A stochastic model for primary HIV infection: optimal timing of therapy

Expected Effect of Deleterious Mutations on Within-Host Adaptation of Pathogens

Adaptation is a common theme in both pathogen emergence, for example, in zoonotic cross-species transmission, and pathogen control, where adaptation might limit the effect of the immune response and antiviral treatment. When such evolution requires deleterious intermediate mutations, fitness ridges and valleys arise in the pathogen's fitness landscape. The effect of deleterious intermediate mutations on within-host pathogen adaptation is examined with deterministic calculations, appropriate for pathogens replicating in large populations with high error rates. The effect of deleterious intermediate mutations on pathogen adaptation is smaller than their name might suggest: when two mutations are required and each individual single mutation is fully deleterious, the pathogen can jump across the fitness valley by obtaining two mutations at once, leading to a proportion of adapted mutants that is 20-fold lower than that in the situation where the fitness of all mutants is neutral. The negative effects of deleterious intermediates are typically substantially smaller and outweighed by the fitness advantages of the adapted mutant. Moreover, requiring a specific mutation order has a substantially smaller effect on pathogen adaptation than the effect of all intermediates being deleterious. These results can be rationalized when the number of routes of mutation available to the pathogen is calculated, providing a simple approach to estimate the effect of deleterious mutations. The calculations discussed here are applicable when the effect of deleterious mutations on the within-host adaptation of pathogens is assessed, for example, in the context of zoonotic emergence, antigenic escape, and drug resistance.

IMPORTANCE

Adaptation is critical for pathogens after zoonotic transmission into a new host species or to achieve antigenic immune escape and drug resistance. Using a deterministic approach, the effects of deleterious intermediate mutations on pathogen adaptation were calculated while avoiding commonly made simplifications that do not apply to large pathogen populations replicating with high mutation rates. Perhaps unexpectedly, pathogen adaptation does not halt when the intermediate mutations are fully deleterious. The negative effects of deleterious mutations are substantially outweighed by the fitness gains of adaptation. To gain an understanding of the effect of deleterious mutations on pathogen adaptation, a simple approach that counts the number of routes available to the pathogen with and without deleterious intermediate mutations is introduced. This methodology enables a straightforward calculation of the proportion of the pathogen population that will cross a fitness valley or traverse a fitness ridge, without reverting to more complicated mathematical models.

Evolutionary rescue: linking theory for conservation and medicine

Evolutionary responses that rescue populations from extinction when drastic environmental changes occur can be friend or foe. The field of conservation biology is concerned with the survival of species in deteriorating global habitats. In medicine, in contrast, infected patients are treated with chemotherapeutic interventions, but drug resistance can compromise eradication of pathogens. These contrasting biological systems and goals have created two quite separate research communities, despite addressing the same central question of whether populations will decline to extinction or be rescued through evolution. We argue that closer integration of the two fields, especially of theoretical understanding, would yield new insights and accelerate progress on these applied problems. Here, we overview and link mathematical modelling approaches in these fields, suggest specific areas with potential for fruitful exchange, and discuss common ideas and issues for empirical testing and prediction.

Quantifying the fitness advantage of polymerase substitutions in Influenza A/H7N9 viruses during adaptation to humans

Adaptation of zoonotic influenza viruses towards efficient human-to-human transmissibility is a substantial public health concern. The recently emerged A/H7N9 influenza viruses in China provide an opportunity for quantitative studies of host-adaptation, as human-adaptive substitutions in the PB2 gene of the virus have been found in all sequenced human strains, while these substitutions have not been detected in any non-human A/H7N9 sequences. Given the currently available information, this observation suggests that the human-adaptive PB2 substitution might confer a fitness advantage to the virus in these human hosts that allows it to rise to proportions detectable by consensus sequencing over the course of a single human infection. We use a mathematical model of within-host virus evolution to estimate the fitness advantage required for a substitution to reach predominance in a single infection as a function of the duration of infection and the fraction of mutant present in the virus population that initially infects a human. The modeling results provide an estimate of the lower bound for the fitness advantage of this adaptive substitution in the currently sequenced A/H7N9 viruses. This framework can be more generally used to quantitatively estimate fitness advantages of adaptive substitutions based on the within-host prevalence of mutations. Such estimates are critical for models of cross-species transmission and host-adaptation of influenza virus infections.

Computational inference methods for selective sweeps arising in acute HIV infection

During the first weeks of human immunodeficiency virus-1 (HIV-1) infection, cytotoxic T-lymphocytes (CTLs) select for multiple escape mutations in the infecting HIV population. In recent years, methods that use escape mutation data to estimate rates of HIV escape have been developed, thereby providing a quantitative framework for exploring HIV escape from CTL response. Current methods for escape-rate inference focus on a specific HIV mutant selected by a single CTL response. However, recent studies have shown that during the first weeks of infection, CTL responses occur at one to three epitopes and HIV escape occurs through complex mutation pathways. Consequently, HIV escape from CTL response forms a complex, selective sweep that is difficult to analyze. In this work, we develop a model of initial infection, based on the well-known standard model, that allows for a description of multi-epitope response and the complex mutation pathways of HIV escape. Under this model, we develop Bayesian and hypothesis-test inference methods that allow us to analyze and estimate HIV escape rates. The methods are applied to two HIV patient data sets, concretely demonstrating the utility of our approach.

Stochastic model of in-vivo X4 emergence during HIV infection: implications for the CCR5 inhibitor maraviroc

The emergence of X4 tropic viral strains throughout the course of HIV infection is associated with poorer prognostic outcomes and faster progressions to AIDS than for patients in whom R5 viral strains predominate. Here we investigate a stochastic model to account for the emergence of X4 virus via mutational intermediates of lower fitness that exhibit dual/mixed (D/M) tropism, and employ the model to investigate whether the administration of CCR5 blockers in-vivo is likely to promote a shift towards X4 tropism. We show that the proposed stochastic model can account for X4 emergence with a median time of approximately 4 years post-infection as a result of: 1.) random stochastic mutations in the V3 region of env during the reverse transcription step of infection; 2.) increasing numbers of CXCR4-expressing activated naive CD4+ T cells with declining total CD4+ T cell counts, thereby providing increased numbers of activated target cells for productive infection by X4 virus. Our model indicates that administration of the CCR5 blocker maraviroc does not promote a shift towards X4 tropism, assuming sufficient efficacy of background therapy (BT). However our modelling also indicates that administration of maraviroc as a monotherapy or with BT of suboptimal efficacy can promote emergence of X4 tropic virus, resulting in accelerated progression to AIDS. Taken together, our results demonstrate that maraviroc is safe and effective if co-administered with sufficiently potent BT, but that suboptimal BT may promote X4 emergence and accelerated progression to AIDS. These results underscore the clinical importance for careful selection of BT when CCR5 blockers are administered in-vivo.

Population biological principles of drug-resistance evolution in infectious diseases

The emergence of resistant pathogens in response to selection pressure by drugs and their possible disappearance when drug use is discontinued are evolutionary processes common to many pathogens. Population biological models have been used to study the dynamics of resistance in viruses, bacteria, and eukaryotic microparasites both at the level of the individual treated host and of the treated host population. Despite the existence of generic features that underlie such evolutionary dynamics, different conclusions have been reached about the key factors affecting the rate of resistance evolution and how to best use drugs to minimise the risk of generating high levels of resistance. Improved understanding of generic versus specific population biological aspects will help to translate results between different studies, and allow development of a more rational basis for sustainable drug use than exists at present.

Modelling the impact of acute infection dynamics on the accumulation of HIV-1 mutations

Events over the past year have brought hope and have re-energized the interest in targeting pre-infection or early infection period with preventative or therapeutic interventions such as vaccines and pre-exposure prophylaxis (PrEP). In breakthrough infections, the incidence, long term prognosis and clinical significance of early infection events is not well understood but it is possible that these early events may be crucial in determining the subsequent course of disease. We use a branching process model in a deterministically varying environment to explore how the dynamics of early infection affects the accumulation of mutations which lay the seeds for long term evolution of drug resistance and immune system evasion. We relate this exploration to regimes of impact, on diversity, of tropical interventions strategies such as PrEP and vaccines. As a metric of diversity we compute the probability of existence of particular genomes which potentially arise. Using several model scenarios, we demonstrate various regimes of 'response' of evolution to 'intervention'. Transient effects of therapeutic interventions early in infection that impose a fitness cost on early viruses can significantly reduce the probability of diversity later during the chronic state of infection. This stands in contrast to the concern that early selective pressure may increase the probability of later existence of drug resistance mutations, for example. The branching process paradigm offers the ability to efficiently compute important indicators of viral diversity, in a framework with a modest number of simplifying assumptions, without simulating the full range of individual level scenarios. These models may be useful to illustrate the impact of vaccines and PrEP on viral evolution in the case of breakthrough infection. They also suggest that new measures of viral diversity which correlate to prognosis should be sought in trials for PrEP and vaccines.

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.

Modeling sequence evolution in acute HIV-1 infection

We describe a mathematical model and Monte Carlo (MC) simulation of viral evolution during acute infection. We consider both synchronous and asynchronous processes of viral infection of new target cells. The model enables an assessment of the expected sequence diversity in new HIV-1 infections originating from a single transmitted viral strain, estimation of the most recent common ancestor (MRCA) of the transmitted viral lineage, and estimation of the time to coalesce back to the MRCA. We also calculate the probability of the MRCA being the transmitted virus or an evolved variant. Excluding insertions and deletions, we assume HIV-1 evolves by base substitution without selection pressure during the earliest phase of HIV-1 infection prior to the immune response. Unlike phylogenetic methods that follow a lineage backwards to coalescence, we compare the observed data to a model of the diversification of a viral population forward in time. To illustrate the application of these methods, we provide detailed comparisons of the model and simulations results to 306 envelope sequences obtained from eight newly infected subjects at a single time point. The data from 68 patients were in good agreement with model predictions, and hence compatible with a single-strain infection evolving under no selection pressure. The diversity of the samples from the other two patients was too great to be explained by the model, suggesting multiple HIV-1-strains were transmitted. The model can also be applied to longitudinal patient data to estimate within-host viral evolutionary parameters.

Transient antiretroviral therapy selecting for common HIV-1 mutations substantially accelerates the appearance of rare mutations

Background

Highly selective antiretroviral (ARV) regimens such as single dose nevirapine (NVP) used for prevention of mother to child transmission (PMTCT) in resource-limited settings produce transient increases in otherwise marginal subpopulations of cells infected by mutant genomes. The longer term implications for accumulation of further resistance mutations are not fully understood.

Methods

We develop a new strain-differentiated hybrid deterministic-stochastic population dynamic type model of healthy and infected cells. We explore how the transient increase in a population of cells transcribed with a common mutation (modelled deterministically), which occurs in response to a short course of monotherapy, has an impact on the risk of appearance of rarer, higher-order, therapy-defeating mutations (modelled stochastically).

Results

Scenarios with a transient of a magnitude and duration such as is known to occur under NVP monotherapy exhibit significantly accelerated viral evolution compared to no-treatment scenarios. We identify a possibly important new biological timescale; namely, the duration of persistence, after a seminal mutation, of a sub-population of cells bearing the new mutant gene, and we show how increased persistence leads to an increased probability that a rare mutant will be present at the moment at which a new treatment regimen is initiated.

Conclusion

Even transient increases in subpopulations of common mutants are associated with accelerated appearance of further rarer mutations. Experimental data on the persistence of small subpopulations of rare mutants, in unfavourable environments, should be sought, as this affects the risk of subverting later regimens.

Stochastic modelling of genotypic drug-resistance for human immunodeficiency virus towards long-term combination therapy optimization

MOTIVATION

Several mathematical models have been investigated for the description of viral dynamics in the human body: HIV-1 infection is a particular and interesting scenario, because the virus attacks cells of the immune system that have a role in the antibody production and its high mutation rate permits to escape both the immune response and, in some cases, the drug pressure. The viral genetic evolution is intrinsically a stochastic process, eventually driven by the drug pressure, dependent on the drug combinations and concentration: in this article the viral genotypic drug resistance onset is the main focus addressed. The theoretical basis is the modelling of HIV-1 population dynamics as a predator-prey system of differential equations with a time-dependent therapy efficacy term, while the viral genome mutation evolution follows a Poisson distribution. The instant probabilities of drug resistance are estimated by means of functions trained from in vitro phenotypes, with a roulette-wheel-based mechanisms of resistant selection. Simulations have been designed for treatments made of one and two drugs as well as for combination antiretroviral therapies. The effect of limited adherence to therapy was also analyzed. Sequential treatment change episodes were also exploited with the aim to evaluate optimal synoptic treatment scenarios.

RESULTS

The stochastic predator-prey modelling usefully predicted long-term virologic outcomes of evolved HIV-1 strains for selected antiretroviral therapy combinations. For a set of widely used combination therapies, results were consistent with findings reported in literature and with estimates coming from analysis on a large retrospective data base (EuResist).

Optimal timing and duration of induction therapy for HIV-1 infection

The tradeoff between the need to suppress drug-resistant viruses and the problem of treatment toxicity has led to the development of various drug-sparing HIV-1 treatment strategies. Here we use a stochastic simulation model for viral dynamics to investigate how the timing and duration of the induction phase of induction–maintenance therapies might be optimized. Our model suggests that under a variety of biologically plausible conditions, 6–10 mo of induction therapy are needed to achieve durable suppression and maximize the probability of eradicating viruses resistant to the maintenance regimen. For induction regimens of more limited duration, a delayed-induction or -intensification period initiated sometime after the start of maintenance therapy appears to be optimal. The optimal delay length depends on the fitness of resistant viruses and the rate at which target-cell populations recover after therapy is initiated. These observations have implications for both the timing and the kinds of drugs selected for induction–maintenance and therapy-intensification strategies.

Clinicians treating HIV infection must balance the need to suppress viral replication against the harmful side effects and significant cost of antiretroviral therapy. Inadequate therapy often results in the emergence of resistant viruses and treatment failure. These difficulties are especially acute in resource-poor settings, where antiretroviral agents are limited. This has prompted an interest in induction–maintenance (IM) treatment strategies, in which brief intensive therapy is used to reduce host viral levels. Induction is followed by a simplified and more easily tolerated maintenance regimen. IM approaches remain an unproven concept in HIV therapy. We have developed a mathematical model to simulate clinical responses to antiretroviral drug therapy. We account for latent infection, partial drug efficacy, cross-resistance, viral recombination, and other factors. This model accurately reflects expected outcomes under single, double, and standard three-drug antiretroviral therapy. When applied to IM therapy, we find that (1) IM is expected to be successful beyond 3 y under a variety of conditions; (2) short-term induction therapy is optimally started several days to weeks after the start of maintenance; and (3) IM therapy may eradicate some preexisting drug-resistant viral strains from the host. Our simulations may help develop new treatment strategies and optimize future clinical trials.

Probability of resistance evolution for exponentially growing virus in the host

Chemotherapy for tumor and pathogenic virus often faces an emergence of resistant mutants, which may lead to medication failure. Here we study the risk of resistance to evolve in a virus population which grows exponentially. We assume that infected cells experience a "proliferation event" of virus at a random time and that the number of newly infected cells from an infected cell follows a Poisson distribution. Virus starts from a single infected cell and the virus infection is detected when the number of infected cells reaches a detection size. Initially virus is sensitive to a drug but later acquires resistance by mutations. We ask the probability that one or more cells infected with drug-resistant virus exist at the time of detection. We derive a formula for the probability of resistance and confirm its accuracy by direct computer simulations. The probability of resistance increases with detection size and mutation rate but decreases with the population growth rate of sensitive virus. The risk of resistance is smaller when more cells are newly infected by viral particles from a single infected cell if the viral growth rate is the same.

Stochastic or deterministic: what is the effective population size of HIV-1?

Various studies have attempted to estimate the effective population size of HIV-1 to determine the strength of stochastic effects in within-host evolution. The largely discrepant estimates, the complexity of the concept of the effective population size and the resulting uncertainty about the underlying assumptions make the interpretation of these estimates difficult. Here, we explain the concept and critically assess the current estimates. We discuss the biologically relevant factors that affect the estimate and use of the effective population size. We argue that these factors lead to an underestimation of the effective population size and, thus, to an overestimation of the strength of stochastic effects in HIV-1 evolution.

Evaluation of HIV-1 kinetic models using quantitative discrimination analysis

MOTIVATION

Since the identification of human immunodeficiency virus (HIV) over twenty years ago, many mathematical models of HIV dynamics have been proposed. The purpose of this study was to evaluate intracellular and intercellular scale HIV models that best described the dynamics of viral and cell titers of a person, where parameters were determined using typically available patient data. In this case, 'best' was defined as the model most capable of describing experimental patient data and was determined by Bayesian-based model discrimination analysis and the ability to provide realistic results.

RESULTS

Twenty models of HIV-1 viral dynamics were initially evaluated to determine whether parameters could be obtained from readily available clinical data from established HIV-1 patients with stable disease. Based on this analysis, three models were chosen for further examination and comparison. Parameters were estimated using experimental data from a cohort of 338 people monitored for up to 2484 days. The models were evaluated using a Bayesian technique to determine which model was most probable. The model ultimately selected as most probable was overwhelmingly favored relative to the remaining two models, and it accounted for uninfected cells, infected cells and cytotoxic T lymphocyte dynamics. The authors developed a fourth model for comparison purposes by combining the features of the original three models. Parameters were estimated for the new model and the statistical analysis was repeated for all four models. The model that was initially favored was selected again upon model discrimination analysis.

CONTACT

srivasta@engr.uconn.edu.

Modeling HIV dynamics and antiviral response with consideration of time-varying drug exposures, adherence and phenotypic sensitivity

Highly active antiretroviral therapies consisting of reverse transcriptase inhibitor drugs and protease inhibitor drugs, which can rapidly suppress HIV below the limit of detection, are currently the most effective treatment for HIV infected patients. In spite of this, many patients fail to achieve viral suppression, probably due to existing or developing drug resistance, poor adherence, pharmacokinetic problems and other clinical factors. In this paper, we develop a viral dynamic model to evaluate how time-varying drug exposure and drug susceptibility affect antiviral response. Plasma concentrations, in turn, are modeled using a standard pharmacokinetic (PK) one-compartment open model with first order absorption and elimination as a function of fixed individual PK parameters and dose times. Imperfect adherence is considered as missed doses in PK models. We discuss the analytic properties of the viral dynamic model and study how time-varying treatment efficacies affect antiviral responses, specifically viral load and T cell counts. The relationship between actual failure time (the time at which the viral growth rate changes from negative to positive) and detectable failure time (the time at which viral load rebounds to above the limit of detection) is investigated. We find that an approximately linear relationship can be used to estimate the actual rebound failure time from the detectable rebound failure time. In addition, the effect of adherence on antiviral response is studied. In particular, we examine how different patterns of adherence affect antiviral response. Results suggest that longer sequences of missed doses increase the chance of treatment failure and accelerate the failure. Simulation experiments are presented to illustrate the relationship between antiviral response and pharmacokinetics, time-varying adherence and drug resistance. The proposed models and methods may be useful in AIDS clinical trial simulations.

Memory in retroviral quasispecies: experimental evidence and theoretical model for human immunodeficiency virus

Viral quasispecies may possess a molecular memory of their past evolutionary history, imprinted on minority components of the mutant spectrum. Here we report experimental evidence and a theoretical model for memory in retroviral quasispecies in vivo. Apart from replicative memory associated with quasispecies dynamics, retroviruses may harbour a "cellular" or "anatomical" memory derived from their integrative cycle and the presence of viral reservoirs in body compartments. Three independent sets of data exemplify the two kinds of memory in human immunodeficiency virus type 1 (HIV-1). The data provide evidence of re-emergence of sequences that were hidden in cellular or anatomical compartments for extended periods of infection, and recovery of a quasispecies from pre-existing genomes. We develop a three-component model that incorporates the essential features of the quasispecies dynamics of retroviruses exposed to selective pressures. Significantly, a numerical study based on this model is in agreement with the experimental data, further supporting the existence of both replicative and reservoir memory in retroviral quasispecies.

Computer simulations of slow progression of human immunodeficiency virus infection and relapse during anti-HIV treatment with reverse transcriptase inhibitors and protease inhibitors

Human immunodeficiency virus (HIV) infection and acquired immunodeficiency syndrome (AIDS) have been very serious problems since the 1980s. The progression of HIV infection into AIDS can be suppressed to some extent with reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs); however, there are some serious problems with treatments using the anti-HIV drugs (e.g. very high expense, complicated administration, and drug resistance). Hence, more studies on HIV and the development of more effective anti-HIV treatments are required. We consider it important to understand the complex dynamics involved in HIV infection, and we therefore propose new mathematical models of HIV infection. In the modeling, we have paid attention to the nonlinear relations between stimuli and responses (i.e., when responses are plotted against the logarithm of stimuli, a sigmoid curve is obtained), and to lymphoid organs which seem more important than the blood compartment (i.e., lymphoid organs are major reservoirs of HIV virions and contain most of the lymphocytes). Using the models, we have found that viral antigenic mutation plays an important role in the slow progression in the chronic phase of HIV infection. We have also found that viral antigenic mutation can cause relapse of HIV infection when the inhibition rate of anti-HIV drugs is low and that viral antigenic mutation cannot cause relapse when the inhibition rate is high.

Response to highly active antiretroviral therapy according to duration of HIV infection

OBJECTIVE

To evaluate whether duration of HIV-1 infection influences the response to highly active antiretroviral therapy (HAART).

DESIGN

Prospective study of individuals (Italian Seroconversion Study cohort) with well-estimated dates of HIV-1 seroconversion.

METHODS

This analysis included 277 participants who began HAART (defined as three antiretroviral drugs used in combination). Cox regression models were used to evaluate the association between duration of infection (as categorical variable [</=3, 3-7.5, >7.5 years from seroconversion] or continuous variable) and an immunologic (rise in CD4 count >100 cells/mm3) and a virologic (decline in plasma HIV-RNA to unquantifiable levels) outcome. All analyses were stratified by center of recruitment and adjustment, when used, was for gender, age at inception of HAART, injection drug use, previous antiretroviral therapy, lag-time between positive and negative HIV test result, year of starting HAART, clinical stage, CD4 count, and HIV-RNA at time of HAART.

RESULTS

HAART was initiated a median of 6.4 years after seroconversion. There was a median follow-up of 1.6 years after starting HAART to the calendar cut-off (November 1999). One-hundred-eighty-one (65.3%) patients experienced a decline in viral load to below quantifiable levels and 184 (66.4%) experienced a rise in CD4 >100 cells/mm3. In the Cox models, by 1-year increase in duration of infection, we estimated a lower crude hazard of achieving a CD4 count increase >100 cells (relative hazard [RH], 0.96; 95% confidence interval [CI], 0.92-1.01; p =.09), and a lower hazard of reaching an unquantifiable level of plasma HIV-RNA (RH, 0.97; 95%CI, 0.93-1.02; p =.20). After adjustment, these values became 0.99 (95%CI, 0.93-1.04; p =.62) and 0.98 (95%CI, 0.93-1.04; p =.48), respectively. When duration of HIV infection was considered as a categorical variable, the results were consistent with those already described.

CONCLUSIONS

These results suggest that the duration of HIV infection does not seem to play an important independent role in determining the virologic and immunologic responses to HAART.

Risks and benefits of structured antiretroviral drug therapy interruptions in HIV-1 infection

BACKGROUND

Structured interruptions of antiretroviral therapy of HIV-1 infected individuals are currently being tested in clinical trials to study the effect interruptions have on the immune responses and control of virus replication.

OBJECTIVE

To investigate the potential risks and benefits of interrupted therapy using standard population dynamical models of HIV replication kinetics.

METHODS

Standard population dynamical models were used to study the effect of structured therapy interruptions on the immune effector cells, the latent cell compartment and the emergence of drug resistance.

CONCLUSIONS

The models suggest that structured therapy interruption only leads to transient or sustained virus control if the immune effector cells increase during therapy. This increase must more than counterbalance the increase in susceptible target cells induced by therapy. The risk of inducing drug resistance by therapy interruptions or the risk of repopulating the pool of latent cells during drug-free periods may be small if the virus population remains at levels considerably below baseline. However, if the virus load increases during drug-free periods to levels similar to or higher than baseline before therapy, both these risks increase dramatically.

Immunological transitions in response to antigenic mutation during viral infection

Antigenic variation is an important factor in viral persistence and disease progression. We analyze immunological changes which occur in response to antigenic mutation during chronic viral infection. Using an established model of viral and immune system dynamics, we determine which qualitative shifts in the immune response can be elicited by the appearance of a new mutant. We find that antigenic mutation can cause dramatic shifts in the magnitude and type of anti-viral immune response. For example, the appearance of a mutant can elicit a new immune response which recognizes the original viral strain. We also find that novel strains of the virus which replicate more slowly than existing viral strains are able to invade and survive, even when the immune system is capable of mounting an immune response against the mutant.

A competition model for viral inhibition of host cell proliferation

Some viruses encode proteins that promote cell proliferation while others, such as the human immunodeficiency virus (HIV), encode proteins that prevent cell division. It has been hypothesized that the selective advantage determining which strategy evolves depends on the ability of the virus to induce a cellular environment which maximizes both virus production and cell life span. In HIV, the protein that causes cell cycle arrest is Vpr. In this paper, we develop a mathematical model, based on difference equations, to study the competition between two genotypes of HIV - one that encodes this protein (Vpr+) and one that does not (Vpr-). In particular, we are interested in parameters that could be different between the in vitro condition, where the Vpr- genotype dominates, and the in vivo condition, where the Vpr+ genotype dominates. Our model indicates that the infected cell death-rate, the viral half-life, and the dynamics of the target cell population all effect the competition dynamics between the Vpr+ and Vpr- viral genotypes. Perturbing any of these parameters from the in vitro estimates while holding the others fixed has no affect on the competition outcome, i. e., the Vpr- genotype dominates. Perturbing the infected cell death-rate and the target cell source causes a switch in competitive outcome, although not necessarily at values, which represent the in vivo condition. Adding a perturbation in the viral half-life from in vitro to in vivo condition results in a switch of the competitive advantage from the Vpr- genotype to the Vpr+ genotype with parameters for all three mechanisms set to estimated in vivo values.