we determine conditions for persistence of both virus strains. We fit our models to virus titers from horses (foals) with severe combined immunodeficiency to estimate virus-host parameters and to validate analytical results.

Mathematical models of HIV replication and pathogenesis

This review outlines how mathematical models have been helpful, and continue to be so, for obtaining insights into the in vivo dynamics of HIV infection. The review starts with a discussion of a basic mathematical model that has been frequently used to study HIV dynamics. Some crucial results are described, including the estimation of key parameters that characterize the infection, and the generation of influential theories which argued that in vivo virus evolution is a key player in HIV pathogenesis. Subsequently, more recent concepts are reviewed that have relevance for disease progression, including the multiple infection of cells and the direct cell-to-cell transmission of the virus through the formation of virological synapses. These are important mechanisms that can influence the rate at which HIV spreads through its target cell population, which is tightly linked to the rate at which the disease progresses towards AIDS.

Effects of replicative fitness on competing HIV strains

We develop an n-strain model to show the effects of replicative fitness of competing viral strains exerting selective density-dependant infective pressure on each other. A two strain model is used to illustrate the results. A perturbation technique and numerical simulations were used to establish the existence and stability of steady states. More than one infected steady states governed by the replicative fitness resulted from the model exhibiting either strain replacement or co-infection. We found that the presence of two or more HIV strains could result in a disease-free state that, in general, is not globally stable.

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

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

Evolutionary analysis of human immunodeficiency virus type 1 therapies based on conditionally replicating vectors

Efforts to reduce the viral load of human immunodeficiency virus type 1 (HIV-1) during long-term treatment are challenged by the evolution of anti-viral resistance mutants. Recent studies have shown that gene therapy approaches based on conditionally replicating vectors (CRVs) could have many advantages over anti-viral drugs and other approaches to therapy, potentially including the ability to circumvent the problem of evolved resistance. However, research to date has not explored the evolutionary consequences of long-term treatment of HIV-1 infections with conditionally replicating vectors. In this study, we analyze a computational model of the within-host co-evolutionary dynamics of HIV-1 and conditionally replicating vectors, using the recently proposed ‘therapeutic interfering particle’ as an example. The model keeps track of the stochastic process of viral mutation, and the deterministic population dynamics of T cells as well as different strains of CRV and HIV-1 particles. We show that early in the co-infection, mutant HIV-1 genotypes that escape suppression by CRV therapy appear; this is similar to the dynamics observed in drug treatments and other gene therapies. In contrast to other treatments, however, the CRV population is able to evolve and catch up with the dominant HIV-1 escape mutant and persist long-term in most cases. On evolutionary grounds, gene therapies based on CRVs appear to be a promising tool for long-term treatment of HIV-1. Our model allows us to propose design principles to optimize the efficacy of this class of gene therapies. In addition, because of the analogy between CRVs and naturally-occurring defective interfering particles, our results also shed light on the co-evolutionary dynamics of wild-type viruses and their defective interfering particles during natural infections.

A long-standing challenge in efforts to control human immunodeficiency virus type 1 (HIV-1) is the rapid evolution of the virus. Any effective therapy quickly gives rise to so-called escape mutants of the virus, potentially resulting in treatment failure. A distinct class of gene therapy based on conditionally replicating vectors has been suggested to have potential to circumvent the problem of viral evolutionary escape. A conditionally replicating vector cannot replicate on its own, but when it coinfects the same cell with HIV-1, it is packaged into a virion-like particle and can be transmitted from cell to cell. Importantly, these vectors replicate using the same machinery that HIV-1 uses, and so they mutate at the same rate. This opens the possibility that conditionally replicating vectors could ‘keep up’ with HIV-1 evolution and prevent HIV-1 escape. In this study, we present mathematical analyses of the co-evolutionary dynamics of HIV-1 and conditionally replicating vectors within a patient. Our results show that with proper genetic design, conditionally replicating vectors can keep pace with HIV-1 evolution, leading to persistent reduction in HIV-1 viral loads. Therefore, this class of gene therapies shows potential for ‘evolution-proof’ control of HIV-1, and merits further investigation in laboratory trials.

Modelling the course of an HIV infection: insights from ecology and evolution

The Human Immunodeficiency Virus (HIV) is one of the most threatening viral agents. This virus infects approximately 33 million people, many of whom are unaware of their status because, except for flu-like symptoms right at the beginning of the infection during the acute phase, the disease progresses more or less symptom-free for 5 to 10 years. During this asymptomatic phase, the virus slowly destroys the immune system until the onset of AIDS when opportunistic infections like pneumonia or Kaposi’s sarcoma can overcome immune defenses. Mathematical models have played a decisive role in estimating important parameters (e.g., virion clearance rate or life-span of infected cells). However, most models only account for the acute and asymptomatic latency phase and cannot explain the progression to AIDS. Models that account for the whole course of the infection rely on different hypotheses to explain the progression to AIDS. The aim of this study is to review these models, present their technical approaches and discuss the robustness of their biological hypotheses. Among the few models capturing all three phases of an HIV infection, we can distinguish between those that mainly rely on population dynamics and those that involve virus evolution. Overall, the modeling quest to capture the dynamics of an HIV infection has improved our understanding of the progression to AIDS but, more generally, it has also led to the insight that population dynamics and evolutionary processes can be necessary to explain the course of an infection.

COEXISTENCE OF THE STRAINS INDUCED BY MUTATION

In this paper, we propose a two strain epidemic model with single host population. It is assumed that strain one can mutate into strain two. Also latent-stage progression age and mutation are incorporated into the model. Stability of equilibria (including the disease free equilibrium, dominant equilibria and the coexistence equilibrium) is investigated and it is found that they are locally stable under suitable and biological feasible constraints. Results indicate that the competition exclusion and coexistence of the two strains are possible depending on the mutation. Numerical simulations are also performed to illustrate these results.

Partitioning regulatory mechanisms of within-host malaria dynamics using the effective propagation number

Immune clearance and resource limitation (via red blood cell depletion) shape the peaks and troughs of malaria parasitemia, which in turn affect disease severity and transmission. Quantitatively partitioning the relative roles of these effects through time is challenging. Using data from rodent malaria, we estimated the effective propagation number, which reflects the relative importance of contrasting within-host control mechanisms through time and is sensitive to the inoculating parasite dose. Our analysis showed that the capacity of innate responses to restrict initial parasite growth saturates with parasite dose and that experimentally enhanced innate immunity can affect parasite density indirectly via resource depletion. Such a statistical approach offers a tool to improve targeting of drugs or vaccines for human therapy by revealing the dynamics and interactions of within-host regulatory mechanisms.

Analysis of a vaccine model with cross-immunity: when can two competing infectious strains coexist?

We analyse here the vaccine model with cross-immunity proposed by Porco and Blower [1]. Porco and Blower [1] show that vaccination can shift the competitive balance in favour of a strain that, without vaccination, would be out-competed and that vaccination can also promote coexistence of different strains, something that normally is not expected [2]. Their results have been mainly obtained through numerical simulations, so that the conditions under which a shift in competitive balance or coexistence occurs have not been fully established. We give a rather complete description of its behaviour, at least in terms of equilibria. We find the exact conditions under which vaccination may lead to a shift in competitive balance and show that, under these conditions, there always exist a range of vaccination rates under which a coexistence equilibrium exists. We also find that a coexistence equilibrium exists (and is unstable) in a 'bi-stability' region, where both monomorphic equilibria are stable. This fact has been rarely observed in models of competition between pathogen strains.

Two optimal mutation rates in obligate pathogens subject to deleterious mutation

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

Epidemiological and clinical consequences of within-host evolution

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

Relative replication capacity of phenotypic SIV variants during primary infections differs with route of inoculation

Background

Previous studies of human and simian immunodeficiency virus (HIV and SIV) have demonstrated that adaptive mutations selected during the course of infection alter viral replicative fitness, persistence, and pathogenicity. What is unclear from those studies is the impact of transmission on the replication and pathogenicity of the founding virus population. Using the SIV-macaque model, we examined whether the route of infection would affect the establishment and replication of two SIVmne variants of distinct in vitro and in vivo biological characteristics. For these studies, we performed dual-virus inoculations of pig-tailed macaques via intrarectal or intravenous routes with SIVmneCl8, a miminally pathogenic virus, and SIVmne027, a highly pathogenic variant that replicates more robustly in CD4⁺ T cells.

Results

The data demonstrate that SIVmne027 is the dominant virus regardless of the route of infection, indicating that the capacity to replicate efficiently in CD4⁺ T cells is important for fitness. Interestingly, in comparison to intravenous co-infection, intrarectal inoculation enabled greater relative replication of the less pathogenic virus, SIVmneCl8. Moreover, a higher level of SIVmneCl8 replication during primary infection of the intrarectally inoculated macaques was associated with lower overall plasma viral load and slower decline in CD4⁺ T cells, even though SIVmne027 eventually became the dominant virus.

Conclusions

These results suggest that the capacity to replicate in CD4⁺ T cells is a significant determinant of SIV fitness and pathogenicity. Furthermore, the data also suggest that mucosal transmission may support early replication of phenotypically diverse variants, while slowing the rate of CD4⁺ T cell decline during the initial stages of infection.

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

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

Understanding the HIV coreceptor switch from a dynamical perspective

BACKGROUND

The entry of HIV into its target cells is facilitated by the prior binding to the cell surface molecule CD4 and a secondary coreceptor, mostly the chemokine receptors CCR5 or CXCR4. In early infection CCR5-using viruses (R5 viruses) are mostly dominant while a receptor switch towards CXCR4 occurs in about 50% of the infected individuals (X4 viruses) which is associated with a progression of the disease. There are many hypotheses regarding the underlying dynamics without yet a conclusive understanding.

RESULTS

While it is difficult to isolate key factors in vivo we have developed a minimal in silico model based on the approaches of Nowak and May to investigate the conditions under which the receptor switch occurs. The model allows to investigate the evolution of viral strains within a probabilistic framework along the three stages of disease from primary and latent infection to the onset of AIDS with a a sudden increase in viral load which goes along with the impairment of the immune response. The model is specifically applied to investigate the evolution of the viral quasispecies in terms of R5 and X4 viruses which directly translates into the composition of viral load and consequently the question of the coreceptor switch.

CONCLUSION

The model can explain the coreceptor switch as a result of a dynamical change in the underlying environmental conditions in the host. The emergence of X4 strains does not necessarily result in the dominance of X4 viruses in viral load which is more likely to occur in the model after some time of chronic infection. A better understanding of the conditions leading to the coreceptor switch is especially of interest as CCR5 blockers have recently been licensed as drugs which suppress R5 viruses but do not seem to necessarily induce a coreceptor switch.

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

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

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

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

BACKGROUND

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

RESULTS

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

CONCLUSION

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

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

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

Accelerated immunodeficiency by anti-CCR5 treatment in HIV infection

In 50% of progressing HIV-1 patients, CXCR4-tropic (X4) virus emerges late in infection, often overtaking CCR5-tropic (R5) virus as the dominant viral strain. This "phenotypic switch" is strongly associated with rapidly declining CD4(+) T cell counts and AIDS onset, yet its causes remain unknown. Here, we analyze a mathematical model for the mechanism of X4 emergence in late-stage HIV infection and use this analysis to evaluate the utility of a promising new class of antiretroviral drugs -- CCR5 inhibitors -- in dual R5, X4 infection. The model shows that the R5-to-X4 switch occurs as CD4(+) T cell activation levels increase above a threshold and as CD4(+) T cell counts decrease below a threshold during late-stage HIV infection. Importantly, the model also shows that highly active antiretroviral therapy (HAART) can inhibit X4 emergence but that monotherapy with CCR5 blockers can accelerate X4 onset and immunodeficiency if X4 infection of memory CD4(+) T cells occurs at a high rate. Fortunately, when CXCR4 blockers or HAART are used in conjunction with CCR5 blockers, this risk of accelerated immunodeficiency is eliminated. The results suggest that CCR5 blockers will be more effective when used in combination with CXCR4 blockers and caution against CCR5 blockers in the absence of an effective HAART regimen or during HAART failure.

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

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

HIV-1 Transmission, Replication Fitness and Disease Progression

Upon transmission, human immunodeficiency virus type 1 (HIV-1) establishes infection of the lymphatic reservoir, leading to profound depletion of the memory CD4+ T cell population despite the induction of the adaptive immune response. The rapid evolution and association of viral variants having distinct characteristics during different stages of infection, the level of viral burden, and rate of disease progression suggest a role for viral variants in this process. Here, we review the literature on HIV-1 variants and disease and discuss the importance of viral fitness for transmission and disease.

Modeling HIV infection dynamics: the role of recombination in the development of drug resistance

The benefit of recombination to HIV remains unclear because just as recombination can induce the association of favorable mutations and accelerate the development of multidrug resistance, it can also dissociate favorable combinations of mutations. The confounding influences of mutation, random genetic drift, selection and epistatic interactions between multiple resistance loci render the role of recombination difficult to unravel experimentally. Mathematical models provide valuable insights into the influence of recombination on the genomic diversification of HIV and the development of drug resistance in patients undergoing therapy, capture several recent experimental observations of HIV recombination quantitatively, and set the stage for the establishment of a robust framework for the identification of improved treatment protocols and guidelines for drug development.

Immunity and protection by live attenuated HIV/SIV vaccines

Live attenuated virus vaccines have shown the greatest potential to protect against simian immunodeficiency virus (SIV) infection, a model for human immunodeficiency virus (HIV). Immunity against the vaccine virus is thought to mediate protection. However, it is shown computationally that the opposite might be true. According to the model, the initial growth of the challenge strain, its peak load, and its potential to be pathogenic is higher if immunity against the vaccine virus is stronger. This is because the initial growth of the challenge strain is mainly determined by virus competition rather than immune suppression. The stronger the immunity against the vaccine strain, the weaker its competitive ability relative to the challenge strain, and the lower the level of protection. If the vaccine virus does protect the host against a challenge, it is because the competitive interactions between the viruses inhibit the initial growth of the challenge strain. According to these arguments, an inverse correlation between the level of attenuation and the level of protection is expected, and this has indeed been observed in experimental data.

Invasion thresholds and the evolution of nonequilibrium virulence

The enterprise of virulence management attempts to predict how social practices and other factors affect the evolution of parasite virulence. These predictions are often based on parasite optima or evolutionary equilibria derived from models of host-parasite dynamics. Yet even when such models accurately capture the parasite optima, newly invading parasites will typically not be at their optima. Here we show that parasite invasion of a host population can occur despite highly nonoptimal virulence. Fitness improvements soon after invasion may proceed through many steps with wide changes in virulence, because fitness depends on transmission as well as virulence, and transmission improvements can overwhelm nonoptimal virulence. This process is highly sensitive to mutation supply and the strength of selection. Importantly, the same invasion principle applies to the evolution of established parasites, whenever mutants arise that overcome host immunity/resistance. A host population may consequently experience repeated invasions of new parasite variants and possible large shifts in virulence as it evolves in an arms race with the parasite. An experimental study of phage lysis time and examples of mammalian viruses matching some of these characteristics are reviewed.

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

Infectious pathogens compete and are subject to natural selection at multiple levels. For example, viral strains compete for access to host resources within an infected host and, at the same time, compete for access to susceptible hosts within the host population. Here we propose a novel approach to study the interplay between within- and between-host competition. This approach allows for a single host to be infected by and transmit two strains of the same pathogen. We do this by nesting a model for the host-pathogen dynamics within each infected host into an epidemiological model. The nesting of models allows the between-host infectivity and mortality rates suffered by infected hosts to be functions of the disease progression at the within-host level. We present a general method for computing the basic reproduction ratio of a pathogen in such a model. We then illustrate our method using a basic model for the within-host dynamics of viral infections, embedded within the simplest susceptible-infected (SI) epidemiological model. Within this nested framework, we show that the virion production rate at the level of the cell-virus interaction leads, via within-host competition, to the presence or absence of between-host level competitive exclusion. In particular, we find that in the absence of mutation the strain that maximizes between-host fitness can outcompete all other strains. In the presence of mutation we observe a complex invasion landscape showing the possibility of coexistence. Although we emphasize the application to human viral diseases, we expect this methodology to be applicable to be many host-parasite systems.