The dual role of dendritic cells in the immune response to human immunodeficiency virus type 1 infection

Three-stage modeling of HIV infection and implications for antiretroviral therapy

We consider a deterministic model of HIV infection that involves macrophages as a long-term active reservoir to describe all three stages of the disease process: the acute stage, chronic infection, and the transition to AIDS. The proposed model is shown to retain crucial properties, such as the positivity of solutions, regardless of variations in model parameters. A dynamical analysis is performed to identify the local stability properties of the viral clearance steady state. This analysis illustrates how chronically infected macrophages can explain the progression to AIDS and provoke viral explosion, while previous models do not. We further demonstrate that the infected T-cell population, even if not responsible for the majority of new infections that lead to viral explosion, may contribute significantly to the transition amongst the three stages of infection. Moreover, we explore the implications of the model for the administration of antiretroviral therapy (ART) and provide quantitative estimates that emphasize the time sensitive nature of treatment initiation and the level of drug efficacy. Finally, we study the effects of treatment interruption on the disease dynamics predicted by the model and elucidate the influence of both interruption time and duration.

The effect of noise in an HIV infection model with cytotoxic T-lymphocyte impairment

The human immunodeficiency virus (HIV) interacts with the immune cells within the human body, where the environment is uncertain and noisy. Stochastic models can successfully encapsulate the effect of such a noisy environment compared to their deterministic counterparts. The human immune system is complex but well-coordinated with various immune cells like C D ⁴T cells, dendritic cells, and cytotoxic T-lymphocyte (CTL) cells, among many others. The CTL can kill the antigenic cells after its recognition. However, the efficacy of CTL in removing the infected C D ⁴T cells is progressively compromised in HIV-infected individuals. This paper considers a noise-induced HIV-immune cell interaction model with immune impairment. A multiplicative white noise is introduced in the infection rate parameter to represent the fluctuations around the average value of the rate parameter as a causative effect of the noise. We analyzed the deterministic and stochastic models and prescribed sufficient conditions for infection eradication and persistence. It is determined under what parametric restrictions the asymptotic solutions of the noise-induced system will be a limiting case of the deterministic solutions. Simulation results revealed that the solutions of the deterministic system either converge to a CTL-dominated interior equilibrium or a CTL-free immunodeficient equilibrium, depending on the initial values of the system. Stochastic analysis divulged that higher noise might be helpful in the infection removal process. The extinction time of infected C D ⁴T cells for some fixed immune impairment gradually decreases with increasing noise intensity and follows the power law.

A Novel Framework for Modeling Person-to-Person Transmission of Respiratory Diseases

From the beginning of the COVID-19 pandemic, researchers assessed the impact of the disease in terms of loss of life, medical load, economic damage, and other key metrics of resiliency and consequence mitigation; these studies sought to parametrize the critical components of a disease transmission model and the resulting analyses were informative but often lacked critical parameters or a discussion of parameter sensitivities. Using SARS-CoV-2 as a case study, we present a robust modeling framework that considers disease transmissibility from the source through transport and dispersion and infectivity. The framework is designed to work across a range of particle sizes and estimate the generation rate, environmental fate, deposited dose, and infection, allowing for end-to-end analysis that can be transitioned to individual and population health models. In this paper, we perform sensitivity analysis on the model framework to demonstrate how it can be used to advance and prioritize research efforts by highlighting critical parameters for further analyses.

Backward bifurcation in within-host HIV models

The activation and proliferation of naive CD4 T cells produce helper T cells, and increase the susceptible population in the presence of HIV. This may cause backward bifurcation. To verify this, we construct a simple within-host HIV model that includes the key variables, namely healthy naive CD4 T cells, helper T cells, infected CD4 T cells and virus. When the viral basic reproduction number R₀ is less than unity, we show theoretically and numerically that bistability for R_C<R₀<1 can be caused by a backward bifurcation due to a new susceptible population produced by activation of healthy naive CD4 T cells that become helper T cells. An extended model including the CTL dynamics may also show this backward bifurcation. In the case that the homeostatic source of healthy naive CD4 T cells is large, R_C is approximately the threshold for HIV to persist independent of initial conditions. The backward bifurcation may still occur even when we consider latent infections of naive CD4 T cells. Thus to control the spread of within-host HIV, it may be necessary for treatment to reduce the reproduction number below R_C.

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.

Modeling Kick-Kill Strategies toward HIV Cure

Although combinatorial antiretroviral therapy (cART) potently suppresses the virus, a sterile or functional cure still remains one of the greatest therapeutic challenges worldwide. Reservoirs are infected cells that can maintain HIV persistence for several years in patients with optimal cART, which is a leading obstacle to eradicate the virus. Despite the significant progress that has been made in our understanding of the diversity of cells that promote HIV persistence, many aspects that are critical to the development of effective therapeutic approaches able to purge the latent CD4+ T cell reservoir are poorly understood. Simultaneous purging strategies known as “kick-kill” have been pointed out as promising therapeutic approaches to eliminate the viral reservoir. However, long-term outcomes of purging strategies as well as the effect on the HIV reservoir are still largely fragmented. In this context, mathematical modeling can provide a rationale not only to evaluate the impact on the HIV reservoir but also to facilitate the formulation of hypotheses about potential therapeutic strategies. This review aims to discuss briefly the most recent mathematical modeling contributions, harnessing our knowledge toward the uncharted territory of HIV eradication. In addition, problems associated with current models are discussed, in particular, mathematical models consider only T cell responses but HIV control may also depend on other cell responses as well as chemokines and cytokines dynamics.

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.

Tropism of CPMV to Professional Antigen Presenting Cells Enables a Platform to Eliminate Chronic Infections

Chronic viral infections (e.g., HIV, HBV, HCV) represent a significant source of morbidity and mortality with over 500 million people infected worldwide. Dendritic cells (DCs) and macrophages are key cell types for productive viral replication and persistent systemic infection. We demonstrate that the plant virus cowpea mosaic virus (CPMV) displays tropism for such antigen presenting cells in both mice and humans, thus making it an ideal candidate for targeted drug delivery toward viral infections. Furthermore, we show inhibition of a key host protein for viral infection, site-1 protease (S1P), using the small molecule PF-429242 in the model pathogen arenavirus lymphocytic choriomeningitis virus (LCMV) limits viral growth. By packaging PF-429242 in CPMV, we are able to control drug release and efficiently deliver the drug. This sets the groundwork for utilizing the natural tropism of CPMV for a therapeutic approach that specifically targets cell types most commonly subverted by chronic viruses.

The effect of vaccination to dendritic cell and immune cell interaction in HIV disease progression

In this research paper, our main objective is to find out the meticulous role of activated dendritic cells (DCs) during the human immunodeficiency virus (HIV) infection process. DCs play a dual role by enhancing both HIV infection progression, as well as antiviral immune response. To explore the implications of these dual roles, we have formulated our mathematical model and analyzed the model by both analytical and numerical approaches. By using an impulsive differential equation, we have studied the effect of DC-based vaccination. Analytically we have determined the threshold value of drug dosage and dosing interval for optimum levels of infection. We have also investigated the effect of perfect adherence of drug dose on the immune cell count in extreme cases and observed that, systematic drug dose of the immune cells leads to its maximum level.

Dynamics of HIV infection in lymphoid tissue network

Human immunodeficiency virus (HIV) is a fast replicating ribonucleic acid virus, which can easily mutate in order to escape the effects of drug administration. Hence, understanding the basic mechanisms underlying HIV persistence in the body is essential in the development of new therapies that could eradicate HIV infection. Lymphoid tissues are the primary sites of HIV infection. Despite the recent progress in real-time monitoring technology, HIV infection dynamics in a whole body is unknown. Mathematical modeling and simulations provide speculations on global behavior of HIV infection in the lymphatic system. We propose a new mathematical model that describes the spread of HIV infection throughout the lymphoid tissue network. In order to represent the volume difference between lymphoid tissues, we propose the proportionality of several kinetic parameters to the lymphoid tissues' volume distribution. Under this assumption, we perform extensive numerical computations in order to simulate the spread of HIV infection in the lymphoid tissue network. Numerical computations simulate single drug treatments of an HIV infection. One of the important biological speculations derived from this study is a drug saturation effect generated by lymphoid network connection. This implies that a portion of reservoir lymphoid tissues to which drug is not sufficiently delivered would inhibit HIV eradication despite of extensive drug injection.

A MATHEMATICAL MODEL FOR THE TREATMENT OF AIDS-RELATED KAPOSI'S SARCOMA

We formulate a mathematical model to study the dynamics of HIV-1 related Kaposi's Sarcoma (KS) pathogenesis. KS progression is modeled as a dual process involving the primary infection of B cells, which sustains HHV-8 replication and the secondary infection of progenitor cells by HHV-8, which sustains the KS cell replication. We incorporate the pharmacodynamics of highly active antiretroviral therapy (HAART), or combination therapy (HAART plus KS therapy) and consider how each treatment strategy alters the disease progression. Our results indicate that administration of HAART to individuals co-infected with the HIV-1 and HHV-8 viruses can greatly amplify the therapeutic response of low-dose KS therapies. We have found that adherence levels above 85% can significantly reduce the risk of KS and HIV for a treatment periods under 1 year. For longer treatment periods, however, at least 90% adherence level is recommended.

Computational study to determine when to initiate and alternate therapy in HIV infection

HIV is a widespread viral infection without cure. Drug treatment has transformed HIV disease into a treatable long-term infection. However, the appearance of mutations within the viral genome reduces the susceptibility of HIV to drugs. Therefore, a key goal is to extend the time until patients exhibit resistance to all existing drugs. Current HIV treatment guidelines seem poorly supported as practitioners have not achieved a consensus on the optimal time to initiate and to switch antiretroviral treatments. We contribute to this discussion with predictions derived from a mathematical model of HIV dynamics. Our results indicate that early therapy initiation (within 2 years postinfection) is critical to delay AIDS progression. For patients who have not received any therapy during the first 3 years postinfection, switch in response to virological failure may outperform proactive switching strategies. In case that proactive switching is opted, the switching time between therapies should not be larger than 100 days. Further clinical trials are needed to either confirm or falsify these predictions.

HIV-1 Trans Infection of CD4(+) T Cells by Professional Antigen Presenting Cells

Since the 1990s we have known of the fascinating ability of a complex set of professional antigen presenting cells (APCs; dendritic cells, monocytes/macrophages, and B lymphocytes) to mediate HIV-1 trans infection of CD4(+) T cells. This results in a burst of virus replication in the T cells that is much greater than that resulting from direct, cis infection of either APC or T cells, or trans infection between T cells. Such APC-to-T cell trans infection first involves a complex set of virus subtype, attachment, entry, and replication patterns that have many similarities among APC, as well as distinct differences related to virus receptors, intracellular trafficking, and productive and nonproductive replication pathways. The end result is that HIV-1 can sequester within the APC for several days and be transmitted via membrane extensions intracellularly and extracellularly to T cells across the virologic synapse. Virus replication requires activated T cells that can develop concurrently with the events of virus transmission. Further research is essential to fill the many gaps in our understanding of these trans infection processes and their role in natural HIV-1 infection.

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.

Host immune responses that promote initial HIV spread

The host inflammatory response to HIV invasion is a necessary component of the innate antiviral activity that vaccines and early interventions seek to exploit/enhance. However, the response is dependent on CD4+ T-helper cell 1 (Th1) recruitment and activation. It is this very recruitment of HIV-susceptible target cells that is associated with the initial viral proliferation. Hence, global enhancement of the inflammatory response by T-cells and dendritic cells will likely feed viral propagation. Mucosal entry sites contain inherent pathways, in the form of natural regulatory T-cells (nTreg), that globally dampen the inflammatory response. We created a model of this inflammatory response to virus as well as inherent nTreg-mediated regulation of Th1 recruitment and activation. With simulations using this model we sought to address the net effect of nTreg activation and its specific functions as well as identify mechanisms of the natural inflammatory response that are best targeted to inhibit viral spread without compromising initial antiviral activity. Simulation results provide multiple insights that are relevant to developing intervention strategies that seek to exploit natural immune processes: (i) induction of the regulatory response through nTreg activation expedites viral proliferation due to viral production by nTreg itself and not to reduced Natural Killer (NK) cell activity; (ii) at the same time, induction of the inflammation response through either DC activation or Th1 activation expedites viral proliferation; (iii) within the inflammatory pathway, the NK response is an effective controller of viral proliferation while DC-mediated stimulation of T-cells is a significant driver of viral proliferation; and (iv) nTreg-mediated DC deactivation plays a significant role in slowing viral proliferation by inhibiting T-cell stimulation, making this function an aide to the antiviral immune response.

A hybrid multi-compartment model of granuloma formation and T cell priming in tuberculosis

Tuberculosis is a worldwide health problem with 2 billion people infected with Mycobacterium tuberculosis (Mtb, the bacteria causing TB). The hallmark of infection is the emergence of organized structures of immune cells forming primarily in the lung in response to infection. Granulomas physically contain and immunologically restrain bacteria that cannot be cleared. We have developed several models that spatially characterize the dynamics of the host-mycobacterial interaction, and identified mechanisms that control granuloma formation and development. In particular, we published several agent-based models (ABMs) of granuloma formation in TB that include many subtypes of T cell populations, macrophages as well as key cytokine and chemokine effector molecules. These ABM studies emphasize the important role of T-cell related mechanisms in infection progression, such as magnitude and timing of T cell recruitment, and macrophage activation. In these models, the priming and recruitment of T cells from the lung draining lymph node (LN) was captured phenomenologically. In addition to these ABM studies, we have also developed several multi-organ models using ODEs to examine trafficking of cells between, for example, the lung and LN. While we can predict temporal dynamic behaviors, those models are not coupled to the spatial aspects of granuloma. To this end, we have developed a multi-organ model that is hybrid: an ABM for the lung compartment and a non-linear system of ODE representing the lymph node compartment. This hybrid multi-organ approach to study TB granuloma formation in the lung and immune priming in the LN allows us to dissect protective mechanisms that cannot be achieved using the single compartment or multi-compartment ODE system. The main finding of this work is that trafficking of important cells known as antigen presenting cells from the lung to the lymph node is a key control mechanism for protective immunity: the entire spectrum of infection outcomes can be regulated by key immune cell migration rates. Our hybrid multi-organ implementation suggests that effector CD4+ T cells can rescue the system from a persistent infection and lead to clearance once a granuloma is fully formed. This could be effective as an immunotherapy strategy for latently infected individuals.

A multifaceted approach to modeling the immune response in tuberculosis

Tuberculosis (TB) is a deadly infectious disease caused by Mycobacterium tuberculosis (Mtb). No available vaccine is reliable and, although treatment exists, approximately 2 million people still die each year. The hallmark of TB infection is the granuloma, a self-organizing structure of immune cells forming in the lung and lymph nodes in response to bacterial invasion. Protective immune mechanisms play a role in granuloma formation and maintenance; these act over different time/length scales (e.g., molecular, cellular, and tissue scales). The significance of specific immune factors in determining disease outcome is still poorly understood, despite incredible efforts to establish several animal systems to track infection progression and granuloma formation. Mathematical and computational modeling approaches have recently been applied to address open questions regarding host-pathogen interaction dynamics, including the immune response to Mtb infection and TB granuloma formation. This provides a unique opportunity to identify factors that are crucial to a successful outcome of infection in humans. These modeling tools not only offer an additional avenue for exploring immune dynamics at multiple biological scales but also complement and extend knowledge gained via experimental tools. We review recent modeling efforts in capturing the immune response to Mtb, emphasizing the importance of a multiorgan and multiscale approach that has tuneable resolution. Together with experimentation, systems biology has begun to unravel key factors driving granuloma formation and protective immune response in TB. WIREs Syst Biol Med 2011 3 479-489 DOI: 10.1002/wsbm.131

Innate immune activation in primary HIV-1 infection

There is growing evidence that highlights the role of the immune response during acute human immunodeficiency virus type 1 (HIV-1) infection in the control or development of disease. The adaptive immune responses do not appear until after HIV-1 infection is already well established, so the role of earlier and faster-responding innate immunity needs to be more closely scrutinized. In particular, 2 aspects of innate immunity for which there are growing research developments will be examined in this review: the actions of type I interferons and natural killer cells. These two components of the innate immune response contribute to viral control both by killing infected cells and by modulating other immune cells that develop. However, the role of interferon α in immune activation is a double-edged sword, causing recruitment of adaptive immune cells that can assist in viral control but concurrently contributing to immune activation-dependent disease progression. Understanding the complexity of how innate responses affect the outcome of HIV-1 infection will help in the development of vaccines that can use innate immunity to enhance viral control with minimal pathogenesis.

Model of colonic inflammation: immune modulatory mechanisms in inflammatory bowel disease

Inflammatory bowel disease (IBD) is an immunoinflammatory illness of the gut initiated by an immune response to bacteria in the microflora. The resulting immunopathogenesis leads to lesions in epithelial lining of the colon through which bacteria may infiltrate the tissue causing recurring bouts of diarrhea, rectal bleeding, and malnutrition. In healthy individuals such immunopathogenesis is avoided by the presence of regulatory cells that inhibit the inflammatory pathway. Highly relevant to the search for treatment strategies is the identification of components of the inflammatory pathway that allow regulatory mechanisms to be overridden and immunopathogenesis to proceed. In vitro techniques have identified cellular interactions involved in inflammation-regulation crosstalk. However, tracing immunological mechanisms discovered at the cellular level confidently back to an in vivo context of multiple, simultaneous interactions has met limited success. To explore the impact of specific interactions, we have constructed a system of 29 ordinary differential equations representing different phenotypes of T-cells, macrophages, dendritic cells, and epithelial cells as they move and interact with bacteria in the lumen, lamina propria, and lymphoid tissue of the colon. Simulations revealed the positive inflammatory feedback loop formed by inflammatory M1 macrophage activation of T-cells as a driving force underlying the immunopathology of IBD. Furthermore, strategies that remove M1 from the site of infection, by either (i) increasing its potential to switch to a regulatory M2 phenotype or (ii) increasing the rate of reversion (for M1 and M2 alike) to a resting state, cease immunopathogenesis even as bacteria are eliminated by other inflammatory cells. Based on these results, we identify macrophages and their mechanisms of plasticity as key targets for mucosal inflammation intervention strategies. In addition, we propose that the primary mechanism behind the association of PPARgamma mutation with IBD is its ability to mediate the M1 to M2 switch.

HIV and mature dendritic cells: Trojan exosomes riding the Trojan horse?

Exosomes are secreted cellular vesicles that can induce specific CD4⁺ T cell responses in vivo when they interact with competent antigen-presenting cells like mature dendritic cells (mDCs). The Trojan exosome hypothesis proposes that retroviruses can take advantage of the cell-encoded intercellular vesicle traffic and exosome exchange pathway, moving between cells in the absence of fusion events in search of adequate target cells. Here, we discuss recent data supporting this hypothesis, which further explains how DCs can capture and internalize retroviruses like HIV-1 in the absence of fusion events, leading to the productive infection of interacting CD4⁺ T cells and contributing to viral spread through a mechanism known as trans-infection. We suggest that HIV-1 can exploit an exosome antigen-dissemination pathway intrinsic to mDCs, allowing viral internalization and final trans-infection of CD4⁺ T cells. In contrast to previous reports that focus on the ability of immature DCs to capture HIV in the mucosa, this review emphasizes the outstanding role that mature DCs could have promoting trans-infection in the lymph node, underscoring a new potential viral dissemination pathway.

Utilizing the FIV model to understand dendritic cell dysfunction and the potential role of dendritic cell immunization in HIV infection

Dendritic cells (DC) are potent antigen presenting cells which initiate and coordinate the immune response making them central targets of and attractive candidates for manipulation in chronic lentiviral infections. Emerging evidence suggests that DC immune function is disrupted during both acute and chronic infection with human immunodeficiency virus (HIV), simian immunodeficiency virus (SIV), and feline immunodeficiency virus (FIV). Despite some early promising data, the use of DC for lentiviral immunotherapy has not fulfilled its expected potential and has been complicated by the large number of variables involved in DC harvesting, purifying, and antigen loading. Pre-clinical studies aimed at identifying successful strategies for DC augmentation of current HIV treatment protocols are needed. Over the past two decades, the FIV model for HIV infection has increased the understanding of retroviral pathogenesis, and studies have begun using the FIV model to study DC dysfunction and DC-mediated immunotherapy. Careful consideration of the many variables involved in DC function and therapy should help develop protocols to explore the potential of DC vaccine-based therapies for lentiviral infection.

Immune impairment in HIV infection: existence of risky and immunodeficiency thresholds

Results of several studies show that some DC populations are susceptible to HIV. Modulation of DCs by HIV infection, in particular interference of the antigen-presenting function of DCs, is a key aspect in viral pathogenesis and contributes to viral evasion from immunity because the loss of the DC function engenders some impairment effects for a proliferation of CTL responses, which play an important role in the immune response to HIV. As described herein, we use a simple mathematical model to examine virus-immune dynamics over the course of HIV infection in the context of the immune impairment effects. A decrease of the DC number and function during the course of HIV-1 infection is observed. Therefore, we simply assumed that the immune impairment rate increases over the HIV infection. Under the assumption, four processes of the disease progression dynamics of our model are classifiable according to their virological properties. It is particularly interesting a typical disease progression presents a "risky threshold" and an "immunodeficiency threshold". Regarding the former, the immune system might collapse when the impairment rate of HIV exceeds a threshold value (which corresponds to a transcritical bifurcation point). For the latter, the immune system always collapses when the impairment rate exceeds the value (which corresponds to a saddle-node bifurcation point). To test our theoretical framework, we investigate the existence and distribution of these thresholds in 10 patients.

Immune impairment thresholds in HIV infection

Longitudinal studies of patients infected with HIV-1 reveal a long and variable length of asymptomatic phase between infection and development of AIDS. Some HIV infected patients are still asymptomatic after 15 or more years of infection but some patients develop AIDS within 2 years. The mechanistic basis of the disease progression has remained obscure but many researchers have been trying to explain it. For example, the possible importance of viral diversity for the disease progression and the development of AIDS has been very well worked out in the early-1990s, especially by some important works of Martin A. Nowak. These studies can give an elegant explanation for a variability of asymptomatic phase. Here, a simple mathematical model was used to propose a new explanation for a variable length of asymptomatic phase. The main idea is that the immune impairment rate increases over the HIV infection. Our model suggested the existence of so-called "Risky threshold" and "Immunodeficiency threshold" on the impairment rate. The former implies that immune system may collapse when the impairment rate of HIV exceeds the threshold value. The latter implies that immune system always collapses when the impairment rate exceeds the value. We found that the length of asymptomatic phase is determined stochastically between these threshold values depending on the virological and immunological states. Furthermore, we investigated a distribution of the length of asymptomatic phase and a survival rate of the immune responses in one HIV patient.