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Global Dynamics of a Delayed HIV-1 Infection Model with CTL Immune Response  [PDF]
Yunfei Li,Rui Xu,Zhe Li,Shuxue Mao
Discrete Dynamics in Nature and Society , 2011, DOI: 10.1155/2011/673843
Abstract: A delayed HIV-1 infection model with CTL immune response is investigated. By using suitable Lyapunov functionals, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection is less than or equal to unity; if the basic reproduction ratio for CTL immune response is less than or equal to unity and the basic reproduction ratio for viral infection is greater than unity, the CTL-inactivated infection equilibrium is globally asymptotically stable; if the basic reproduction ratio for CTL immune response is greater than unity, the CTL-activated infection equilibrium is globally asymptotically stable. 1. Introduction Recently, many mathematical models have been developed to describe the infection with HIV-1 (human immunodeficiency virus 1). By investigating these models, researchers have gained much important knowledge about the HIV-1 pathogenesis and have enhanced progress in the understanding of HIV-1 infection (see, e.g., [1–4]). It is pointed out by the work of [5] that immune response is universal and necessary to eliminate or control the disease during viral infections. In particular, as a part of innate response, cytotoxic T lymphocytes (CTLs) play a particularly important role in antiviral defense by attacking infected cells. Thus, many authors have studied the mathematical modelling of viral dynamics with CTL immune response (see, e.g., [5–9]). In [7], Nowak and Bangham considered an HIV-1 infection model with CTL immune response which is described by the following differential equations: where , , , and represent the densities of uninfected target cells, infected cells, virions, and CTL cells at time , respectively. Uninfected cells are produced at rate , die at rate , and become infected cells at rate . Infected cells are produced from uninfected cells at rate and die at rate . The parameter accounts for the strength of the lytic component. Free virions are produced from uninfected cells at rate and are removed at rate . The parameter is the death rate for CTLs, and describes the rate of CTL immune response activated by the infected cells. Moreover, infection rate plays an important role in the modelling of epidemic dynamics. Holling type-II functional response seems more reasonable than the bilinear incidence rate (see, [10]). In [11], by stability analysis, Song and Avidan obtained that the system with the bilinear incidence rate was an extreme case of the model with Holling type-II functional response term. In [3, 4, 7], the researchers used ordinary differential equations
Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response  [PDF]
Haibin Wang,Rui Xu
Discrete Dynamics in Nature and Society , 2013, DOI: 10.1155/2013/169427
Abstract: An HIV-1 infection model with latently infected cells and delayed immune response is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is established and the existence of Hopf bifurcations at the CTL-activated infection equilibrium is also studied. By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection ; if the basic reproduction ratio for viral infection and the basic reproduction ratio for CTL immune response , the CTL-inactivated infection equilibrium is globally asymptotically stable. If the basic reproduction ratio for CTL immune response , the global stability of the CTL-activated infection equilibrium is also derived when the time delay . Numerical simulations are carried out to illustrate the main results. 1. Introduction Mathematical and computational models of the human immune response under HIV-1 infection have received great attention in recent years [1–9]. It is a useful tool of better understanding disease dynamics and making prediction of disease outbreak and evaluations of prevention strategies and drug therapy strategies used against HIV-1 infection. It is well known that when HIV-1 enters the body, it targets cells with CD4 receptors, including the CD4+ T-cells, the main driver of the immune response. Recent studies have shown that a significant proportion of CD4+ T-cells are infected by the virus, and that this specific population of T-cells might be preferentially infected [10]. In human’s immune system, cytotoxic T lymphocytes (CTLs) play an important role in antiviral defense by attacking infected cells. Therefore, it is important and yet has been a hot topic to formulate models to explain the exhaustion of the CD4+ T-cells and CTLs. Such models involve the concentrations of uninfected CD4+ T-cells, , infected CD4+ T-cells that are producing virus, , free virus, , and CTLs, . A basic mathematical model describing HIV-1 infection dynamics that has been studied in [1, 2] is of the form where uninfected, susceptible CD4+ T-cells are created from sources within the body at a rate, , uninfected CD4+ T-cells die at rate and become infected at rate , where is the rate constant describing the infection process; infected cells die at rate and are lysed by CTLs at a rate ; free virus is produced from infected cells at rate and is removed at rate . The CTLs expand at a rate and decay at a rate . Time delays cannot be
Global Stability of HIV Infection of CD4+ T Cells and Macrophages with CTL Immune Response and Distributed Delays  [PDF]
A. M. Elaiw,R. M. Abukwaik,E. O. Alzahrani
Computational and Mathematical Methods in Medicine , 2013, DOI: 10.1155/2013/653204
Abstract: We study the global stability of a human immunodeficiency virus (HIV) infection model with Cytotoxic T Lymphocytes (CTL) immune response. The model describes the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic reproduction number and the immune response reproduction number . We have proven that, if , then the uninfected steady state is globally asymptotically stable (GAS), if , then the infected steady state without CTL immune response is GAS, and, if , then the infected steady state with CTL immune response is GAS. 1. Introduction One of the most diseases that have attracted the attention of many mathematicians is the acquired immunodeficiency syndrome (AIDS) caused by human immunodeficiency virus (HIV). HIV infects the CD4+ T cell which plays the central role in the immune system. Mathematical modeling and model analysis of HIV dynamics are important to discover the dynamical behaviors of the viral infection process and estimating key parameter values which leads to development of efficient antiviral drug therapies. Several mathematical models have been proposed to describe the HIV dynamics with CD4+ T cells [1–15]. In these papers, the Cytotoxic T Lymphocytes (CTL) immune response was not taken into account. The role of CTL is universal and necessary to eliminate or control the disease during viral infections. In particular, as a part of innate response, CTL plays a particularly important rate in antiviral defense by attacking infected cells. The basic HIV infection model which takes into consideration the CTL immune response has been proposed in [16] as The state variables describe the plasma concentrations of , the uninfected CD4+ T cells; , the infected CD4+ T cells; , the free virus particles; and , the CTL cells at time . Here, (1) describes the population dynamics of the uninfected CD4+ T cells, where represents the rate of new uninfected cells that are generated from sources within the body, is the death rate constant, and is the infection rate constant at which a target cell becomes infected via contacting with virus. Equation (2) describes the population dynamics of the infected CD4+ T cells and shows that they die with rate constant and are killed by the CTL immune response with rate constant . Equation (3)
Global stability of a delay differential equation of hepatitis B virus infection with immune response  [cached]
Jinliang Wang,Xinxin Tian
Electronic Journal of Differential Equations , 2013,
Abstract: The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number $Re_0$ and CTL immune-response reproduction number $Re_1$. When $Re_0 leq 1$, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when $Re_1 leq 1 < Re_0$, the CTL-inactivated infection equilibrium exists and is globally asymptotically stable, which means that CTLs immune response would not be activated and viral infection becomes chronic; and when $Re_1 > 1$, the CTL-activated infection equilibrium exists and is globally asymptotically stable, in this case the infection causes a persistent CTLs immune response. Our model is formulated by incorporating a Cytotoxic T lymphocytes (CTLs) immune response to recent work [Gourley, Kuang, Nagy, J. Bio. Dyn., 2(2008), 140-153] to model the role in antiviral by attacking virus infected cells. Our analysis provides a quantitative understandings of HBV replication dynamics in vivo and has implications for the optimal timing of drug treatment and immunotherapy in chronic HBV infection.
The hope for an HIV vaccine based on induction of CD8+ T lymphocytes: a review
Watkins, David I;
Memórias do Instituto Oswaldo Cruz , 2008, DOI: 10.1590/S0074-02762008000200001
Abstract: the only long-term and cost-effective solution to the human immunodeficiency virus (hiv) epidemic in the developing world is a vaccine that prevents individuals from becoming infected or, once infected, from passing the virus on to others. there is currently little hope for an aids vaccine. conventional attempts to induce protective antibody and cd8+ lymphocyte responses against hiv and simian immunodeficiency virus (siv) have failed. the enormous diversity of the virus has only recently been appreciated by vaccinologists, and our assays to determine cd8+ lymphocyte antiviral efficacy are inadequate. the central hypothesis of a ctl-based vaccine is that particularly effective cd8+ lymphocytes directed against at least five epitopes that are derived from regions under functional and structural constraints will control replication of pathogenic siv. this would be somewhat analogous to control of virus replication by triple drug therapy or neutralizing antibodies.
Unique CRF01_AE Gag CTL Epitopes Associated with Lower HIV-Viral Load and Delayed Disease Progression in a Cohort of HIV-Infected Thais  [PDF]
Masahiko Mori, Busarawan Sriwanthana, Nuanjun Wichukchinda, Chetsada Boonthimat, Naho Tsuchiya, Toshiyuki Miura, Panita Pathipvanich, Koya Ariyoshi, Pathom Sawanpanyalert
PLOS ONE , 2011, DOI: 10.1371/journal.pone.0022680
Abstract: Cytotoxic T Lymphocytes (CTLs) play a central role in controlling HIV-replication. Although numerous CTL epitopes have been described, most are in subtype B or C infection. Little is known about CTL responses in CRF01_AE infection. Gag CTL responses were investigated in a cohort of 137 treatment-na?ve HIV-1 infected Thai patients with high CD4+ T cell counts, using gIFN Enzyme-Linked Immunospot (ELISpot) assays with 15-mer overlapping peptides (OLPs) derived from locally dominant CRF01_AE Gag sequences. 44 OLPs were recognized in 112 (81.8%) individuals. Both the breadth and magnitude of the CTL response, particularly against the p24 region, positively correlated with CD4+ T cell count and inversely correlated with HIV viral load. The breadth of OLP response was also associated with slower progression to antiretroviral therapy initiation. Statistical analysis and single peptide ELISpot assay identified at least 17 significant associations between reactive OLP and HLA in 12 OLP regions; 6 OLP-HLA associations (35.3%) were not compatible with previously reported CTL epitopes, suggesting that these contained new CTL Gag epitopes. A substantial proportion of CTL epitopes in CRF01_AE infection differ from subtype B or C. However, the pattern of protective CTL responses is similar; Gag CTL responses, particularly against p24, control viral replication and slow clinical progression.
Rates of CTL Killing in Persistent Viral Infection In Vivo  [PDF]
Marjet Elemans ,Arnaud Florins,Luc Willems,Becca Asquith
PLOS Computational Biology , 2014, DOI: doi/10.1371/journal.pcbi.1003534
Abstract: The CD8+ cytotoxic T lymphocyte (CTL) response is an important defence against viral invasion. Although CTL-mediated cytotoxicity has been widely studied for many years, the rate at which virus-infected cells are killed in vivo by the CTL response is poorly understood. To date the rate of CTL killing in vivo has been estimated for three virus infections but the estimates differ considerably, and killing of HIV-1-infected cells was unexpectedly low. This raises questions about the typical anti-viral capability of CTL and whether CTL killing is abnormally low in HIV-1. We estimated the rate of killing of infected cells by CD8+ T cells in two distinct persistent virus infections: sheep infected with Bovine Leukemia Virus (BLV) and humans infected with Human T Lymphotropic Virus type 1 (HTLV-1) which together with existing data allows us to study a total of five viruses in parallel. Although both BLV and HTLV-1 infection are characterised by large expansions of chronically activated CTL with immediate effector function ex vivo and no evidence of overt immune suppression, our estimates are at the lower end of the reported range. This enables us to put current estimates into perspective and shows that CTL killing of HIV-infected cells may not be atypically low. The estimates at the higher end of the range are obtained in more manipulated systems and may thus represent the potential rather than the realised CTL efficiency.
Implications of CTL-Mediated Killing of HIV-Infected Cells during the Non-Productive Stage of Infection  [PDF]
Christian L. Althaus,Rob J. De Boer
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0016468
Abstract: Patients infected with HIV exhibit orders of magnitude differences in their set-point levels of the plasma viral load. As to what extent this variation is due to differences in the efficacy of the cytotoxic T lymphocyte (CTL) response in these patients is unclear. Several studies have shown that HIV-infected CD4+ T cells also present viral epitopes that are recognized by CTLs before the productive stage of infection, i.e., during the intracellular eclipse phase before the infected cell starts to produce new viral particles. Here, we use mathematical modeling to investigate the potential impact of early killing of HIV-infected cells on viral replication. We suggest that the majority of CTL-mediated killing could occur during the viral eclipse phase, and that the killing of virus-producing cells could be substantially lower at later stages due to MHC-I-down-regulation. Such a mechanism is in agreement with several experimental observations that include CD8+ T cell depletion and antiretroviral drug treatment. This indicates a potentially important role of CTL-mediated killing during the non-productive stage of HIV-infected cells.
Antibody-Dependent Cellular Cytotoxicity and NK Cell-Driven Immune Escape in HIV Infection: Implications for HIV Vaccine Development  [PDF]
Gamze Isitman,Ivan Stratov,Stephen J. Kent
Advances in Virology , 2012, DOI: 10.1155/2012/637208
Abstract: The HIV-1 genome is malleable and a difficult target tot vaccinate against. It has long been recognised that cytotoxic T lymphocytes and neutralising antibodies readily select for immune escape HIV variants. It is now also clear that NK cells can also select for immune escape. NK cells force immune escape through both direct Killer-immunoglobulin-like receptor (KIR)-mediated killing as well as through facilitating antibody-dependent cellular cytotoxicity (ADCC). These newer finding suggest NK cells and ADCC responses apply significant pressure to the virus. There is an opportunity to harness these immune responses in the design of more effective HIV vaccines. 1. Introduction The human immunodeficiency virus (HIV-1) pandemic is causing substantial morbidity and mortality across the globe, particularly in developing countries. Antiretroviral drug therapy for HIV is highly effective in controlling disease; however, eradication of HIV-1 is currently not feasible so treatment is life long and is both expensive and leads to considerable toxicity and drug resistance. A vaccine is widely viewed as being essential to controlling the epidemic. Several advanced efforts to develop an effective vaccine have failed or shown only marginal efficacy to date [1–4]. One of the greatest challenges in developing a vaccine against HIV is to overcome its ability to constantly mutate and escape anti-HIV immune responses. This high mutation rate is a direct result of the presence of the virus’ low fidelity RNA polymerase enzyme as well as the high levels of recombination it undergoes [5, 6]. A measure of the pressure immune responses apply is through their ability to force viral mutations that result in escape from immune recognition. Both CTLs and Nabs have long been reported to select for immune escape variants during the course of HIV-1 infection [7, 8]. Much effort in vaccine development centers on inducing broad and potent CTL (cytotoxic T lymphocyte) and Nab (Neutralizing antibody) responses to conserved viral epitopes and restricting opportunities for viral escape. However, it is now also recognised other immune responses, such as antibody-dependent cellular cytotoxicity (ADCC) and NK cells, select for immune escape variants, suggesting additional immune responses apply significant pressure to the virus [9]. ADCC responses mediated by effector NK cells may be useful responses to induce by vaccination. This paper summarizes current thinking on immune escape from anti-HIV immune responses. 2. CTL Escape and the Road to Reduced Viral Fitness Immune escape from HIV was first
Quantification of the Relative Importance of CTL, B Cell, NK Cell, and Target Cell Limitation in the Control of Primary SIV-Infection  [PDF]
Marjet Elemans ,Rodolphe Thiébaut,Amitinder Kaur,Becca Asquith
PLOS Computational Biology , 2011, DOI: 10.1371/journal.pcbi.1001103
Abstract: 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.
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