The role of antigenic stimulation and cytotoxic T cell activity in regulating the long-term immunopathogenesis of HIV: mechanisms and clinical implications

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.

Large Variations in HIV-1 Viral Load Explained by Shifting-Mosaic Metapopulation Dynamics

The viral population of HIV-1, like many pathogens that cause systemic infection, is structured and differentiated within the body. The dynamics of cellular immune trafficking through the blood and within compartments of the body has also received wide attention. Despite these advances, mathematical models, which are widely used to interpret and predict viral and immune dynamics in infection, typically treat the infected host as a well-mixed homogeneous environment. Here, we present mathematical, analytical, and computational results that demonstrate that consideration of the spatial structure of the viral population within the host radically alters predictions of previous models. We study the dynamics of virus replication and cytotoxic T lymphocytes (CTLs) within a metapopulation of spatially segregated patches, representing T cell areas connected by circulating blood and lymph. The dynamics of the system depend critically on the interaction between CTLs and infected cells at the within-patch level. We show that for a wide range of parameters, the system admits an unexpected outcome called the shifting-mosaic steady state. In this state, the whole body’s viral population is stable over time, but the equilibrium results from an underlying, highly dynamic process of local infection and clearance within T-cell centers. Notably, and in contrast to previous models, this new model can explain the large differences in set-point viral load (SPVL) observed between patients and their distribution, as well as the relatively low proportion of cells infected at any one time, and alters the predicted determinants of viral load variation.

A novel metapopulation model of HIV suggests that within-host infections are characterized by a highly dynamic process of localized infection followed by clearance within T cell centers.

When a person is infected with HIV, the initial peak level of virus in the blood is usually very high before a lower, relatively stable level is reached and maintained for the duration of the chronic infection. This stable level is known as the set-point viral load (SPVL) and is associated with severity of infection. SPVL is also highly variable among patients, ranging from 100 to a million copies of the virus per mL of blood. The replicative capacity of the infecting virus and the strength of the immune response both influence SPVL. However, standard mathematical models show that variation in these two factors cannot easily reproduce the observed distribution of SPVL among patients. Standard models typically treat infected individuals as well-mixed systems, but in reality viral replication is localised in T-cell centres, or patches, found in secondary lymphoid tissue. To account for this population structure, we developed a carefully parameterised metapopulation model. We find the system can reach a steady state at which the viral load in the blood is relatively stable, representing SPVL, but surprisingly, the patches are highly dynamic, characterised by bursts of infection followed by elimination of virus due to localised host immune responses. Significantly, this model can reproduce the wide distribution of SPVLs found among infected individuals for realistic distributions of viral replicative capacity and strength of immune response. Our model can also be used in the future to understand other aspects of chronic HIV infection.

Effects of neutralizing antibodies on escape from CD8+ T-cell responses in HIV-1 infection

Despite substantial advances in our knowledge of immune responses against HIV-1 and of its evolution within the host, it remains unclear why control of the virus eventually breaks down. Here, we present a new theoretical framework for the infection dynamics of HIV-1 that combines antibody and CD8⁺ T-cell responses, notably taking into account their different lifespans. Several apparent paradoxes in HIV pathogenesis and genetics of host susceptibility can be reconciled within this framework by assigning a crucial role to antibody responses in the control of viraemia. We argue that, although escape from or progressive loss of quality of CD8⁺ T-cell responses can accelerate disease progression, the underlying cause of the breakdown of virus control is the loss of antibody induction due to depletion of CD4⁺ T cells. Furthermore, strong antibody responses can prevent CD8⁺ T-cell escape from occurring for an extended period, even in the presence of highly efficacious CD8⁺ T-cell responses.

Backward bifurcations, turning points and rich dynamics in simple disease models

In this paper, dynamical systems theory and bifurcation theory are applied to investigate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous investigations of epidemiology, in-host disease, and autoimmunity. These closely related models display interesting dynamical behaviors including bistability, recurrence, and regular oscillations, each of which has possible clinical or public health implications. In this contribution we elucidate the key role of backward bifurcations in the parameter regimes leading to the behaviors of interest. We demonstrate that backward bifurcations with varied positions of turning points facilitate the appearance of Hopf bifurcations, and the varied dynamical behaviors are then determined by the properties of the Hopf bifurcation(s), including their location and direction. A Maple program developed earlier is implemented to determine the stability of limit cycles bifurcating from the Hopf bifurcation. Numerical simulations are presented to illustrate phenomena of interest such as bistability, recurrence and oscillation. We also discuss the physical motivations for the models and the clinical implications of the resulting dynamics.

Stochastic modelling of viral blips in HIV-1-infected patients: effects of inhomogeneous density fluctuations

We propose a stochastic model of HIV-1 infection dynamics under HAART in order to analyse the origin and dynamics of the so-called viral blips, i.e. episodes of transient viremia that occur in the phase of where the disease remains in a latent state during which the viral load raises above the detection limit of standard clinical assays. Based on prior work in the subject, we consider an infection model in which latently infected cell compartment sustains a residual (latent) infection over long periods of time. Unlike previous models, we include the effects of inhomogeneities in cell and virus concentration in the blood stream. We further consider the effect of burst virion production. By comparing with the experimental results obtained during a study in which intensive sampling was carried out on HIV-1-infected patients undergoing HAART over a long period of time, we conclude that our model supports the hypothesis that viral blips are consistent with random fluctuations around the average viral load. We further observe that agreement between our simulation results and the blip statistics obtained in the aforementioned study improves when burst virion production is considered. We also study the effect of sample manipulation artifacts on the results produced by our model, in particular, that of the post-extraction handling time, i.e. the time elapsed between sample extraction and actual test. Our results support the notion that the statistics of viral blips can be critically affected by such artifacts.

Stochastic population switch may explain the latent reservoir stability and intermittent viral blips in HIV patients on suppressive therapy

Highly active antiretroviral therapy can suppress plasma viral loads of HIV-1 infected individuals to below the detection limit of standard clinical assays. However, low-level viremia still persists. Many patients also have transient viral load measurements above the detection limit (the so-called "viral blips"). The latent reservoir consisting of latently infected CD4+ T cells represents a major obstacle to HIV-1 eradication. These cells can be activated to produce virions but the size of the latent reservoir is relatively stable. The mechanisms underlying low viral load persistence, emergence of intermittent viral blips and stability of the latent reservoir are not well understood. Cellular and viral transcription factors play an important role in the establishment and maintenance of HIV-1 latency. Infected cells with intermediate transcriptional activities may either revert to a latent state or become highly activated and produce virions due to intracellular perturbations. Here we develop a mathematical model that includes such stochastic population switch. We demonstrate that the model can generate a stable latent reservoir, intermittent viral blips, as well as low-level viremia persistence. Latently infected cells with intermediate transcription activities may maintain their size through a high level of homeostatic proliferation, while cells with low transcriptional activities are likely to be maintained through the reversion from cells with intermediate transcription activities. Simulations also suggest that treatment intensification or activation therapy may not help to eradicate the latent reservoir. Blocking the proliferation of latently infected cells might be a good strategy. These results provide more insights into the long-term dynamics of virus and latently infected cells in HIV patients on suppressive therapy and may help to develop novel treatment strategies.

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.

Immune activation promotes evolutionary conservation of T-cell epitopes in HIV-1

HIV, unlike other viruses, may benefit from immune recognition by preserving the sequence of its T cell epitopes, thereby enhancing transmission between cells.

The immune system should constitute a strong selective pressure promoting viral genetic diversity and evolution. However, HIV shows lower sequence variability at T-cell epitopes than elsewhere in the genome, in contrast with other human RNA viruses. Here, we propose that epitope conservation is a consequence of the particular interactions established between HIV and the immune system. On one hand, epitope recognition triggers an anti-HIV response mediated by cytotoxic T-lymphocytes (CTLs), but on the other hand, activation of CD4⁺ helper T lymphocytes (T_H cells) promotes HIV replication. Mathematical modeling of these opposite selective forces revealed that selection at the intrapatient level can promote either T-cell epitope conservation or escape. We predict greater conservation for epitopes contributing significantly to total immune activation levels (immunodominance), and when T_H cell infection is concomitant to epitope recognition (trans-infection). We suggest that HIV-driven immune activation in the lymph nodes during the chronic stage of the disease may offer a favorable scenario for epitope conservation. Our results also support the view that some pathogens draw benefits from the immune response and suggest that vaccination strategies based on conserved T_H epitopes may be counterproductive.

A key component of the immune response against viruses and other pathogens is the recognition of short foreign protein sequences called epitopes. However, viruses can escape the immune system by mutating, so epitopes should accumulate high levels of genetic variability. This has been documented in several human viruses, but in HIV, unexpectedly, epitopes tend to be relatively conserved. Here, we propose that this is a consequence of the peculiar interactions that occur between HIV and the immune system. As with other viruses, recognition of HIV epitopes promotes the activation of cytotoxic and helper T lymphocytes, which then orchestrate a cellular immune response. However, HIV infects helper T lymphocytes as their target cell in the body and does so more efficiently when these cells have been activated to participate in an immune response. Mathematical modeling showed that, in some cases, HIV may take advantage of immune activation, thus favoring epitope conservation. This should be more likely to occur with epitopes that trigger more vigorous T-cell responses, and during the process known as “trans-infection,” in which helper T lymphocytes are infected while being activated. Our results highlight the potential advantages of an HIV vaccination strategy based on epitopes that stimulate cytotoxic T lymphocytes without specifically stimulating helper T lymphocytes.

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

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

Transmission selects for HIV-1 strains of intermediate virulence: a modelling approach

Recent data shows that HIV-1 is characterised by variation in viral virulence factors that is heritable between infections, which suggests that viral virulence can be naturally selected at the population level. A trade-off between transmissibility and duration of infection appears to favour viruses of intermediate virulence. We developed a mathematical model to simulate the dynamics of putative viral genotypes that differ in their virulence. As a proxy for virulence, we use set-point viral load (SPVL), which is the steady density of viral particles in blood during asymptomatic infection. Mutation, the dependency of survival and transmissibility on SPVL, and host effects were incorporated into the model. The model was fitted to data to estimate unknown parameters, and was found to fit existing data well. The maximum likelihood estimates of the parameters produced a model in which SPVL converged from any initial conditions to observed values within 100–150 years of first emergence of HIV-1. We estimated the 1) host effect and 2) the extent to which the viral virulence genotype mutates from one infection to the next, and found a trade-off between these two parameters in explaining the variation in SPVL. The model confirms that evolution of virulence towards intermediate levels is sufficiently rapid for it to have happened in the early stages of the HIV epidemic, and confirms that existing viral loads are nearly optimal given the assumed constraints on evolution. The model provides a useful framework under which to examine the future evolution of HIV-1 virulence.

Recent studies have suggested that virulence in HIV-1 is partly a characteristic of the virus which is carried from one infection to the next. An infection with intermediate virulence will produce more transmissions during the infectious lifetime because it optimises the trade-off between rate of transmission and duration of infection. Natural selection acts on the heritable variation to increase the relative prevalence of strains with intermediate virulence. In this study we model the evolution of virulence in the viral population as these more successful strains are preferentially transmitted. We fit this model to data from transmitting couples, and find that the model fits the data well. We use this fit to estimate the contribution of the host and the virus to virulence, which complements recent estimates of the heritability of virulence. We also estimate the rate at which the viral determinants of virulence evolve between infections, and this provides predictions for how rapidly the virulence of HIV-1 evolves in a population. We suggest that natural selection on transmissibility results in substantial evolution of virulence in the population. This is sufficiently rapid for virulence to have reached current levels over the available timescale of the human epidemic.

A stochastic model of latently infected cell reactivation and viral blip generation in treated HIV patients

Motivated by viral persistence in HIV+ patients on long-term anti-retroviral treatment (ART), we present a stochastic model of HIV viral dynamics in the blood stream. We consider the hypothesis that the residual viremia in patients on ART can be explained principally by the activation of cells latently infected by HIV before the initiation of ART and that viral blips (clinically-observed short periods of detectable viral load) represent large deviations from the mean. We model the system as a continuous-time, multi-type branching process. Deriving equations for the probability generating function we use a novel numerical approach to extract the probability distributions for latent reservoir sizes and viral loads. We find that latent reservoir extinction-time distributions underscore the importance of considering reservoir dynamics beyond simply the half-life. We calculate blip amplitudes and frequencies by computing complete viral load probability distributions, and study the duration of viral blips via direct numerical simulation. We find that our model qualitatively reproduces short small-amplitude blips detected in clinical studies of treated HIV infection. Stochastic models of this type provide insight into treatment-outcome variability that cannot be found from deterministic models.

Superinfection with a heterologous HIV strain per se does not lead to faster progression

BACKGROUND

It has been suggested that superinfection of HIV positive individuals with heterologous HIV strains could lead to faster progression to AIDS, generating concern over the risks of exposure to new infections in those already infected.

METHODS

A mathematical model of the within-host dynamics of two sequential infections with strains of HIV describing activation and infection of immune cells was developed. Multiple stochastic realizations describing progression to AIDS in the individual were generated, comparing the situation with and without superinfection.

RESULTS

It was found that the susceptibility of immune cells to dual infection is crucial to the outcome of HIV superinfection. A low susceptibility leads to competitive exclusion between the strains and a high susceptibility may lead to co-existence if the superinfecting strain is sufficiently fit. It was also found that only superinfection with a fitter strain leads to faster progression to AIDS, rather than superinfection per se.

CONCLUSION

In theory, a superinfection event with a heterologous strain of HIV does not lead to faster progression to AIDS. Unless superinfection allows the spread of fitter virus, it should not be of concern for public health.

Modeling latently infected cell activation: viral and latent reservoir persistence, and viral blips in HIV-infected patients on potent therapy

Although potent combination therapy is usually able to suppress plasma viral loads in HIV-1 patients to below the detection limit of conventional clinical assays, a low level of viremia frequently can be detected in plasma by more sensitive assays. Additionally, many patients experience transient episodes of viremia above the detection limit, termed viral blips, even after being on highly suppressive therapy for many years. An obstacle to viral eradication is the persistence of a latent reservoir for HIV-1 in resting memory CD4(+) T cells. The mechanisms underlying low viral load persistence, slow decay of the latent reservoir, and intermittent viral blips are not fully characterized. The quantitative contributions of residual viral replication to viral and the latent reservoir persistence remain unclear. In this paper, we probe these issues by developing a mathematical model that considers latently infected cell activation in response to stochastic antigenic stimulation. We demonstrate that programmed expansion and contraction of latently infected cells upon immune activation can generate both low-level persistent viremia and intermittent viral blips. Also, a small fraction of activated T cells revert to latency, providing a potential to replenish the latent reservoir. By this means, occasional activation of latently infected cells can explain the variable decay characteristics of the latent reservoir observed in different clinical studies. Finally, we propose a phenomenological model that includes a logistic term representing homeostatic proliferation of latently infected cells. The model is simple but can robustly generate the multiphasic viral decline seen after initiation of therapy, as well as low-level persistent viremia and intermittent HIV-1 blips. Using these models, we provide a quantitative and integrated prospective into the long-term dynamics of HIV-1 and the latent reservoir in the setting of potent antiretroviral therapy.

Modeling HIV persistence, the latent reservoir, and viral blips

HIV-1 eradication from infected individuals has not been achieved with the prolonged use of highly active antiretroviral therapy (HAART). The cellular reservoir for HIV-1 in resting memory CD4(+) T cells remains a major obstacle to viral elimination. The reservoir does not decay significantly over long periods of time but is able to release replication-competent HIV-1 upon cell activation. Residual ongoing viral replication may likely occur in many patients because low levels of virus can be detected in plasma by sensitive assays and transient episodes of viremia, or HIV-1 blips, are often observed in patients even with successful viral suppression for many years. Here we review our current knowledge of the factors contributing to viral persistence, the latent reservoir, and blips, and mathematical models developed to explore them and their relationships. We show how mathematical modeling has helped improve our understanding of HIV-1 dynamics in patients on HAART and of the quantitative events underlying HIV-1 latency, reservoir stability, low-level viremic persistence, and emergence of intermittent viral blips. We also discuss treatment implications related to these studies.

Asymmetric division of activated latently infected cells may explain the decay kinetics of the HIV-1 latent reservoir and intermittent viral blips

Most HIV-infected patients when treated with combination antiretroviral therapy achieve viral loads that are below the current limit of detection of standard assays after a few months. Despite this, virus eradication from the host has not been achieved. Latent, replication-competent HIV-1 can generally be identified in resting memory CD4(+) T cells in patients with "undetectable" viral loads. Turnover of these cells is extremely slow but virus can be released from the latent reservoir quickly upon cessation of therapy. In addition, a number of patients experience transient episodes of viremia, or HIV-1 blips, even with suppression of the viral load to below the limit of detection for many years. The mechanisms underlying the slow decay of the latent reservoir and the occurrence of intermittent viral blips have not been fully elucidated. In this study, we address these two issues by developing a mathematical model that explores a hypothesis about latently infected cell activation. We propose that asymmetric division of latently infected cells upon sporadic antigen encounter may both replenish the latent reservoir and generate intermittent viral blips. Interestingly, we show that occasional replenishment of the latent reservoir induced by reactivation of latently infected cells may reconcile the differences between the divergent estimates of the half-life of the latent reservoir in the literature.

Immunologic, virologic, and clinical consequences of episodes of transient viremia during suppressive combination antiretroviral therapy

OBJECTIVE

To investigate immunologic, virologic, and clinical consequences of episodes of transient viremia in patients with sustained virologic suppression.

METHODS

From the AIDS Therapy Evaluation Project, Netherlands cohort, 4447 previously therapy-naive patients were selected who were on continuous combination antiretroviral therapy and had initial success (2 consecutive HIV RNA measurements <50 copies/mL). During episodes of viral suppression (RNA <50 copies/mL), low-level viremia (RNA 50 to 1000 copies/mL), or high-level viremia (RNA >1000 copies/mL) after initial success, the occurrence of therapy changes, drug resistance, and clinical events was assessed.

RESULTS

During 11,187 person-years of follow-up, 1281 (28.8%) patients had at least 1 RNA measurement >50 copies/mL. Among 8069 episodes, there were 5989 (74.2%) episodes of suppression, 1711 (21.2%) episodes of low-level viremia, and 369 (4.6%) episodes of high-level viremia. Most episodes of low-level viremia consisted of < or =2 RNA measurements (93.7%), were without clinical events or therapy changes (79.6%), and were without changes in CD4 cell counts. Therapy changes (52.3% of episodes) and resistance (23.3%) were frequently observed during high-level viremia.

CONCLUSIONS

Episodes of low-level viremia are frequent and short lasting, and the low proportion of episodes with clinical events suggests that leaving therapy unchanged is a clinically acceptable strategy. In contrast, high-level viremia is associated with resistance and is often followed by therapy changes.

Late entry to HIV care limits the impact of anti-retroviral therapy in The Netherlands

Objective

To explain differences in survival in the first three years of combination anti-retroviral therapy (cART) between HIV treatment centres in the Netherlands.

Methodology/Principal Findings

We developed a mathematical simulation model, parameterised using data from the ATHENA cohort that describes patients entering care, being monitored and starting cART. Three scenarios were used to represent three treatment centres with widely varying mortality rates on cART that were differentiated by: (i) the distribution of CD4 counts of patients entering care; (ii) the age distribution of patients entering care; (iii) the average rate of monitoring the patients not on cART. At the level of the treatment centre, the fraction of Dutch MSM dying in the first three years of treatment ranged from 0% to 8%. The mathematical model captured the large variation in observed mortality between the three treatment centres. Manipulating the age-distribution of patients or the frequency of monitoring did not affect the model predictions. In contrast, when the same national average distribution of CD4 count at entry was used in all the scenarios, the variation in predicted mortality between all centres was diminished.

Conclusions/Significance

Patients entering care with low CD4 counts appears to be the main source of variation in the mortality rates between Dutch treatment centres. Recruiting HIV-infected individuals to care earlier could lead to substantial improvements in cART outcomes. For example, if patients were to present with at least 400 CD4 cells/mm³, as they do already in some centres, then our model predicts that the mortality in the first three years of cART could be reduced by approximately 20%.

The impact of monitoring HIV patients prior to treatment in resource-poor settings: insights from mathematical modelling

BACKGROUND

The roll-out of antiretroviral treatment (ART) in developing countries concentrates on finding patients currently in need, but over time many HIV-infected individuals will be identified who will require treatment in the future. We investigated the potential influence of alternative patient management and ART initiation strategies on the impact of ART programmes in sub-Saharan Africa.

METHODS AND FINDINGS

We developed a stochastic mathematical model representing disease progression, diagnosis, clinical monitoring, and survival in a cohort of 1,000 hypothetical HIV-infected individuals in Africa. If individuals primarily enter ART programmes when symptomatic, the model predicts that only 25% will start treatment and, on average, 6 life-years will be saved per person treated. If individuals are recruited to programmes while still healthy and are frequently monitored, and CD4(+) cell counts are used to help decide when to initiate ART, three times as many are expected to be treated, and average life-years saved among those treated increases to 15. The impact of programmes can be improved further by performing a second CD4(+) cell count when the initial value is close to the threshold for starting treatment, maintaining high patient follow-up rates, and prioritising monitoring the oldest (> or = 35 y) and most immune-suppressed patients (CD4(+) cell count < or = 350). Initiating ART at higher CD4(+) cell counts than WHO recommends leads to more life-years saved, but disproportionately more years spent on ART.

CONCLUSIONS

The overall impact of ART programmes will be limited if rates of diagnosis are low and individuals enter care too late. Frequently monitoring individuals at all stages of HIV infection and using CD4 cell count information to determine when to start treatment can maximise the impact of ART.

Variation in HIV-1 set-point viral load: epidemiological analysis and an evolutionary hypothesis

The natural course of HIV-1 infection is characterized by a high degree of heterogeneity in viral load, not just within patients over time, but also between patients, especially during the asymptomatic stage of infection. Asymptomatic, or set-point, viral load has been shown to correlate with both decreased time to AIDS and increased infectiousness. The aim of this study is to characterize the epidemiological impact of heterogeneity in set-point viral load. By analyzing two cohorts of untreated patients, we quantify the relationships between both viral load and infectiousness and the duration of the asymptomatic infectious period. We find that, because both the duration of infection and infectiousness determine the opportunities for the virus to be transmitted, this suggests a trade-off between these contributions to the overall transmission potential. Some public health implications of variation in set-point viral load are discussed. We observe that set-point viral loads are clustered around those that maximize the transmission potential, and this leads us to hypothesize that HIV-1 could have evolved to optimize its transmissibility, a form of adaptation to the human host population. We discuss how this evolutionary hypothesis can be tested, review the evidence available to date, and highlight directions for future research.

Transient viremia, plasma viral load, and reservoir replenishment in HIV-infected patients on antiretroviral therapy

When antiretroviral therapy (ART) is administered for long periods to HIV-1-infected patients, most achieve viral loads that are "undetectable" by standard assay methods (ie, HIV-1 RNA <50 copies/mL). Despite sustaining viral loads lower than the level of detection, a number of patients experience unexplained episodes of transient viremia or viral "blips." We propose that transient activation of the immune system by infectious agents may explain these episodes of viremia. Using 2 different mathematical models, one in which blips arise because of target cell activation and subsequent infection and another in which latent cell activation generates blips, we establish a nonlinear (power law) relationship between blip amplitude and viral load (under ART) that suggest blips should be of lower amplitude, and thus harder to detect, as increasingly potent therapy is used. This effect can be more profound than is predicted by simply lowering the baseline viral load from which blips originate. Finally, we suggest that sporadic immune activation may elevate the level of chronically infected cells and replenish viral reservoirs, including the latent cell reservoir, providing a mechanism for recurrent viral blips and low levels of viremia under ART.

Role of avidity and breadth of the CD4 T cell response in progression to AIDS

The great variability in the time between infection with HIV and the onset of AIDS has been the object of intense study. In the current work, we examine a mathematical model that focuses on the role of immune response variability between patients. We study the effect of variation in both the avidity and the breadth of the immune response on within-patient disease dynamics, viral setpoint and time to AIDS. We conclude that immune response variability can explain the observed variability in disease progression to a large extent. It turns out that the avidity, more than the breadth of the immune response, determines disease progression, and that the average avidity of the five best clones is a much better correlate for disease progression than the total number of clones responding. For the design of vaccines, this would suggest that, if given the choice between stimulating a broader, but average avidity response or a narrower high-avidity response, the latter option would yield better control of virus load and consequently slow down disease progression.

The effect on treatment comparisons of different measurement frequencies in human immunodeficiency virus observational databases

Data collected in a routine clinical setting are frequently used to compare antiretroviral treatments for human immunodeficiency virus (HIV). Differences in the frequency of measurement of HIV RNA levels and CD4-positive T-lymphocyte cell counts introduce a possible source of bias into estimates of the difference in effectiveness between treatments. The authors investigated the size of this bias when survival analysis methods are used to compare the initial efficacy of antiretroviral regimens. Data sets of clinical markers were simulated by use of differential equations that model the interaction between HIV and human T-cells. Cox proportional hazards and parametric models were fitted to the simulated data sets to evaluate the bias and coverage of 95% confidence intervals for the difference between regimens. The authors' results demonstrate that differences in the frequency of follow-up can substantially bias estimated treatment differences if methods do not correctly account for the intervals between measurements and if the statistical model chosen does not fit the data well. Analyses using methods applicable to interval-censored data reduce the bias. In the Athena cohort of HIV-infected individuals in the Netherlands from 1999 to 2003, there are differences in measurement frequency between current regimens that are of sufficient magnitude to conclude incorrectly that some regimens are more effective than others.

On the intra-host dynamics of HIV-1 infections

An extension of a previously proposed theory for the pathogenesis of AIDS is presented and analyzed using a mathematical modelling approach. This theory is based on the observation that human immunodeficiency virus type 1 (HIV-1) predominantly infects and replicates in (CD4+)-T cells, and that the infection process within an infected individual is characterized by ongoing generation and selection of HIV variants with increasing reproductive capacity. This evolutionary process is considered to be the reason for the gradual loss of immunocompetence and the final destruction of the immune system observed in most patients. The extension presented here incorporates the effect of the permanently increasing susceptibility of (CD4+)-T cell clones, as a result of the evolutionary process. The presented model reproduces and possibly explains a wide variety of findings about the HIV infection process. Numerical results indicate that the effect of the initial dose is minimal, and restricted to the primary phase of infection. According to the model predictions the impact of the HIV evolutionary speed is crucial for the progression to disease. An important progression determinant is the initial infection rate, being a component of the viral reproductive capacity. An influential role in disease progression seems to be played by the initial (CD4+)-T cell count.

Potential Public Health Impact of Imperfect HIV Type 1 Vaccines

The potential public health impact of imperfect human immunodeficiency virus (HIV) type 1 vaccines was examined by use of deterministic mathematical models of virus transmission. Imperfect vaccines are defined as those that act to favorably alter the typical clinical course of disease in those immunized who acquire infection. The properties examined include a lengthened incubation period; reduced virus load, which acts to lower infectiousness; reduced susceptibility on exposure to infection; and an increase in risk behaviors by those vaccinated. Analyses suggest that, although imperfect vaccines would struggle to block transmission via cohort vaccination of those entering the sexually active age classes, they could have a substantial public health impact, as measured by reduced prevalence and mortality induced by acquired immunodeficiency syndrome (AIDS), provided the case reproductive number of HIV-1 among vaccinated individuals (R(0v)) was less than that among unvaccinated individuals (R(0)). This requires that any lengthening in the incubation period and, hence, the time period over which an infected vaccine recipient can transmit to susceptible sex partners, as well as any increase in risk behaviors, are more than offset by other effects, such as reduced susceptibility to infection and reduced infectiousness. Numerical studies based on a more complex model, which included representation of age, sex, heterogeneity in sexual activity, variable infectiousness, and different mixing patterns between risk groups, were used to confirm the general insights gained from a simple deterministic model.

Antigen-driven T-cell turnover

A mathematical model is developed to characterize the distribution of cell turnover rates within a population of T lymphocytes. Previous models of T-cell dynamics have assumed a constant uniform turnover rate; here we consider turnover in a cell pool subject to clonal proliferation in response to diverse and repeated antigenic stimulation. A basic framework is defined for T-cell proliferation in response to antigen, which explicitly describes the cell cycle during antigenic stimulation and subsequent cell division. The distribution of T-cell turnover rates is then calculated based on the history of random exposures to antigens. This distribution is found to be bimodal, with peaks in cell frequencies in the slow turnover (quiescent) and rapid turnover (activated) states. This distribution can be used to calculate the overall turnover for the cell pool, as well as individual contributions to turnover from quiescent and activated cells. The impact of heterogeneous turnover on the dynamics of CD4(+) T-cell infection by HIV is explored. We show that our model can resolve the paradox of high levels of viral replication occurring while only a small fraction of cells are infected.

Quantification of intrinsic residual viral replication in treated HIV-infected patients

The intrinsic rate of viral replication in HIV-infected patients treated with antiretroviral combination therapy is estimated by using a mathematical model of viral dynamics. This intrinsic replication is found to be episodic, varying considerably in quantity between patients (even among those achieving long-term undetectable levels of viremia) and is always reduced by increasing the potency of the antiviral drug regimen. The analysis reveals that even in conditions of perfect patient adherence and drug penetration a substantial level of residual viral replication is expected. The rate of evolution in the viral quasispecies, and thus also the probability of new drug-resistant viral strains being created, is proportional to the total amount of residual viral replication. Under most circumstances, the viral population continues to turn over rapidly during therapy, albeit at a much reduced level.