Reduction of HIV concentration during acute infection: independence from a specific immune response

Modeling dynamics of acute HIV infection incorporating density-dependent cell death and multiplicity of infection

Understanding the dynamics of acute HIV infection can offer valuable insights into the early stages of viral behavior, potentially helping uncover various aspects of HIV pathogenesis. The standard viral dynamics model explains HIV viral dynamics during acute infection reasonably well. However, the model makes simplifying assumptions, neglecting some aspects of HIV infection. For instance, in the standard model, target cells are infected by a single HIV virion. Yet, cellular multiplicity of infection (MOI) may have considerable effects in pathogenesis and viral evolution. Further, when using the standard model, we take constant infected cell death rates, simplifying the dynamic immune responses. Here, we use four models-1) the standard viral dynamics model, 2) an alternate model incorporating cellular MOI, 3) a model assuming density-dependent death rate of infected cells and 4) a model combining (2) and (3)-to investigate acute infection dynamics in 43 people living with HIV very early after HIV exposure. We find that all models qualitatively describe the data, but none of the tested models is by itself the best to capture different kinds of heterogeneity. Instead, different models describe differing features of the dynamics more accurately. For example, while the standard viral dynamics model may be the most parsimonious across study participants by the corrected Akaike Information Criterion (AICc), we find that viral peaks are better explained by a model allowing for cellular MOI, using a linear regression analysis as analyzed by R2. These results suggest that heterogeneity in within-host viral dynamics cannot be captured by a single model. Depending on the specific aspect of interest, a corresponding model should be employed.

Mathematical Models of HIV-1 Dynamics, Transcription, and Latency

HIV-1 latency is a major barrier to curing infections with antiretroviral therapy and, consequently, to eliminating the disease globally. The establishment, maintenance, and potential clearance of latent infection are complex dynamic processes and can be best described with the help of mathematical models followed by experimental validation. Here, we review the use of viral dynamics models for HIV-1, with a focus on applications to the latent reservoir. Such models have been used to explain the multi-phasic decay of viral load during antiretroviral therapy, the early seeding of the latent reservoir during acute infection and the limited inflow during treatment, the dynamics of viral blips, and the phenomenon of post-treatment control. Finally, we discuss that mathematical models have been used to predict the efficacy of potential HIV-1 cure strategies, such as latency-reversing agents, early treatment initiation, or gene therapies, and to provide guidance for designing trials of these novel interventions.

SARS-coronavirus-2 infections: biological instabilities characterized by order parameters

A four-variable virus dynamics TIIV model was considered that involves infected cells in an eclipse phase. The state space description of the model was transferred into an amplitude space description which is the appropriate general, nonlinear physics framework to describe instabilities. In this context, the unstable eigenvector or order parameter of the model was determined. Subsequently, a model-based analysis of viral load data from eight symptomatic COVID-19 patients was conducted. For all patients, it was found that the initial SARS-CoV-2 infection evolved along the respective patient-specific order parameter, as expected by theoretical considerations. The order parameter amplitude that described the initial virus multiplication showed doubling times between 30 minutes and 3 hours. Peak viral loads of patients were linearly related to the amplitudes of the patient order parameters. Finally, it was found that the patient order parameters determined qualitatively and quantitatively the relationships between the increases in virus-producing infected cells and infected cells in the eclipse phase. Overall, the study echoes the 40 years old suggestion by Mackey and Glass to consider diseases as instabilities.

New SHIVs and Improved Design Strategy for Modeling HIV-1 Transmission, Immunopathogenesis, Prevention and Cure

Previously, we showed that substitution of HIV-1 Env residue 375-Ser by bulky aromatic residues enhances binding to rhesus CD4 and enables primary HIV-1 Envs to support efficient replication as simian-human immunodeficiency virus (SHIV) chimeras in rhesus macaques (RMs). Here, we test this design strategy more broadly by constructing SHIVs containing ten primary Envs corresponding to HIV-1 subtypes A, B, C, AE and AG. All ten SHIVs bearing wildtype Env375 residues replicated efficiently in human CD4+ T cells, but only one replicated efficiently in primary rhesus cells. This was a subtype AE SHIV that naturally contained His at Env375. Replacement of wildtype Env375 residues by Trp, Tyr, Phe or His in the other nine SHIVs led to efficient replication in rhesus CD4+ T cells in vitro and in vivo Nine SHIVs containing optimized Env375 alleles were grown large-scale in primary rhesus CD4+ T cells to serve as challenge stocks in preclinical prevention trials. These virus stocks were genetically homogeneous, native-like in Env antigenicity and tier-2 neutralization sensitivity, and transmissible by rectal, vaginal, penile, oral or intravenous routes. To facilitate future SHIV constructions, we engineered a simplified second-generation design scheme and validated it in RMs. Overall, our findings demonstrate that SHIVs bearing primary Envs with bulky aromatic substitutions at Env375 consistently replicate in RMs, recapitulating many features of HIV-1 infection in humans. Such SHIVs are efficiently transmitted by mucosal routes common to HIV-1 infection and can be used to test vaccine efficacy in preclinical monkey trials.ImportanceSHIV infection of Indian rhesus macaques is an important animal model for studying HIV-1 transmission, prevention, immunopathogenesis and cure. Such research is timely, given recent progress with active and passive immunization and novel approaches to HIV-1 cure. Given the multifaceted roles of HIV-1 Env in cell tropism and virus entry, and as a target for neutralizing and non-neutralizing antibodies, Envs selected for SHIV construction are of paramount importance. Until recently, it has been impossible to strategically design SHIVs bearing clinically relevant Envs that replicate consistently in monkeys. This changed with the discovery that bulky aromatic substitutions at residue Env375 confer enhanced affinity to rhesus CD4. Here, we show that 10 new SHIVs bearing primary HIV-1 Envs with residue 375 substitutions replicated efficiently in RMs and could be transmitted efficiently across rectal, vaginal, penile and oral mucosa. These findings suggest an expanded role for SHIVs as a model of HIV-1 infection.

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.

The relationship between the infecting dose of a pathogen and the subsequent viral dynamics is unclear in many disease settings, and this relationship has implications for both the timing and the required efficacy of antiviral therapy. Since experimental challenge studies often employ higher doses of virus than would generally be present in natural infection assessment of this relationship is particularly important for translation of findings. In this study we used mathematical modelling of viral load data from a multi-dose study of Zika virus infection in a macaque model to describe the impact of varying the dose of Zika virus on model parameters, and developed a novel mathematical model incorporating viral interference with the innate immune response.

Varying Inoculum Dose to Assess the Roles of the Immune Response and Target Cell Depletion by the Pathogen in Control of Acute Viral Infections

It is difficult to determine whether an immune response or target cell depletion by the infectious agent is most responsible for the control of acute primary infection. Both mechanisms can explain the basic dynamics of an acute infection-exponential growth of the pathogen followed by control and clearance-and can also be represented by many different differential equation models. Consequently, traditional model comparison techniques using time series data can be ambiguous or inconclusive. We propose that varying the inoculum dose and measuring the subsequent infectious load can rule out target cell depletion by the pathogen as the main control mechanism. Infectious load can be any measure that is proportional to the number of infected cells, such as viraemia. We show that a twofold or greater change in infectious load is unlikely when target cell depletion controls infection, regardless of the model details. Analyzing previously published data from mice infected with influenza, we find the proportion of lung epithelial cells infected was 21-fold greater (95% confidence interval 14-32) in the highest dose group than in the lowest. This provides evidence in favor of an alternative to target cell depletion, such as innate immunity, in controlling influenza infections in this experimental system. Data from other experimental animal models of acute primary infection have a similar pattern.

Hepatitis C virus modelled as an indirectly transmitted infection highlights the centrality of injection drug equipment in disease dynamics

The hepatitis C virus (HCV) epidemic often occurs through the persistence of injection drug use. Mathematical models have been useful in understanding various aspects of the HCV epidemic, and especially, the importance of new treatment measures. Until now, however, few models have attempted to understand HCV in terms of an interaction between the various actors in an HCV outbreak-hosts, viruses and the needle injection equipment. In this study, we apply perspectives from the ecology of infectious diseases to model the transmission of HCV among a population of injection drug users. The products of our model suggest that modelling HCV as an indirectly transmitted infection-where the injection equipment serves as an environmental reservoir for infection-facilitates a more nuanced understanding of disease dynamics, by animating the underappreciated actors and interactions that frame disease. This lens may allow us to understand how certain public health interventions (e.g. needle exchange programmes) influence HCV epidemics. Lastly, we argue that this model is of particular importance in the light of the modern opioid epidemic, which has already been associated with outbreaks of viral diseases.

Within-host modeling of blood-stage malaria

Malaria infection continues to be a major health problem worldwide and drug resistance in the major human parasite species, Plasmodium falciparum, is increasing in South East Asia. Control measures including novel drugs and vaccines are in development, and contributions to the rational design and optimal usage of these interventions are urgently needed. Infection involves the complex interaction of parasite dynamics, host immunity, and drug effects. The long life cycle (48 hours in the common human species) and synchronized replication cycle of the parasite population present significant challenges to modeling the dynamics of Plasmodium infection. Coupled with these, variation in immune recognition and drug action at different life cycle stages leads to further complexity. We review the development and progress of "within-host" models of Plasmodium infection, and how these have been applied to understanding and interpreting human infection and animal models of infection.

Modeling the Effects of Morphine-Altered Virus Specific Antibody Responses on HIV/SIV Dynamics

Drugs of abuse, such as opiates, have been widely associated with enhancing HIV replication, accelerating disease progression and diminishing host-immune responses, thereby making it harder to effectively manage HIV infection. It is thus important to study the effects of drugs of abuse on HIV-infection and immune responses. Here, we develop mathematical models that incorporate the effects of morphine-altered antibody responses on HIV/SIV dynamics. Based on fitting the model to experimental data from simian immunodeficiency virus (SIV) infections in control and morphine-addicted macaques, we found that two of the most significant effects of virus specific antibodies are neutralizing viral particles and enhancing viral clearance. Using our model, we quantified how morphine alters virus-specific antibody responses, and how this alteration affects the key components of virus dynamics such as infection rate, virus clearance, viral load, CD4⁺ T cell count, and CD4⁺ T cell loss in SIV-infected macaques under conditioning with morphine. We found that in a subpopulation of SIV-infected morphine addicted macaques, the presence of drugs of abuse may cause significantly diminished antibody responses, resulting in more severe infection with increased SIV infectivity, a decreased viral clearance rate, increased viral load, and higher CD4⁺ T cell loss.

Modeling the measles paradox reveals the importance of cellular immunity in regulating viral clearance

Measles virus (MV) is a highly contagious member of the Morbillivirus genus that remains a major cause of childhood mortality worldwide. Although infection induces a strong MV-specific immune response that clears viral load and confers lifelong immunity, transient immunosuppression can also occur, leaving the host vulnerable to colonization from secondary pathogens. This apparent contradiction of viral clearance in the face of immunosuppression underlies what is often referred to as the 'measles paradox', and remains poorly understood. To explore the mechanistic basis underlying the measles paradox, and identify key factors driving viral clearance, we return to a previously published dataset of MV infection in rhesus macaques. These data include virological and immunological information that enable us to fit a mathematical model describing how the virus interacts with the host immune system. In particular, our model incorporates target cell depletion through infection of host immune cells-a hallmark of MV pathology that has been neglected from previous models. We find the model captures the data well, and that both target cell depletion and immune activation are required to explain the overall dynamics. Furthermore, by simulating conditions of increased target cell availability and suppressed cellular immunity, we show that the latter causes greater increases in viral load and delays to MV clearance. Overall, this signals a more dominant role for cellular immunity in resolving acute MV infection. Interestingly, we find contrasting dynamics dominated by target cell depletion when viral fitness is increased. This may have wider implications for animal morbilliviruses, such as canine distemper virus (CDV), that cause fatal target cell depletion in their natural hosts. To our knowledge this work represents the first fully calibrated within-host model of MV dynamics and, more broadly, provides a new platform from which to explore the complex mechanisms underlying Morbillivirus infection.

Modeling the immune response to HIV infection

The interplay between immune response and HIV is intensely studied via mathematical modeling, with significant insights but few direct answers. In this short review, we highlight advances and knowledge gaps across different aspects of immunity. In particular, we identify the innate immune response and its role in priming the adaptive response as ripe for modeling. The latter have been the focus of most modeling studies, but we also synthesize key outstanding questions regarding effector mechanisms of cellular immunity and development of broadly neutralizing antibodies. Thus far, most modeling studies aimed to infer general immune mechanisms; we foresee that significant progress will be made next by detailed quantitative fitting of models to data, and prediction of immune responses.

The dynamics of simian immunodeficiency virus after depletion of CD8+ cells

Human immunodeficiency virus infection is still one of the most important causes of morbidity and mortality in the world, with a disproportionate human and economic burden especially in poorer countries. Despite many years of intense research, an aspect that still is not well understood is what (immune) mechanisms control the viral load during the prolonged asymptomatic stage of infection. Because CD8+ T cells have been implicated in this control by multiple lines of evidence, there has been a focus on understanding the potential mechanisms of action of this immune effector population. One type of experiment used to this end has been depleting these cells with monoclonal antibodies in the simian immunodeficiency virus-macaque model and then studying the effect of that depletion on the viral dynamics. Here we review what these experiments have told us. We emphasize modeling studies to interpret the changes in viral load observed in these experiments, including discussion of alternative models, assumptions and interpretations, as well as potential future experiments.

Insight into treatment of HIV infection from viral dynamics models

The odds of living a long and healthy life with HIV infection have dramatically improved with the advent of combination antiretroviral therapy. Along with the early development and clinical trials of these drugs, and new field of research emerged called viral dynamics, which uses mathematical models to interpret and predict the time-course of viral levels during infection and how they are altered by treatment. In this review, we summarize the contributions that virus dynamics models have made to understanding the pathophysiology of infection and to designing effective therapies. This includes studies of the multiphasic decay of viral load when antiretroviral therapy is given, the evolution of drug resistance, the long-term persistence latently infected cells, and the rebound of viremia when drugs are stopped. We additionally discuss new work applying viral dynamics models to new classes of investigational treatment for HIV, including latency-reversing agents and immunotherapy.

Correlation Between Anti-gp41 Antibodies and Virus Infectivity Decay During Primary HIV-1 Infection

Recent experiments have suggested that the infectivity of simian immunodeficiency virus (SIV) and human immunodeficiency virus type-1 (HIV-1) in plasma decreases over time during primary infection. Because anti-gp41 antibodies are produced early during HIV-1 infection and form antibody-virion complexes, we studied if such early HIV-1 specific antibodies are correlated with the decay in HIV-1 infectivity. Using a viral dynamic model that allows viral infectivity to decay and frequent early viral load data obtained from 6 plasma donors we estimate that HIV-1 infectivity begins to decay after about 2 weeks of infection. The length of this delay is consistent with the time before antibody-virion complexes were detected in the plasma of these donors and is correlated (p = 0.023, r = 0.87) with the time for antibodies to be first detected in plasma. Importantly, we identify that the rate of infectivity decay is significantly correlated with the rate of increase in plasma anti-gp41 IgG concentration (p = 0.046, r = 0.82) and the increase in IgM+IgG anti-gp41 concentration (p = 8.37 × 10⁻⁴, r = 0.98). Furthermore, we found that the viral load decay after the peak did not have any significant correlation with the rate of anti-gp41 IgM or IgG increase. These results indicate that early anti-gp41 antibodies may cause viral infectivity decay, but may not contribute significantly to controlling post-peak viral load, likely due to insufficient quantity or affinity. Our findings may be helpful to devise strategies, including antibody-based vaccines, to control acute HIV-1 infection.

Incomplete inhibition of HIV infection results in more HIV infected lymph node cells by reducing cell death

HIV has been reported to be cytotoxic in vitro and in lymph node infection models. Using a computational approach, we found that partial inhibition of transmissions of multiple virions per cell could lead to increased numbers of live infected cells. If the number of viral DNA copies remains above one after inhibition, then eliminating the surplus viral copies reduces cell death. Using a cell line, we observed increased numbers of live infected cells when infection was partially inhibited with the antiretroviral efavirenz or neutralizing antibody. We then used efavirenz at concentrations reported in lymph nodes to inhibit lymph node infection by partially resistant HIV mutants. We observed more live infected lymph node cells, but with fewer HIV DNA copies per cell, relative to no drug. Hence, counterintuitively, limited attenuation of HIV transmission per cell may increase live infected cell numbers in environments where the force of infection is high.

The HIVvirus infects cells of the immune system. Once inside, it hijacks the cellular molecular machineries to make more copies of itself, which are then transmitted to new host cells. HIV eventually kills most cells it infects, either in the steps leading to the infection of the cell, or after the cell is already producing virus. HIV can spread between cells in two ways, known as cell-free or cell-to-cell. In the first, individual viruses are released from infected cells and move randomly through the body in the hope of finding new cells to infect. In the second, infected cells interact directly with uninfected cells. The second method is often much more successful at infecting new cells since they are exposed to multiple virus particles.

HIV infections can be controlled by using combinations of antiretroviral drugs, such as efavirenz, to prevent the virus from making more of itself. With a high enough dose, the drugs can in theory completely stop HIV infections, unless the virus becomes resistant to treatment. However, some patients continue to use these drugs even after the virus they are infected with develops resistance. It is not clear what effect taking ineffective, or partially effective, drugs has on how HIV progresses.

Using efavirenz, Jackson, Hunter et al. partially limited the spread of HIV between human cells grown in the laboratory. The experiments mirrored the situation where a partially resistant HIV strain spreads through the body. The results show that the success of cell-free infection is reduced as drug dose increases. Yet paradoxically, in cell-to-cell infection, the presence of drug caused more cells to become infected. This can be explained by the fact that, in cell-to-cell spread, each cell is exposed to multiple copies of the virus. The drug dose reduced the number of viral copies per cell without stopping the virus from infecting completely. The reduced number of viral copies per cell made it more likely that infected cells would survive the infection long enough to produce virus particles themselves.

Viruses that can kill cells, such as HIV, must balance the need to make more of themselves against the speed that they kill their host cell to maximize the number of infected cells. If transmission between cells is too effective and too many virus particles are delivered to the new cell, the virus may not manage to infect new hosts before killing the old ones. These findings highlight this delicate balance. They also indicate a potential issue in using drugs to treat partially resistant virus strains. Without care, these treatments could increase the number of infected cells in the body, potentially worsening the effects of living with HIV.

A Quasi-Steady-State Approximation to the Basic Target-Cell-Limited Viral Dynamics Model with a Non-Cytopathic Effect

Analysis of previously published target-cell limited viral dynamic models for pathogens such as HIV, hepatitis, and influenza generally rely on standard techniques from dynamical systems theory or numerical simulation. We use a quasi-steady-state approximation to derive an analytic solution for the model with a non-cytopathic effect, that is, when the death rates of uninfected and infected cells are equal. The analytic solution provides time evolution values of all three compartments of uninfected cells, infected cells, and virus. Results are compared with numerical simulation using clinical data for equine infectious anemia virus, a retrovirus closely related to HIV, and the utility of the analytic solution is discussed.

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.

Mathematical Models of HIV Latency

Viral latency is a major barrier to curing HIV infection with antiretroviral therapy, and consequently, for eliminating the disease globally. The establishment, maintenance, and potential clearance of latent infection are complex dynamic processes and can be best understood and described with the help of mathematical models. Here we review the use of viral dynamics models for HIV, with a focus on applications to the latent reservoir. Such models have been used to explain the multiphasic decay of viral load during antiretroviral therapy, the early seeding of the latent reservoir during acute infection and the limited inflow during treatment, the dynamics of viral blips, and the phenomenon of posttreatment control. In addition, mathematical models have been used to predict the efficacy of potential HIV cure strategies, such as latency-reversing agents, early treatment initiation, or gene therapies, and to provide guidance for designing trials of these novel interventions.

Modeling the Effects of Morphine on Simian Immunodeficiency Virus Dynamics

Complications of HIV-1 infection in individuals who utilize drugs of abuse is a significant problem, because these drugs have been associated with higher virus replication and accelerated disease progression as well as severe neuropathogenesis. To gain further insight it is important to quantify the effects of drugs of abuse on HIV-1 infection dynamics. Here, we develop a mathematical model that incorporates experimentally observed effects of morphine on inducing HIV-1 co-receptor expression. For comparison we also considered viral dynamic models with cytolytic or noncytolytic effector cell responses. Based on the small sample size Akaike information criterion, these models were inferior to the new model based on changes in co-receptor expression. The model with morphine affecting co-receptor expression agrees well with the experimental data from simian immunodeficiency virus infections in morphine-addicted macaques. Our results show that morphine promotes a target cell subpopulation switch from a lower level of susceptibility to a state that is about 2-orders of magnitude higher in susceptibility to SIV infection. As a result, the proportion of target cells with higher susceptibility remains extremely high in morphine conditioning. Such a morphine-induced population switch not only has adverse effects on the replication rate, but also results in a higher steady state viral load and larger CD4 count drops. Moreover, morphine conditioning may pose extra obstacles to controlling viral load during antiretroviral therapy, such as pre-exposure prophylaxis and post infection treatments. This study provides, for the first time, a viral dynamics model, viral dynamics parameters, and related analytical and simulation results for SIV dynamics under drugs of abuse.

Models of Viral Population Dynamics

Models of viral population dynamics have contributed enormously to our understanding of the pathogenesis and transmission of several infectious diseases, the coevolutionary dynamics of viruses and their hosts, the mechanisms of action of drugs, and the effectiveness of interventions. In this chapter, we review major advances in the modeling of the population dynamics of the human immunodeficiency virus (HIV) and briefly discuss adaptations to other viruses.

Asymptotic behavior of HIV-1 epidemic model with infinite distributed intracellular delays

In this study, asymptotic analysis of an HIV-1 epidemic model with distributed intracellular delays is proposed. One delay term represents the latent period which is the time when the target cells are contacted by the virus particles and the time the contacted cells become actively infected and the second delay term represents the virus production period which is the time when the new virions are created within the cell and are released from the cell. The infection free equilibrium and the chronic-infection equilibrium have been shown to be locally asymptotically stable by using Rouths Hurwiths criterion and general theory of delay differential equations. Similarly, by using Lyapunov functionals and LaSalle’s invariance principle, it is proved that if the basic reproduction ratio is less than unity, then the infection-free equilibrium is globally asymptotically stable, and if the basic reproduction ratio is greater than unity, the chronic-infection equilibrium is globally asymptotically stable. Finally, numerical results with conclusion are discussed.

Broad CTL Response in Early HIV Infection Drives Multiple Concurrent CTL Escapes

Recent studies have highlighted the ability of HIV to escape from cytotoxic T lymphocyte (CTL) responses that concurrently target multiple viral epitopes. Yet, the viral dynamics involved in such escape are incompletely understood. Previous analyses have made several strong assumptions regarding HIV escape from CTL responses such as independent or non-concurrent escape from individual CTL responses. Using experimental data from evolution of HIV half genomes in four patients we observe concurrent viral escape from multiple CTL responses during early infection (first 100 days of infection), providing confirmation of a recent result found in a study of one HIV-infected patient. We show that current methods of estimating CTL escape rates, based on the assumption of independent escapes, are biased and perform poorly when CTL escape proceeds concurrently at multiple epitopes. We propose a new method for analyzing longitudinal sequence data to estimate the rate of CTL escape across multiple epitopes; this method involves few parameters and performs well in simulation studies. By applying our novel method to experimental data, we find that concurrent multiple escapes occur at rates between 0.03 and 0.4 day⁻¹, a relatively broad range that reflects uncertainty due to sparse sampling and wide ranges of parameter values. However, we show that concurrent escape at rates 0.1–0.2 day⁻¹ across multiple epitopes is consistent with our patient datasets.

Since the early 1990s, cytotoxic T lymphocytes (CTLs) have been known to play an important role in HIV infection with CTLs targeting HIV epitopes and, in turn, HIV escapes arising through mutations in the targeted epitopes. Over the past decade, studies have shown that CTL responses concurrently target multiple HIV epitopes, yet the effect of concurrent responses on HIV dynamics and evolution is not well understood. Through an analysis of patient datasets and a novel statistical method, we show that during early HIV infection concurrent CTL responses drive concurrent HIV escapes at multiple epitopes with significant pressure, suggesting a complex picture in which HIV simultaneously explores multiple mutational pathways to escape from broad and potent CTL response.

HIV Replication Is Not Controlled by CD8+ T Cells during the Acute Phase of the Infection in Humanized Mice

HIV replication follows a well-defined pattern during the acute phase of the infection in humans. After reaching a peak during the first few weeks after infection, viral replication resolves to a set-point thereafter. There are still uncertainties regarding the contribution of CD8⁺ T cells in establishing this set-point. An alternative explanation, supported by in silico modeling, would imply that viral replication is limited by the number of available targets for infection, i.e. CD4⁺CCR5⁺ T cells. Here, we used NOD.SCID.gc^-/- mice bearing human CD4⁺CCR5⁺ and CD8⁺ T cells derived from CD34⁺ progenitors to investigate the relative contribution of both in viral control after the peak. Using low dose of a CCR5-tropic HIV virus, we observed an increase in viral replication followed by “spontaneous” resolution of the peak, similar to humans. To rule out any possible role for CD8⁺ T cells in viral control, we infected mice in which CD8⁺ T cells had been removed by a depleting antibody. Globally, viral replication was not affected by the absence of CD8⁺ T cells. Strikingly, resolution of the viral peak was equally observed in mice with or without CD8⁺ T cells, showing that CD8⁺ T cells were not involved in viral control in the early phase of the infection. In contrast, a marked and specific loss of CCR5-expressing CD4⁺ T cells was observed in the spleen and in the bone marrow, but not in the blood, of infected animals. Our results strongly suggest that viral replication during the acute phase of the infection in humanized mice is mainly constrained by the number of available targets in lymphoid tissues rather than by CD8⁺ T cells.

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

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

Potential future impact of a partially effective HIV vaccine in a southern African setting

Background

It is important for public health and within the HIV vaccine development field to understand the potential population level impact of an HIV vaccine of partial efficacy—both in preventing infection and in reducing viral load in vaccinated individuals who become infected—in the context of a realistic future implementation scenario in resource limited settings.

Methods

An individual level model of HIV transmission, progression and the effect of antiretroviral therapy was used to predict the outcome to 2060 of introduction in 2025 of a partially effective vaccine with various combinations of efficacy characteristics, in the context of continued ART roll-out in southern Africa.

Results

In the context of our base case epidemic (in 2015 HIV prevalence 28% and incidence 1.7 per 100 person years), a vaccine with only 30% preventative efficacy could make a substantial difference in the rate with which HIV incidence declines; the impact on incidence in relative terms is projected to increase over time, with a projected 67% lower HIV incidence in 2060 compared with no vaccine introduction. The projected mean decline in the general adult population death rate 2040–2060 is 11%. A vaccine with no prevention efficacy but which reduces viral load by 1 log is predicted to result in a modest (14%) reduction in HIV incidence and an 8% reduction in death rate in the general adult population (mean 2040–2060). These effects were broadly similar in multivariable uncertainty analysis.

Interpretation

Introduction of a partially effective preventive HIV vaccine would make a substantial long-term impact on HIV epidemics in southern Africa, in addition to the effects of ART. Development of an HIV vaccine, even of relatively low apparent efficacy at the individual level, remains a critical global public health goal.

Quantitative analysis of the processes and signaling events involved in early HIV-1 infection of T cells

Lymphocyte invasion by HIV-1 is a complex, highly regulated process involving many different types of molecules that is prompted by the virus's association with viral receptors located at the cell-surface membrane that culminates in the formation of a fusion pore through which the virus enters the cell. A great deal of work has been done to identify the key actors in the process and determine the regulatory interactions; however, there have been no reports to date of attempts being made to fully understand the system dynamics through a systemic, quantitative modeling approach. In this paper, we introduce a dynamic mathematical model that integrates the available information on the molecular events involved in lymphocyte invasion. Our model shows that moesin activation is induced by virus signaling, while filamin-A is mobilized by the receptor capping. Actin disaggregation from the cap is facilitated by cofilin. Cofilin is inactivated by HIV-1 signaling in activated lymphocytes, while in resting lymphocytes another signal is required to activate cofilin in the later stages in order to accelerate the decay of the aggregated actin as a restriction factor for the viral entry. Furthermore, stopping the activation signaling of moesin is sufficient to liberate the actin filaments from the cap. The model also shows the positive effect of gelsolin on actin capping by means of the nucleation effect. These findings allow us to propose novel approaches in the search for new therapeutic strategies. In particular, gelsolin inhibition is seen as a promising target for preventing HIV-1 entry into lymphocytes, due to its role in facilitating the capping needed for the invasion. Also it is shown that HIV-1 should overcome the cortical actin barrier during early infection and predicts the different susceptibility of CD4+ T cells to be infected in terms of actin cytoskeleton dynamics driven by associated cellular factors.

Current understanding of HIV-1 and T-cell adaptive immunity: progress to date

The cellular immune response to human immunodeficiency virus (HIV) has different components originating from both the adaptive and innate immune systems. HIV cleverly utilizes the host machinery to survive by its intricate nature of interaction with the host immune system. HIV evades the host immune system at innate ad adaptive, allows the pathogen to replicate and transmit from one host to another. Researchers have shown that HIV has multipronged effects especially on the adaptive immunity, with CD4(+) cells being the worst effect T-cell populations. Various analyses have revealed that, the exposure to HIV results in clonal expansion and excessive activation of the immune system. Also, an abnormal process of differentiation has been observed suggestive of an alteration and blocks in the maturation of various T-cell subsets. Additionally, HIV has shown to accelerate immunosenescence and exhaustion of the overtly activated T-cells. Apart from causing phenotypic changes, HIV has adverse effects on the functional aspect of the immune system, with evidences implicating it in the loss of the capacity of T-cells to secrete various antiviral cytokines and chemokines. However, there continues to be many aspects of the immune- pathogenesis of HIV that are still unknown and thus required further research in order to convert the malaise of HIV into a manageable epidemic.

DYNAMICS OF A NON-AUTONOMOUS HIV-1 INFECTION MODEL WITH DELAYS

In this paper, following a previous paper ([32] Permanence and extinction of a non-autonomous HIV-1 model with two time delays, preprint) on the permanence and extinction of a delayed non-autonomous HIV-1 within-host model, we introduce and investigate a delayed HIV-1 model including maximum homeostatic proliferation rate of CD4+T-cells and varying coefficients. By applying the asymptotic analysis theory and oscillation theory, we show: (i) the system will be permanent when the threshold value R*> 1, and for this case we also obtain the explicit estimate of the eventual lower bound of the HIV-1 virus load; (ii) the threshold value R* < 1 implies the extinction of the virus. Furthermore, we obtain that the threshold dynamics is in agreement with that of the corresponding autonomous system, which extends the classic results for the system with constant coefficients. Numerical simulations are also given to illustrate our main results, and in particular, some sensitivity test of R*is established.

A MATHEMATICAL MODEL ON CTL MEDIATED CONTROL OF HIV INFECTION IN A LONG-TERM DRUG THERAPY

Bonhoeffer et al.1studied the long-term dynamics of HIV drug therapy and virus load dynamics. It is well known that highly active anti retroviral therapy (HAART) can effectively control the HIV replication. It is also well known that reverse transcriptase inhibitors (RTIs) could block new infection and as a result control HIV infection. The positive feedback control on such dynamics plays an important role and CD4+T cells are not only produced from a source but also produced from existing T cells. The present investigation takes into account these factors in the original model of Bonhoeffer et al. The optimal control therapy and the effect of time delay in the positive feedback control function have been investigated. Numerical simulation of the nonlinear model has confirmed our analytical studies.

Modeling the within-host dynamics of HIV infection

The new field of viral dynamics, based on within-host modeling of viral infections, began with models of human immunodeficiency virus (HIV), but now includes many viral infections. Here we review developments in HIV modeling, emphasizing quantitative findings about HIV biology uncovered by studying acute infection, the response to drug therapy and the rate of generation of HIV variants that escape immune responses. We show how modeling has revealed many dynamical features of HIV infection and how it may provide insight into the ultimate cure for this infection.

HOW SELF-PROLIFERATION OF CD4+T CELLS AFFECT THE HIV DYNAMICS IN AN IN-HOST TARGET-CELL LIMITED HIV MODEL WITH SATURATION INFECTION RATE: A QUASI-STEADY-STATE APPROXIMATION ANALYSIS

In this study, we consider two target-cell limited models with saturation type infection rate and intracellular delay: one without self-proliferation and the other with self-proliferation of activated CD4+T cells. We discuss about the local and global behavior of both the systems in presence and absence of intracellular delay. It is shown that the endemic equilibrium of a target-cell limited model would be unstable in presence and absence of intracellular delay only when self-proliferation of activated CD4+T cell is considered. Otherwise, all positive solutions converge to the endemic equilibrium or disease-free equilibrium depending on whether the basic reproduction ratio is greater than or less than unity. Our study suggests that amplitude of oscillation is negatively correlated with the constant input rate of CD4+T cell when intracellular delay is absent or low. However, they are positively correlated if the delay is too high. Amplitude of oscillation, on the other hand, is always positively correlated with the proliferation rate of CD4+T cell for all delay. Our mathematical and simulation analysis also suggest that there are many potential contributors who are responsible for the variation of CD4+T cells and virus particles in the blood plasma of HIV patients.

Global threshold dynamics in an HIV virus model with nonlinear infection rate and distributed invasion and production delays

We consider a mathematical model that describes the interactions of the HIV virus, CD4 cells and CTLs within host, which is a modification of some existing models by incorporating (i) two distributed kernels reflecting the variance of time for virus to invade into cells and the variance of time for invaded virions to reproduce within cells; (ii) a nonlinear incidence function f for virus infections, and (iii) a nonlinear removal rate function h for infected cells. By constructing Lyapunov functionals and subtle estimates of the derivatives of these Lyapunov functionals, we shown that the model has the threshold dynamics: if the basic reproduction number (BRN) is less than or equal to one, then the infection free equilibrium is globally asymptotically stable, meaning that HIV virus will be cleared; whereas if the BRN is larger than one, then there exist an infected equilibrium which is globally asymptotically stable, implying that the HIV-1 infection will persist in the host and the viral concentration will approach a positive constant level. This together with the dependence/independence of the BRN on f and h reveals the effect of the adoption of these nonlinear functions.

Where have all the parasites gone? Modelling early malaria parasite sequestration dynamics

Traditional approaches to measuring the level of malaria infection involve counting the proportion of parasite-infected red blood cells (iRBC) in circulating blood, known as parasitaemia. However, iRBC can also accumulate within the microvasculature of tissues and organs, a process called sequestration. Thus measurements of parasitemia do not necessarily reflect the total parasite burden (TPB). Recent experimental advances have allowed TPB measurements to be made in humans and experimental models. TPB is particularly important because it is the best current predictor of malaria disease severity and death in humans. Understanding the relationship between freely circulating iRBC versus tissue-sequestered iRBC is an important question in infection dynamics. The recent ability to experimentally measure the dynamics of iRBC in blood and tissue during murine malaria provides an exciting potential window into sequestration, but new modeling approaches are clearly required to understand these interactions. We present a model of malaria dynamics during early infection that incorporates iRBC that both circulate in the blood and sequester in tissue microvasculature. We explore the effect that perturbations to the system have on the ratio of the number of iRBC between these compartments, and consider which changes are most consistent with experimental data from mice. Using this model we predict an increase in the clearance rate of sequestered iRBCs around the time when mild symptoms become apparent, but a more pronounced increase in the rate of sequestration of iRBCs associated with the onset of severe malaria symptoms.

A hunter virus that targets both infected cells and HIV free virions: implications for therapy

The design of ‘hunter’ viruses aimed at destroying human immunodeficiency virus (HIV) infected cells is an active area of research that has produced promising results in vitro. Hunters are designed to target exposed viral envelope proteins in the membranes of infected cells, but there is evidence that the hunter may also target envelope proteins of free HIV, inducing virus-virus fusion. In order to predict the effects of this fusion on therapy outcomes and determine whether fusion ability is advantageous for hunter virus design, we have constructed a model to account for the possibility of hunter-HIV fusion. The study was based on a target cell-limited model of HIV infection and it examined the hunter therapeutic effect on recovering the HIV main target cells, the activated CD4⁺ T lymphocytes. These cells assist in setting up an immune response to opportunistic infections. The study analyzed the hunter dual mechanisms to control infection and because of diverse estimates for viral production and clearance of HIV, simulations were examined at rates spanning an order of magnitude. Results indicate that without hunter-HIV fusion ability, hunters that kill HIV-infected cells lead to a substantial recovery of healthy cell population at both low and high HIV turnover rates. When hunter-HIV fusion is included, cell recovery was particularly enhanced at lower HIV turnover rates. This study shows that the fusion ability, in addition to hunter infection ability, could be a favorable attribute for improving the efficacy of hunter-viral therapy. These results provide support for the potential use of engineered viruses to control HIV and other viral infections.

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

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

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

On the role of CD8 T cells in the control of persistent infections

The control of pathogen density during infections is typically assumed to be the result of a combination of resource limitation (loss of target cells that the pathogen can infect), innate immunity, and specific immunity. The contributions of these factors have been considered in acute infections, which are characterized by having a short duration. What controls the pathogen during persistent infections is less clear, and is complicated by two factors. First, specific immune responses become exhausted if they are subject to chronic stimulation. Exhaustion has been best characterized for CD8 T cell responses, and occurs through a combination of cell death and loss of functionality of surviving cells. Second, new nonexhausted T cells can immigrate from the thymus during the infection, and may play a role in the control of the infection. In this article, we formulate a partial-differential-equation model to describe the interaction between these processes, and use this model to explore how thymic influx and exhaustion might affect the ability of CD8 T cell responses to control persistent infections. We find that although thymic influx can play a critical role in the maintenance of a limited CD8 T cell response during persistent infections, this response is not sufficiently large to play a significant role in controlling the infection. In doing so, our results highlight the importance of resource limitation and innate immunity in the control of persistent infections.

Acute HIV infection: it takes more than guts

PURPOSE OF REVIEW

To understand the cellular and molecular mechanisms of acute HIV pathogenesis.

RECENT FINDINGS

Recent studies have given us new insights into the mechanisms of acute HIV pathogenesis by demonstrating the 'systemic' destruction of the CD4 memory T cell compartment. This destruction occurs well before the emergence of a strong and broad immune response, highlighting the failure of the immune response to contain early viral infection and destruction. However, recent data also suggest that very few founder populations of cells are infected early, at the portal of entry, making them ideal targets for vaccine-induced immune responses that may aid in the effective control of early infection and transmission.

SUMMARY

HIV causes a massive destruction of memory CD4 T cells during the early acute phase of infection. This destruction proceeds largely in the absence of emerging antiviral immune responses, and severely disables the ability of the immune system to generate secondary immune responses. Early preservation of the memory CD4 compartment by shifting emphasis of antiretroviral therapeutic strategies to early treatment, and development of vaccines that can induce strong and broad immune responses, will be critical to prevent the destructive effects of early HIV infection.

Basic stochastic models for viral infection within a host

Stochastic differential equation (SDE) models are formulated for intra-host virus-cell dynamics during the early stages of viral infection, prior to activation of the immune system. The SDE models incorporate more realism into the mechanisms for viral entry and release than ordinary differential equation (ODE) models and show distinct differences from the ODE models. The variability in the SDE models depends on the concentration, with much greater variability for small concentrations than large concentrations. In addition, the SDE models show significant variability in the timing of the viral peak. The viral peak is earlier for viruses that are released from infected cells via bursting rather than via budding from the cell membrane.

Evolutionary dynamics of HIV at multiple spatial and temporal scales

Infectious diseases remain a formidable challenge to human health, and understanding pathogen evolution is crucial to designing effective therapeutics and control strategies. Here, we review important evolutionary aspects of HIV infection, highlighting the concept of selection at multiple spatial and temporal scales. At the smallest scale, a single cell may be infected by multiple virions competing for intracellular resources. Recombination and phenotypic mixing introduce novel evolutionary dynamics. As the virus spreads between cells in an infected individual, it continually evolves to circumvent the immune system. We discuss evolutionary mechanisms of HIV pathogenesis and progression to AIDS. Viral spread throughout the human population can lead to changes in virulence and the transmission of immune-evading variation. HIV emerged as a human pathogen due to selection occurring between different species, adapting from related viruses of primates. HIV also evolves resistance to antiretroviral drugs within a single infected host, and we explore the possibility for the spread of these strains between hosts, leading to a drug-resistant epidemic. We investigate the role of latency, drug-protected compartments, and direct cell-to-cell transmission on viral evolution. The introduction of an HIV vaccine may select for viral variants that escape vaccine control, both within an individual and throughout the population. Due to the strong selective pressure exerted by HIV-induced morbidity and mortality in many parts of the world, the human population itself may be co-evolving in response to the HIV pandemic. Throughout the paper, we focus on trade-offs between costs and benefits that constrain viral evolution and accentuate how selection pressures differ at different levels of selection.

PREDICTING THE PROBABILITY OF PERSISTENCE OF HIV INFECTION WITH THE STANDARD MODEL

It is not well understood why the transmission of HIV may have a small probability of occurrence despite frequent high risk exposures or ongoing contact between members of a discordant couple. We explore the possible contributions made by distributions of system parameters beginning with the standard three-component differential equation model for the growth of a HIV virion population in an infected host in the absence of drug therapy. The overall dynamical behavior of the model is determined by the set of values of six parameters, some of which describe host immune system properties and others which describe virus properties. There may be one or two critical points whose natures play a key role in determining the outcome of infection and in particular whether the HIV population will persist or become extinct. There are two cases which may arise. In the first case, there is only one critical point P1at biological values and this is an asymptotically stable node. The system ends up with zero virions and so the host becomes HIV-free. In the second case, there are two critical points P1and P2at biological values. Here P1is an unstable saddle point and P2is an asymptotically stable spiral point with a non-zero virion level. In this case the HIV population persists unless parameters change. We let the parameter values take random values from distributions based on empirical data, but suitably truncated, and determine the probabilities of occurrence of the various combinations of critical points. From these simulations the probability that an HIV infection will persist, across a population, is estimated. It is found that with conservatively estimated distributions of parameters, within the framework of the standard 3-component model, the chances that a within-host HIV population will become extinct is between 0.6% and 6.9%. With less conservative parameter estimates, the probability is estimated to be as high as 24%. The many complicating factors related to the transmission and possible spontaneous elimination of the virus and the need for experimental data to clarify whether transient infections may occur are discussed. More realistic yet complicated higher dimensional models are likely to yield smaller probabilities of extinction.

REVIEW OF HIV MODELS: THE ROLE OF THE NATURAL IMMUNE RESPONSE AND IMPLICATIONS FOR TREATMENT

We present a review and comparison of several recent differential equations models of treatment of HIV-1 infection. We seek to clarify the role of the natural anti-HIV immune response and determine its effect upon optimal treatment schemes. In this paper, we consider systems in which treatment is expressed as a forcing function, as well as those in which we determine optimal treatment via control theoretic techniques. The primary goal of this study is to compare treatment schemes for systems in which a natural nonconstant immune response of the patient is considered explicitly with those that consider implicitly a constant non-specific immune response. We find that when the natural immune response can be boosted sufficiently, drug levels may not need to be as high as previously supposed. This implies that a treatment scenario in which intervals of drug treatment are alternated with some form of immune-boosting therapy may be highly beneficial in terms of reducing toxicity to the patient. Additionally, in developing countries where HIV infection is widespread and sufficient funds are not available to supply rigourous drug regimens, the implications of these models are profound, as they suggest methods of treating HIV at a minimal cost.

A SEMI-STOCHASTIC MODEL FOR HIV POPULATION DYNAMICS

A semi-stochastic model is developed and investigated for human immunodeficiency virus type-1 (HIV-1) population dynamics. The model includes both stochastic parts (changes of CD4+ T cells) and deterministic parts (changes of free virions). Using the best currently available parameter values, we estimate the distributions of the time of occurrence and the magnitude of the early peak in virions. We investigated the effects of varying parameter values on mean solutions in order to assess the stochastic effects of between-patient variability. Numerical simulation shows that the lower the infection rate, the higher the death rate of the infected cells, more rapid clearance of virions and lower rate of virion emission by the infected cells result in lower speed of infection progression and magnitude but a greater variability in response. We also examine the probability that a small viral inoculum fails to establish an infection. Further, we theoretically quantify the expected variability around the infected equilibrium for each population by using diffusion approximation.

A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data

Mathematical models have made considerable contributions to our understanding of HIV dynamics. Introducing time delays to HIV models usually brings challenges to both mathematical analysis of the models and comparison of model predictions with patient data. In this paper, we incorporate two delays, one the time needed for infected cells to produce virions after viral entry and the other the time needed for the adaptive immune response to emerge to control viral replication, into an HIV-1 model. We begin model analysis with proving the positivity and boundedness of the solutions, local stability of the infection-free and infected steady states, and uniform persistence of the system. By developing a few Lyapunov functionals, we obtain conditions ensuring global stability of the steady states. We also fit the model including two delays to viral load data from 10 patients during primary HIV-1 infection and estimate parameter values. Although the delay model provides better fits to patient data (achieving a smaller error between data and modeling prediction) than the one without delays, we could not determine which one is better from the statistical standpoint. This highlights the need of more data sets for model verification and selection when we incorporate time delays into mathematical models to study virus dynamics.

Depletion of CD4⁺ T cells abrogates post-peak decline of viremia in SIV-infected rhesus macaques

CD4+ T cells play a central role in the immunopathogenesis of HIV/AIDS, and their depletion during chronic HIV infection is a hallmark of disease progression. However, the relative contribution of CD4+ T cells as mediators of antiviral immune responses and targets for virus replication is still unclear. Here, we have generated data in SIV-infected rhesus macaques (RMs) that suggest that CD4+ T cells are essential in establishing control of virus replication during acute infection. To directly assess the role of CD4+ T cells during primary SIV infection, we in vivo depleted these cells from RMs prior to infecting the primates with a pathogenic strain of SIV. Compared with undepleted animals, CD4+ lymphocyte-depleted RMs showed a similar peak of viremia, but did not manifest any post-peak decline of virus replication despite CD8+ T cell- and B cell-mediated SIV-specific immune responses comparable to those observed in control animals. Interestingly, depleted animals displayed rapid disease progression, which was associated with increased virus replication in non-T cells as well as the emergence of CD4-independent SIV-envelopes. Our results suggest that the antiviral CD4+ T cell response may play an important role in limiting SIV replication, which has implications for the design of HIV vaccines.

Acute HIV-1 Infection

In 2009, the United Nations Estimated that 33.2 Million People worldwide were living with human immunodeficiency virus type 1 (HIV-1) infection and that 2.6 million people had been newly infected. The need for effective HIV-1 prevention has never been greater. In this review, we address recent critical advances in our understanding of HIV-1 transmission and acute HIV-1 infection. Fourth-generation HIV-1 testing, now available worldwide,^, will allow the diagnosis of infection in many patients and may lead to new treatments and opportunities for prevention.

Using modeling to help understand vaginal microbicide functionality and create better products

A summary is presented of a range of mathematical models that relate to topical microbicidal molecules, applied vaginally to inhibit HIV transmission. These models contribute to the fundamental understanding of the functioning of those molecules, as introduced in different delivery systems. They also provide computational tools that can be employed in the practical design and evaluation of vaginal microbicide products. Mathematical modeling can be implemented, using stochastic principles, to understand the probability of infection by sexually transmitted HIV virions. This provides a frame of reference for the deterministic models of the various processes that underlie HIV transmission and its inhibition, including: the temporal and spatial history of HIV migration from semen to vaginal epithelial surfaces and thence to the underlying stroma; the time and spatial distribution of microbicidal drugs as delivered by various vehicles (e.g., gels, rings, films, and tablets)-this is central to understanding microbicide product pharmacokinetics; and the time and space history of the drug interactions with HIV directly and with host cells for HIV within the vaginal environment-this informs the understanding of microbicide pharmacodynamics. Models that characterize microbicide functionality and performance should and can interface with both in vitro and in vivo experimental studies. They can serve as a rapidly applied, inexpensive tool, to facilitate microbicide R&D, in advance of more costly and time consuming clinical trials.

Quantification of the relative importance of CTL, B cell, NK cell, and target cell limitation in the control of primary SIV-infection

CD8+ cytotoxic T lymphocytes (CTLs), natural killer (NK) cells, B cells and target cell limitation have all been suggested to play a role in the control of SIV and HIV-1 infection. However, previous research typically studied each population in isolation leaving the magnitude, relative importance and in vivo relevance of each effect unclear. Here we quantify the relative importance of CTLs, NK cells, B cells and target cell limitation in controlling acute SIV infection in rhesus macaques. Using three different methods, we find that the availability of target cells and CD8+ T cells are important predictors of viral load dynamics. If CTL are assumed to mediate this anti-viral effect via a lytic mechanism then we estimate that CTL killing is responsible for approximately 40% of productively infected cell death, the remaining cell death being attributable to intrinsic, immune (CD8+ T cell, NK cell, B cell) -independent mechanisms. Furthermore, we find that NK cells have little impact on the death rate of infected CD4+ cells and that their net impact is to increase viral load. We hypothesize that NK cells play a detrimental role in SIV infection, possibly by increasing T cell activation.