Modeling the mechanisms of acute hepatitis B virus infection

Mathematical models have been used to understand the factors that govern infectious disease progression in viral infections. Here we focus on hepatitis B virus (HBV) dynamics during the acute stages of the infection and analyze the immune mechanisms responsible for viral clearance. We start by presenting the basic model used to interpret HBV therapy studies conducted in chronically infected patients. We then introduce additional models to study acute infection where immune responses presumably play an important role in determining whether the infection will be cleared or become chronic. We add complexity incrementally and explain each step of the modeling process. Finally, we validate the model against experimental data to determine how well it represents the biological system and, consequently, how useful are its predictions. In particular, we find that a cell-mediated immune response plays an important role in controlling the virus after the peak in viral load.     

What Controls the Acute Viral Infection Following Yellow Fever Vaccination?

Does target cell depletion, innate immunity, or adaptive immunity play the dominant role in controlling primary acute viral infections? Why do some individuals have higher peak virus titers than others? Answering these questions is a basic problem in immunology and can be particularly difficult in humans due to limited data, heterogeneity in responses in different individuals, and limited ability for experimental manipulation. We address these questions for infections following vaccination with the live attenuated yellow fever virus (YFV-17D) by analyzing viral load data from 80 volunteers. Using a mixed effects modeling approach, we find that target cell depletion models do not fit the data as well as innate or adaptive immunity models. Examination of the fits of the innate and adaptive immunity models to the data allows us to select a minimal model that gives improved fits by widely used model selection criteria (AICc and BIC) and explains why it is hard to distinguish between the innate and adaptive immunity models. We then ask why some individuals have over 1000-fold higher virus titers than others and find that most of the variation arises from differences in the initial/maximum growth rate of the virus in different individuals.     

The differential infectivity and staged progression models for the transmission of HIV

Recent studies of HIV RNA in infected individuals show that viral levels vary widely between individuals and within the same individual over time. Individuals with higher viral loads during the chronic phase tend to develop AIDS more rapidly. If RNA levels are correlated with infectiousness, these variations explain puzzling results from HIV transmission studies and suggest that a small subset of infected people may be responsible for a disproportionate number of infections. We use two simple models to study the impact of variations in infectiousness. In the first model, we account for different levels of virus between individuals during the chronic phase of infection, and the increase in the average time from infection to AIDS that goes along with a decreased viral load. The second model follows the more standard hypothesis that infected individuals progress through a series of infection stages, with the infectiousness of a person depending upon his current disease stage. We derive and compare threshold conditions for the two models and find explicit formulas of their endemic equilibria. We show that formulas for both models can be put into a standard form, which allows for a clear interpretation. We define the relative impact of each group as the fraction of infections being caused by that group. We use these formulas and numerical simulations to examine the relative importance of different stages of infection and different chronic levels of virus to the spreading of the disease. The acute stage and the most infectious group both appear to have a disproportionate effect, especially on the early epidemic. Contact tracing to identify super-spreaders and alertness to the symptoms of acute HIV infection may both be needed to contain this epidemic.     

Estimating the Life Course of Influenza A(H3N2) Antibody Responses from Cross-Sectional Data

The immunity of a host population against specific influenza A strains can influence a number of important biological processes, from the emergence of new virus strains to the effectiveness of vaccination programmes. However, the development of an individual’s long-lived antibody response to influenza A over the course of a lifetime remains poorly understood. Accurately describing this immunological process requires a fundamental understanding of how the mechanisms of boosting and cross-reactivity respond to repeated infections. Establishing the contribution of such mechanisms to antibody titres remains challenging because the aggregate effect of immune responses over a lifetime are rarely observed directly. To uncover the aggregate effect of multiple influenza infections, we developed a mechanistic model capturing both past infections and subsequent antibody responses. We estimated parameters of the model using cross-sectional antibody titres to nine different strains spanning 40 years of circulation of influenza A(H3N2) in southern China. We found that “antigenic seniority” and quickly decaying cross-reactivity were important components of the immune response, suggesting that the order in which individuals were infected with influenza strains shaped observed neutralisation titres to a particular virus. We also obtained estimates of the frequency and age distribution of influenza infection, which indicate that although infections became less frequent as individuals progressed through childhood and young adulthood, they occurred at similar rates for individuals above age 30 y. By establishing what are likely to be important mechanisms driving epochal trends in population immunity, we also identified key directions for future studies. In particular, our results highlight the need for longitudinal samples that are tested against multiple historical strains. This could lead to a better understanding of how, over the course of a lifetime, fast, transient antibody dynamics combine with the longer-term immune responses considered here.     

Anti-tumor immunity in adult T-cell leukemia

Adult T-cell leukemia (ATL) occurs in a small population of human T-cell leukemia virus type I (HTLV-I)-infected individuals. It has been noted that ATL is incidentally associated with mother-to-child infection which occurs mainly through breast-feeding, elevated levels of proviral load, and insufficiency in HTLV-I-specific cytotoxic T lymphocyte (CTL) responses. Among these, anti-tumor potentials of HTLV-I-specific CTL have been shown in ex vivo analysis of human HTLV-I-infected individuals and also in vivo experiments by using rat models of HTLV-I-infected lymphomas. In another rat model of HTLV-I-infection, orally infected rats showed significantly higher HTLV-I proviral load but lower HTLV-I-specific cellular immune responses than in intraperitoneally infected rats. As a result, persistent viral load was inversely correlated with levels of virus-specific T-cell responses. HTLV-I-specific T-cell responses in orally infected rats recovered by re-immunization. Conversion of Tax-specific T-cell responses from low to high levels was also observed in an ATL patient who obtained complete remission after hematopoietic stem cell transplantation. These findings suggest that HTLV-I-specific immune unresponsiveness associated with oral HTLV-I infection may be a potential risk factor for development of ATL, allowing expansion of the infected cell reservoir in vivo, and that immunological strategies targeting Tax may potentially reduce the risk of ATL and induce therapeutic effects on ATL.     

Persistence of viral infections on the population level explained by an immunoepidemiological model

We consider a mathematical model of viral spread in a population based on an immune response model embedded in an epidemic network model. The immune response model includes virus load and effector and memory T cells with two possible outcomes depending on parameters: (a) virus clearance and establishment of immune memory and (b) establishment of a non-zero viral presence characterized with increased T-cell concentrations. Isolated individuals can have different immune system parameters and, after a primary infection, can either return to the infection-free state or develop persistent or chronic infection. When individuals are connected in the network, they can reinfect each other. We show that the virus can persist in the epidemic network for indefinite time even if the whole population consists of individuals that are able to clear the virus when isolated from the network. In this case a few individuals with a relatively weak immune response can maintain the infection in the whole population. These results are in contrast to implications of classical epidemiological models that a viral epidemic will end if there is no influx of new susceptibles and if individuals can become immune after infection.     

Viral Dynamics during Structured Treatment Interruptions of Chronic Human Immunodeficiency Virus Type 1 Infection

Although antiviral agents which block human immunodeficiency virus (HIV) replication can result in long-term suppression of viral loads to undetectable levels in plasma, long-term therapy fails to eradicate virus, which generally rebounds after a single treatment interruption. Multiple structured treatment interruptions (STIs) have been suggested as a possible strategy that may boost HIV-specific immune responses and control viral replication. We analyze viral dynamics during four consecutive STI cycles in 12 chronically infected patients with a history (>2 years) of viral suppression under highly active antiretroviral therapy. We fitted a simple model of viral rebound to the viral load data from each patient by using a novel statistical approach that allows us to overcome problems of estimating viral dynamics parameters when there are many viral load measurements below the limit of detection. There is an approximate halving of the average viral growth rate between the first and fourth STI cycles, yet the average time between treatment interruption and detection of viral loads in the plasma is approximately the same in the first and fourth interruptions. We hypothesize that reseeding of viral reservoirs during treatment interruptions can account for this discrepancy, although factors such as stochastic effects and the strength of HIV-specific immune responses may also affect the time to viral rebound. We also demonstrate spontaneous drops in viral load in later STIs, which reflect fluctuations in the rates of viral production and/or clearance that may be caused by a complex interaction between virus and target cells and/or immune responses.     

Zika virus dynamics: Effects of inoculum dose,the innate immune response and viral interference

Experimental Zika virus infection in non-human primates results in acute viral load dynamics that can be well-described by mathematical models. The inoculum dose that would be received in a natural infection setting is likely lower than the experimental infections and how this difference affects the viral dynamics and immune response is unclear. Here we study a dataset of experimental infection of non-human primates with a range of doses of Zika virus. We develop new models of infection incorporating both an innate immune response and viral interference with that response. We find that such a model explains the data better than models with no interaction between virus and the immune response. We also find that larger inoculum doses lead to faster dynamics of infection, but approximately the same total amount of viral production.     

No evidence for homosubtypic immunity of influenza H3 in Mallards following vaccination in a natural experimental system

The Mallard (Anas platyrhynchos) is an important reservoir species for influenza A viruses (IAV), and in this host, prevalence and virus diversity are high. Studies have demonstrated the presence of homosubtypic immunity, where individuals are unlikely to be reinfected with the same subtype within an autumn season. Further, evidence for heterosubtypic immunity exists, whereby immune responses specific for one subtype offer partial or complete protection against related HA subtypes. We utilized a natural experimental system to determine whether homo‐ or heterospecific immunity could be induced following experimental vaccination. Thirty Mallards were vaccinated with an inactivated H3, H6 or a sham vaccine and after seroconversion were exposed to naturally infected wild conspecifics. All ducks were infected within 2 days and had both primary and secondary infections. Overall, there was no observable difference between groups; all individuals were infected with H3 and H10 IAV. At the cessation of the experiment, most individuals had anti‐NP antibodies and neutralizing antibodies against H10. Not all individuals had H3 neutralizing antibodies. The isolated H3 IAVs revealed genetic dissimilarity to the H3 vaccine strain, specifically substitutions in the vicinity of the receptor‐binding site. There was no evidence of vaccine‐induced homosubtypic immunity to H3, a likely result of both a poor H3 immune response in the ducks and H3 immune escape. Likewise, there was no observed heterosubtypic protection related to H6 vaccination. This study highlights the need for experimental approaches to assess how exposure to pathogens and resulting immune processes translates to individual and population disease dynamics.     

Expansion of human T-cell leukemia virus type 1 (HTLV-1) reservoir in orally infected rats: inverse correlation with HTLV-1-specific cellular immune response

Adult T-cell leukemia (ATL) occurs in a small population of human T-cell leukemia virus type 1 (HTLV-1)-infected individuals. Although the critical risk factor for ATL development is not clear, it has been noted that ATL is incidentally associated with mother-to-child infection, elevated proviral loads, and weakness in HTLV-1-specific T-cell immune responses. In the present study, using a rat system, we investigated the relationships among the following conditions: primary HTLV-1 infection, a persistent HTLV-1 load, and host HTLV-1-specific immunity. We found that the persistent HTLV-1 load in orally infected rats was significantly greater than that in intraperitoneally infected rats. Even after inoculation with only 50 infected cells, a persistent viral load built up to considerable levels in some orally infected rats but not in intraperitoneally infected rats. In contrast, HTLV-1-specific cellular immune responses were markedly impaired in orally infected rats. As a result, a persistent viral load was inversely correlated with levels of virus-specific T-cell responses in these rats. Otherwise very weak HTLV-1-specific cellular immune responses in orally infected rats were markedly augmented after subcutaneous reimmunization with infected syngeneic rat cells. These findings suggest that HTLV-1-specific immune unresponsiveness associated with oral HTLV-1 infection may be a potential risk factor for development of ATL, allowing expansion of the infected cell reservoir in vivo, but could be overcome with immunological strategies.     

Plasma viral RNA load predicts disease progression in accelerated feline immunodeficiency virus infection.

Viral RNA load has been shown to indicate disease stage and predict the rapidity of disease progression in human immunodeficiency virus type 1 (HIV-1)-infected individuals. We had previously demonstrated that feline immunodeficiency virus (FIV) RNA levels in plasma correlate with disease stage in infected cats. Here we expand upon those observations by demonstrating that plasma virus load is 1 to 2 logs higher in cats with rapidly progressive FIV disease than in long-term survivors. Differences in plasma FIV RNA levels are evident by 1 to 2 weeks after infection and are consistent throughout infection. We also evaluated humoral immune responses in FIV-infected cats for correlation with survival times. Total anti-FIV antibody titers did not differ between cats with rapidly progressive FIV disease and long-term survivors. These findings indicate that virus replication plays an important role in FIV disease progression, as it does in HIV-1 disease progression. The parallels in virus loads and disease progressions between HIV-1 and FIV support the idea that the accelerated disease model is well suited for the study of therapeutic agents directed at reducing lentiviral replication.     

Coreceptor Switching in HIV-1 Subtype B and Subtype C

We use a mathematical model to determine the factors affecting the delayed or rare coreceptor switch in HIV-1 subtype C infected individuals. The model takes into account the two main target cells for the CXCR4-tropic and CCR5-tropic virus and includes the the lytic and non-lytic immune responses. Computer-based simulations and a sensitivity analysis of the model predict that a persistent immune response suppresses the CXCR4-tropic virus to low levels and hence preventing a phenotypic switch. However, not only should the immune response be persistent, but it should have an efficient lytic immune response rather that an efficient non-lytic response. In addition, we also find that the availability of macrophage cells and enhanced viral kinetics are also crucial for the dominance of the R5 strain. We suggest that an altered host environment probably as a result of immune activation may explain the difference in coreceptor switching kinetics between HIV-1 subtype B and subtype C individuals.     

A Multi-scale Analysis of Influenza A Virus Fitness Trade-offs due to Temperature-dependent Virus Persistence

Successful replication within an infected host and successful transmission between hosts are key to the continued spread of most pathogens. Competing selection pressures exerted at these different scales can lead to evolutionary trade-offs between the determinants of fitness within and between hosts. Here, we examine such a trade-off in the context of influenza A viruses and the differential pressures exerted by temperature-dependent virus persistence. For a panel of avian influenza A virus strains, we find evidence for a trade-off between the persistence at high versus low temperatures. Combining a within-host model of influenza infection dynamics with a between-host transmission model, we study how such a trade-off affects virus fitness on the host population level. We show that conclusions regarding overall fitness are affected by the type of link assumed between the within- and between-host levels and the main route of transmission (direct or environmental). The relative importance of virulence and immune response mediated virus clearance are also found to influence the fitness impacts of virus persistence at low versus high temperatures. Based on our results, we predict that if transmission occurs mainly directly and scales linearly with virus load, and virulence or immune responses are negligible, the evolutionary pressure for influenza viruses to evolve toward good persistence at high within-host temperatures dominates. For all other scenarios, influenza viruses with good environmental persistence at low temperatures seem to be favored.     

Within-Host Models of High and Low Pathogenic Influenza Virus Infections: The Role of Macrophages

The World Health Organization identifies influenza as a major public health problem. While the strains commonly circulating in humans usually do not cause severe pathogenicity in healthy adults, some strains that have infected humans, such as H5N1, can cause high morbidity and mortality. Based on the severity of the disease, influenza viruses are sometimes categorized as either being highly pathogenic (HP) or having low pathogenicity (LP). The reasons why some strains are LP and others HP are not fully understood. While there are likely multiple mechanisms of interaction between the virus and the immune response that determine LP versus HP outcomes, we focus here on one component, namely macrophages (MP). There is some evidence that MP may both help fight the infection and become productively infected with HP influenza viruses. We developed mathematical models for influenza infections which explicitly included the dynamics and action of MP. We fit these models to viral load and macrophage count data from experimental infections of mice with LP and HP strains. Our results suggest that MP may not only help fight an influenza infection but may contribute to virus production in infections with HP viruses. We also explored the impact of combination therapies with antivirals and anti-inflammatory drugs on HP infections. Our study suggests a possible mechanism of MP in determining HP versus LP outcomes, and how different interventions might affect infection dynamics.     

HIV Evolution in Early Infection: Selection Pressures,Patterns of Insertion and Deletion,and the Impact of APOBEC

The pattern of viral diversification in newly infected individuals provides information about the host environment and immune responses typically experienced by the newly transmitted virus. For example, sites that tend to evolve rapidly across multiple early-infection patients could be involved in enabling escape from common early immune responses, could represent adaptation for rapid growth in a newly infected host, or could represent reversion from less fit forms of the virus that were selected for immune escape in previous hosts. Here we investigated the diversification of HIV-1 env coding sequences in 81 very early B subtype infections previously shown to have resulted from transmission or expansion of single viruses (n = 78) or two closely related viruses (n = 3). In these cases, the sequence of the infecting virus can be estimated accurately, enabling inference of both the direction of substitutions as well as distinction between insertion and deletion events. By integrating information across multiple acutely infected hosts, we find evidence of adaptive evolution of HIV-1 env and identify a subset of codon sites that diversified more rapidly than can be explained by a model of neutral evolution. Of 24 such rapidly diversifying sites, 14 were either i) clustered and embedded in CTL epitopes that were verified experimentally or predicted based on the individual''s HLA or ii) in a nucleotide context indicative of APOBEC-mediated G-to-A substitutions, despite having excluded heavily hypermutated sequences prior to the analysis. In several cases, a rapidly evolving site was embedded both in an APOBEC motif and in a CTL epitope, suggesting that APOBEC may facilitate early immune escape. Ten rapidly diversifying sites could not be explained by CTL escape or APOBEC hypermutation, including the most frequently mutated site, in the fusion peptide of gp41. We also examined the distribution, extent, and sequence context of insertions and deletions, and we provide evidence that the length variation seen in hypervariable loop regions of the envelope glycoprotein is a consequence of selection and not of mutational hotspots. Our results provide a detailed view of the process of diversification of HIV-1 following transmission, highlighting the role of CTL escape and hypermutation in shaping viral evolution during the establishment of new infections.     

Variability of HIV infections.

Genetic variation is the hallmark of infections with lentiviruses in general and the human immunodeficiency viruses (HIV-1, HIV-2) in particular. This article reviews both experimental evidence for the variability of the HIV genome during the course of an individual infection and mathematical models that outline the potential importance of antigenic variation as a major factor to drive disease progression. The essential idea is that the virus evades immune pressure by the continuous production of new mutants resistant to current immunological attack. This results in the accumulation of antigenic diversity during the asymptomatic period. The existence of an antigenic diversity threshold is derived from the asymmetric interaction between the virus quasispecies and the CD4 cell population: CD4 cells mount immune responses some of which are directed against specific HIV variants, but each virus strain can induce depletion of all CD4 cells and therefore impair immune responses regardless of their specificity. Therefore, increasing HIV diversity enables the virus population to escape from control by the immune system. In this context the observed genetic variability is responsible for the fact that the virus establishes a persistent infection without being cleared by the immune response and induces immunodeficiency disease after a long and variable incubation period. Mathematical biology has revealed a novel mechanism for viral pathogenesis.     

Immune responses and the emergence of drug-resistant virus strains in vivo

The treatment of viral infections using antiviral drugs has had a significant public health benefit in the setting of human immunodeficiency virus (HIV) infection, and newly developed drugs offer potential benefits in the management of other viral infections, including acute self-limiting infections such as influenza and picornaviruses (including the rhinoviruses that are responsible for a large proportion of 'common colds'). A serious concern with such treatments is that they may lead to the selection of drug-resistant strains. This has been a significant problem in the case of HIV infection. Existing mathematical-modelling studies of drug resistance have focused on the interactions between virus, target cells and infected cells, ignoring the impact of immune responses. Here, we present a model that explores the role of immune responses in the rise of drug-resistant mutants in vivo. We find that drug resistance is unlikely to be a problem if immune responses are maintained above a threshold level during therapy. Alternatively, if immune responses decline at a fast rate and fall below a threshold level during treatment (indicating impaired immunity), the rise of drug-resistant mutants is more likely. This indicates an important difference between HIV, which impairs immunity and for which immune responses have been observed to vanish during treatment, and viral infections such as influenza and rhinoviruses, for which such immune impairment is not present. Drug resistance is much more likely to be a problem in HIV than in acute and self-limiting infections.     

Increased burst size in multiply infected cells can alter basic virus dynamics

ABSTRACT: BACKGROUND: The dynamics of viral infections have been studied extensively in a variety of settings, both experimentally and with mathematical models. The majori-ty of mathematical models assumes that only one virus can infect a given cell at a time. It is, however, clear that especially in the context of high viral load, cells can become infected with multiple copies of a virus, a process called coinfection. This has been best demonstrated experimentally for human immunodeficiency virus (HIV), although it is thought to be equally relevant for a number of other viral infections. In a previously explored mathematical model, the viral output from an infected cell does not depend on the number of viruses that reside in the cell, i.e. viral replication is limited by cellular rather than viral factors. In this case, basic virus dynamics properties are not altered by coinfection. Results: Here, we explore the alternative assumption that multiply infected cells are characterized by an increased burst size and find that this can fundamentally alter model predictions. Under this scenario, establishment of infection may not be solely determined by the basic reproductive ratio of the virus, but can depend on the initial virus load. Upon infection, the virus population need not follow straight exponential growth. Instead, the exponential rate of growth can increase over time as virus load becomes larger. Moreover, the model suggests that the ability of anti-viral drugs to suppress the virus population can depend on the virus load upon initiation of therapy. This is because more coinfected cells, which produce more virus, are present at higher virus loads. Hence, the degree of drug resistance is not only determined by the viral genotype, but also by the prevalence of coinfected cells. Conclusions: Our work shows how an increased burst size in multiply infected cells can alter basic infection dynamics. This forms the basis for future experimental testing of model assumptions and predictions that can distinguish between the different scenarios.     

Transient antiretroviral treatment during acute simian immunodeficiency virus infection facilitates long-term control of the virus

Experimental evidence and mathematical models indicate that CD4+ T-cell help is required to generate memory cytotoxicT-lymphocyte precursors (CTLp) that are capable of persisting without ongoing antigenic stimulation, and that such responses are necessary to clear an infection or to control it in the long term. Here we analyse mathematical models of simian immunodeficiency virus (SIV) replication in macaques, assuming that SIV impairs specific CD4+ T-cell responses. According to the models, fast viral replication during the initial stages of primary infection can result in failure to generate sufficient long-lived memory CTLp required to control the infection in the long term. Modelling of drug therapy during the acute phase of the infection indicates that transient treatment can minimize the amount of virus-induced immune impairment, allowing a more effective initial immune sensitization. The result is the development of high levels of memory CTLp that are capable of controlling SIV replication in the long term, in the absence of continuous treament. In the model, the success of treatment depends crucially on the timing and duration of antiretroviral therapy. Data on SIV-infected macaques receiving transient drug therapy during acute infection support these theoretical predictions. The data and modelling suggest that among subjects controlling SIV replication most efficiently after treatment, there is a positive correlation between cellular immune responses and virus load in the post-acute stage of infection. Among subjects showing less-efficient virus control, the correlation is negative. We discuss our findings in relation to previously published data on HIV infection.     

Vaccination alters the balance between protective immunity, exhaustion, escape, and death in chronic infections

While T cell-based vaccines have the potential to provide protection against chronic virus infections, they also have the potential to generate immunopathology following subsequent virus infection. We develop a mathematical model to investigate the conditions under which T cells lead to protection versus adverse pathology. The model illustrates how the balance between virus clearance and immune exhaustion may be disrupted when vaccination generates intermediate numbers of specific CD8 T cells. Surprisingly, our model suggests that this adverse effect of vaccination is largely unaffected by the generation of mutant viruses that evade T cell recognition and cannot be avoided by simply increasing the quality (affinity) or diversity of the T cell response. These findings should be taken into account when developing vaccines against persistent infections.