HIV-1 infection and low steady state viral loads

Highly active antiretroviral therapy (HAART) reduces the viral burden in human immunodeficiency virus type 1 (HIV-1) infected patients below the threshold of detectability. However, substantial evidence indicates that viral replication persists in these individuals. In this paper we examine the ability of several biologically motivated models of HIV-1 dynamics to explain sustained low viral loads. At or near drug efficacies that result in steady state viral loads below detectability, most models are extremely sensitive to small changes in drug efficacy. We argue that if these models reflect reality many patients should have cleared the virus, contrary to observation. We find that a model in which the infected cell death rate is dependent on the infected cell density does not suffer this shortcoming. The shortcoming is also overcome in two more conventional models that include small populations of cells in which the drug is less effective than in the main population, suggesting that difficulties with drug penetrance and maintenance of effective intracellular drug concentrations in all cells susceptible to HIV infection may underlie ongoing viral replication.     

A hybrid stochastic-deterministic approach to explore multiple infection and evolution in HIV

To study viral evolutionary processes within patients, mathematical models have been instrumental. Yet, the need for stochastic simulations of minority mutant dynamics can pose computational challenges, especially in heterogeneous systems where very large and very small sub-populations coexist. Here, we describe a hybrid stochastic-deterministic algorithm to simulate mutant evolution in large viral populations, such as acute HIV-1 infection, and further include the multiple infection of cells. We demonstrate that the hybrid method can approximate the fully stochastic dynamics with sufficient accuracy at a fraction of the computational time, and quantify evolutionary end points that cannot be expressed by deterministic models, such as the mutant distribution or the probability of mutant existence at a given infected cell population size. We apply this method to study the role of multiple infection and intracellular interactions among different virus strains (such as complementation and interference) for mutant evolution. Multiple infection is predicted to increase the number of mutants at a given infected cell population size, due to a larger number of infection events. We further find that viral complementation can significantly enhance the spread of disadvantageous mutants, but only in select circumstances: it requires the occurrence of direct cell-to-cell transmission through virological synapses, as well as a substantial fitness disadvantage of the mutant, most likely corresponding to defective virus particles. This, however, likely has strong biological consequences because defective viruses can carry genetic diversity that can be incorporated into functional virus genomes via recombination. Through this mechanism, synaptic transmission in HIV might promote virus evolvability.     

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.     

Success of prophylactic antiviral therapy for SARS-CoV-2: Predicted critical efficacies and impact of different drug-specific mechanisms of action

Repurposed drugs that are safe and immediately available constitute a first line of defense against new viral infections. Despite limited antiviral activity against SARS-CoV-2, several drugs are being tested as medication or as prophylaxis to prevent infection. Using a stochastic model of early phase infection, we evaluate the success of prophylactic treatment with different drug types to prevent viral infection. We find that there exists a critical efficacy that a treatment must reach in order to block viral establishment. Treatment by a combination of drugs reduces the critical efficacy, most effectively by the combination of a drug blocking viral entry into cells and a drug increasing viral clearance. Below the critical efficacy, the risk of infection can nonetheless be reduced. Drugs blocking viral entry into cells or enhancing viral clearance reduce the risk of infection more than drugs that reduce viral production in infected cells. The larger the initial inoculum of infectious virus, the less likely is prevention of an infection. In our model, we find that as long as the viral inoculum is smaller than 10 infectious virus particles, viral infection can be prevented almost certainly with drugs of 90% efficacy (or more). Even when a viral infection cannot be prevented, antivirals delay the time to detectable viral loads. The largest delay of viral infection is achieved by drugs reducing viral production in infected cells. A delay of virus infection flattens the within-host viral dynamic curve, possibly reducing transmission and symptom severity. Thus, antiviral prophylaxis, even with reduced efficacy, could be efficiently used to prevent or alleviate infection in people at high risk.     

Residual Viremia in Treated HIV+ Individuals

Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. However, some residual virus remains, below the level of detection, in HIV-infected patients on ART. The source of this viremia is an area of debate: does it derive primarily from activation of infected cells in the latent reservoir, or from ongoing viral replication? Observations seem to be contradictory: there is evidence of short term evolution, implying that there must be ongoing viral replication, and viral strains should thus evolve. However, phylogenetic analyses, and rare emergent drug resistance, suggest no long-term viral evolution, implying that virus derived from activated latent cells must dominate. We use simple deterministic and stochastic models to gain insight into residual viremia dynamics in HIV-infected patients. Our modeling relies on two underlying assumptions for patients on suppressive ART: that latent cell activation drives viral dynamics and that the reproductive ratio of treated infection is less than 1. Nonetheless, the contribution of viral replication to residual viremia in patients on ART may be non-negligible. However, even if the portion of viremia attributable to viral replication is significant, our model predicts (1) that latent reservoir re-seeding remains negligible, and (2) some short-term viral evolution is permitted, but long-term evolution can still be limited: stochastic analysis of our model shows that de novo emergence of drug resistance is rare. Thus, our simple models reconcile the seemingly contradictory observations on residual viremia and, with relatively few parameters, recapitulates HIV viral dynamics observed in patients on suppressive therapy.     

Stochastic theory of early viral infection: continuous versus burst production of virions

Viral production from infected cells can occur continuously or in a burst that generally kills the cell. For HIV infection, both modes of production have been suggested. Standard viral dynamic models formulated as sets of ordinary differential equations can not distinguish between these two modes of viral production, as the predicted dynamics is identical as long as infected cells produce the same total number of virions over their lifespan. Here we show that in stochastic models of viral infection the two modes of viral production yield different early term dynamics. Further, we analytically determine the probability that infections initiated with any number of virions and infected cells reach extinction, the state when both the population of virions and infected cells vanish, and show this too has different solutions for continuous and burst production. We also compute the distributions of times to establish infection as well as the distribution of times to extinction starting from both a single virion as well as from a single infected cell for both modes of virion production.     

A modular framework for multiscale,multicellular, spatiotemporal modeling of acute primary viral infection and immune response in epithelial tissues and its application to drug therapy timing and effectiveness

Simulations of tissue-specific effects of primary acute viral infections like COVID-19 are essential for understanding disease outcomes and optimizing therapies. Such simulations need to support continuous updating in response to rapid advances in understanding of infection mechanisms, and parallel development of components by multiple groups. We present an open-source platform for multiscale spatiotemporal simulation of an epithelial tissue, viral infection, cellular immune response and tissue damage, specifically designed to be modular and extensible to support continuous updating and parallel development. The base simulation of a simplified patch of epithelial tissue and immune response exhibits distinct patterns of infection dynamics from widespread infection, to recurrence, to clearance. Slower viral internalization and faster immune-cell recruitment slow infection and promote containment. Because antiviral drugs can have side effects and show reduced clinical effectiveness when given later during infection, we studied the effects on progression of treatment potency and time-of-first treatment after infection. In simulations, even a low potency therapy with a drug which reduces the replication rate of viral RNA greatly decreases the total tissue damage and virus burden when given near the beginning of infection. Many combinations of dosage and treatment time lead to stochastic outcomes, with some simulation replicas showing clearance or control (treatment success), while others show rapid infection of all epithelial cells (treatment failure). Thus, while a high potency therapy usually is less effective when given later, treatments at late times are occasionally effective. We illustrate how to extend the platform to model specific virus types (e.g., hepatitis C) and add additional cellular mechanisms (tissue recovery and variable cell susceptibility to infection), using our software modules and publicly-available software repository.     

Natural variation in HIV infection: Monte Carlo estimates that include CD8 effector cells

Viral load and CD4 T-cell counts in patients infected with the human immunodeficiency virus (HIV) are commonly used to guide clinical decisions regarding drug therapy or to assess therapeutic outcomes in clinical trials. However, random fluctuations in these markers of infection can obscure clinically significant change. We employ a Monte Carlo simulation to investigate contributing factors in the expected variability in CD4 T-cell count and viral load due solely to the stochastic nature of HIV infection. The simulation includes processes that contribute to the variability in HIV infection including CD4 and CD8 T-cell population dynamics as well as T-cell activation and proliferation. The simulation results may reconcile the wide range of variabilities in viral load observed in clinical studies, by quantifying correlations between viral load measurements taken days or weeks apart. The sensitivity of variability in T-cell count and viral load to changes in the lifetimes of CD4 and CD8 T-cells is investigated, as well as the effects of drug therapy.     

Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models

The dynamics of HIV-1 infection consist of three distinct phases starting with primary infection, then latency and finally AIDS or drug therapy. In this paper we model the dynamics of primary infection and the beginning of latency. We show that allowing for time delays in the model better predicts viral load data when compared to models with no time delays. We also find that our model of primary infection predicts the turnover rates for productively infected T cells and viral totals to be much longer than compared to data from patients receiving anti-viral drug therapy. Hence the dynamics of the infection can change dramatically from one stage to the next. However, we also show that with the data available the results are highly sensitive to the chosen model. We compare the results using analysis and Monte Carlo techniques for three different models and show how each predicts rather dramatic differences between the fitted parameters. We show, using a chi(2) test, that these differences between models are statistically significant and using a jackknifing method, we find the confidence intervals for the parameters. These differences in parameter estimations lead to widely varying conclusions about HIV pathogenesis. For instance, we find in our model with time delays the existence of a Hopf bifurcation that leads to sustained oscillations and that these oscillations could simulate the rapid turnover between viral strains and the appropriate CTL response necessary to control the virus, similar to that of a predator-prey type system.     

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.     

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.     

Modeling the role of macrophages in HIV persistence during antiretroviral therapy

HIV preferentially infects activated CD4+ T cells. Current antiretroviral therapy cannot eradicate the virus. Viral infection of other cells such as macrophages may contribute to viral persistence during antiretroviral therapy. In addition to cell-free virus infection, macrophages can also get infected when engulfing infected CD4+ T cells as innate immune sentinels. How macrophages affect the dynamics of HIV infection remains unclear. In this paper, we develop an HIV model that includes the infection of CD4+ T cells and macrophages via cell-free virus infection and cell-to-cell viral transmission. We derive the basic reproduction number and obtain the local and global stability of the steady states. Sensitivity and viral dynamics simulations show that even when the infection of CD4+ T cells is completely blocked by therapy, virus can still persist and the steady-state viral load is not sensitive to the change of treatment efficacy. Analysis of the relative contributions to viral replication shows that cell-free virus infection leads to the majority of macrophage infection. Viral transmission from infected CD4+ T cells to macrophages during engulfment accounts for a small fraction of the macrophage infection and has a negligible effect on the total viral production. These results suggest that macrophage infection can be a source contributing to HIV persistence during suppressive therapy. Improving drug efficacies in heterogeneous target cells is crucial for achieving HIV eradication in infected individuals.

     

Modeling the Slow CD4+ T Cell Decline in HIV-Infected Individuals

The progressive loss of CD4+ T cell population is the hallmark of HIV-1 infection but the mechanism underlying the slow T cell decline remains unclear. Some recent studies suggested that pyroptosis, a form of programmed cell death triggered during abortive HIV infection, is associated with the release of inflammatory cytokines, which can attract more CD4+ T cells to be infected. In this paper, we developed mathematical models to study whether this mechanism can explain the time scale of CD4+ T cell decline during HIV infection. Simulations of the models showed that cytokine induced T cell movement can explain the very slow decline of CD4+ T cells within untreated patients. The long-term CD4+ T cell dynamics predicted by the models were shown to be consistent with available data from patients in Rio de Janeiro, Brazil. Highly active antiretroviral therapy has the potential to restore the CD4+ T cell population but CD4+ response depends on the effectiveness of the therapy, when the therapy is initiated, and whether there are drug sanctuary sites. The model also showed that chronic inflammation induced by pyroptosis may facilitate persistence of the HIV latent reservoir by promoting homeostatic proliferation of memory CD4+ cells. These results improve our understanding of the long-term T cell dynamics in HIV-1 infection, and support that new treatment strategies, such as the use of caspase-1 inhibitors that inhibit pyroptosis, may maintain the CD4+ T cell population and reduce the latent reservoir size.     

Modeling the short-, middle- and long-term viral load responses for comparing estimated dynamic parameters

A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate antiviral therapies in AIDS clinical trials. This marker can be used to assess the antiviral potency of therapies, but is easily affected by drug exposures, drug resistance and other factors during the long-term treatment evaluation process. The study of HIV dynamics is one of the most important development in recent AIDS research for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. Although many HIV dynamic models have been proposed by AIDS researchers in the last decade, they have only been used to quantify short-term viral dynamics and do not correctly describe long-term virologic responses to antiretroviral treatment. In other words, these simple viral dynamic models can only be used to fit short-term viral load data for estimating dynamic parameters. In this paper, a mechanism-based differential equation models is introduced for characterizing the long-term viral dynamics with antiretroviral therapy. We applied this model to fit different segments of the viral load trajectory data from a simulation experiment and an AIDS clinical trial study, and found that the estimates of dynamic parameters from our modeling approach are very consistent. We may conclude that our model can not only characterize long-term viral dynamics, but can also quantify short- and middle-term viral dynamics. It suggests that if there are enough data in the early stage of the treatment, the results from our modeling based on short-term information can be used to capture the performance of long-term care with HIV-1 infected patients.     

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.     

A Hepatitis C Virus Infection Model with Time-Varying Drug Effectiveness: Solution and Analysis

Simple models of therapy for viral diseases such as hepatitis C virus (HCV) or human immunodeficiency virus assume that, once therapy is started, the drug has a constant effectiveness. More realistic models have assumed either that the drug effectiveness depends on the drug concentration or that the effectiveness varies over time. Here a previously introduced varying-effectiveness (VE) model is studied mathematically in the context of HCV infection. We show that while the model is linear, it has no closed-form solution due to the time-varying nature of the effectiveness. We then show that the model can be transformed into a Bessel equation and derive an analytic solution in terms of modified Bessel functions, which are defined as infinite series, with time-varying arguments. Fitting the solution to data from HCV infected patients under therapy has yielded values for the parameters in the model. We show that for biologically realistic parameters, the predicted viral decay on therapy is generally biphasic and resembles that predicted by constant-effectiveness (CE) models. We introduce a general method for determining the time at which the transition between decay phases occurs based on calculating the point of maximum curvature of the viral decay curve. For the parameter regimes of interest, we also find approximate solutions for the VE model and establish the asymptotic behavior of the system. We show that the rate of second phase decay is determined by the death rate of infected cells multiplied by the maximum effectiveness of therapy, whereas the rate of first phase decline depends on multiple parameters including the rate of increase of drug effectiveness with time.     

Opportunistic infection as a cause of transient viremia in chronically infected HIV patients under treatment with HAART

When highly active antiretroviral therapy is administered for long periods of time to HIV-1 infected patients, most patients achieve viral loads that are “undetectable” by standard assay (i.e., HIV-1 RNA < 50 copies/ml). Yet despite exhibiting sustained viral loads below the level of detection, a number of these patients experience unexplained episodes of transient viremia or viral “blips”. We propose here that transient activation of the immune system by opportunistic infection may explain these episodes of viremia. Indeed, immune activation by opportunistic infection may spur HIV replication, replenish viral reservoirs and contribute to accelerated disease progression. In order to investigate the effects of intercurrent infection on chronically infected HIV patients under treatment with highly active antiretroviral therapy (HAART), we extend a simple dynamic model of the effects of vaccination on HIV infection [Jones, L.E., Perelson, A.S., 2002. Modeling the effects of vaccination on chronically infected HIV-positive patients. JAIDS 31, 369–377] to include growing pathogens. We then propose a more realistic model for immune cell expansion in the presence of pathogen, and include this in a set of competing models that allow low baseline viral loads in the presence of drug treatment. Programmed expansion of immune cells upon exposure to antigen is a feature not previously included in HIV models, and one that is especially important to consider when simulating an immune response to opportunistic infection. Using these models we show that viral blips with realistic duration and amplitude can be generated by intercurrent infections in HAART treated patients.     

Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics

A formal sensitivity analysis is performed on a delay differential equation model for the viral dynamics of an in vivo HIV infection during protease inhibitor therapy. We present results of both a differential analysis as well as a principle component based analysis and provide evidence that suggests the exact times at which specific parameters have the most influence over the solution. We offer insight into the pairwise mathematical relationships between the productively infected T-cell death rate δ, the viral plasma clearance rate c, and the time delay τ between infection and viral production as they relate to the viral dynamics. The results support the claim that the presence of a nonzero delay has a major impact on the model dynamics. Lastly, we comment upon the inadequacies of an alternative principle component based analysis.