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This paper develops a mathematical model to investigate the Human Immunodeficiency Virus (HIV) infection dynamics. The model includes two transmission modes (cell-to-cell and cell-free), two adaptive immune responses (cytotoxic T-lymphocyte (CTL) and antibody), a saturated CTL immune response, and latent HIV infection. The existence and local stability of equilibria are fully characterized by four reproduction numbers. Through sensitivity analyses, we assess the partial rank correlation coefficients of these reproduction numbers and identify that the infection rate via cell-to-cell transmission, the number of new viruses produced by each infected cell during its life cycle, the clearance rate of free virions, and immune parameters have the greatest impact on the reproduction numbers. Additionally, we compare the effects of immune stimulation and cell-to-cell spread on the model's dynamics. The findings highlight the significance of adaptive immune responses in increasing the population of uninfected cells and reducing the numbers of latent cells, infected cells, and viruses. Furthermore, cell-to-cell transmission is identified as a facilitator of HIV transmission. The analytical and numerical results presented in this study contribute to a better understanding of HIV dynamics and can potentially aid in improving HIV management strategies. [ABSTRACT FROM AUTHOR]

This paper formulates and analyzes two mathematical models that describe the within-host dynamics of human immunodeficiency virus type 1 (HIV-1) with impairment of both cytotoxic T lymphocytes (CTLs) and B cells. Both viral transmission (VT) and cellular infection (CT) mechanisms are considered. The second model is a generalization of the first model that includes distributed time delays. For the two models, we establish the non-negativity and boundedness of the solutions, find the basic reproductive numbers, determine all possible steady states and establish the global asymptotic stability properties of all steady states by means of the Lyapunov method. We confirm the theoretical results by conducting numerical simulations. We conduct a sensitivity analysis to show the effect of the values of the parameters on the basic reproductive number. We discuss the results, showing that impaired B cells and CTLs, time delay and latent CT have significant effects on the HIV-1 dynamics. [ABSTRACT FROM AUTHOR]

This paper presents and analyzes two mathematical models for the human immunodeficiency virus type-1 (HIV-1) infection with Cytotoxic T Lymphocyte cell (CTL) immune impairment. These models describe the interactions between healthy CD 4 + T cells, latently and actively infected cells, HIV-1 particles, and CTLs. The healthy CD 4 + T cells might be infected when they make contact with: (i) HIV-1 particles due to virus-to-cell (VTC) contact; (ii) latently infected cells due to latent cell-to-cell (CTC) contact; and (iii) actively infected cells due to active CTC contact. Distributed time delays are considered in the second model. We show the nonnegativity and boundedness of the solutions of the systems. Further, we derive basic reproduction numbers ℜ 0 and ℜ ˜ 0 , that determine the existence and stability of equilibria of our proposed systems. We establish the global asymptotic stability of all equilibria by using the Lyapunov method together with LaSalle's invariance principle. We confirm the theoretical results by numerical simulations. The effect of immune impairment, time delay and CTC transmission on the HIV-1 dynamics are discussed. It is found that weak immunity contributes significantly to the development of the disease. Further, we have established that the presence of time delay can significantly decrease the basic reproduction number and then suppress the HIV-1 replication. On the other hand, the presence of latent CTC spread increases the basic reproduction number and then enhances the viral progression. Thus, neglecting the latent CTC spread in the HIV-1 infection model will lead to an underestimation of the basic reproduction number. Consequently, the designed drug therapies will not be accurate or sufficient to eradicate the viruses from the body. These findings may help to improve the understanding of the dynamics of HIV-1 within a host. [ABSTRACT FROM AUTHOR]

In this paper, a reaction–diffusion–chemotaxis HIV-1 model with a cytotoxic T lymphocyte (CTL) immune response and general sensitivity is investigated. We first prove the global classical solvability and L ∞ -boundedness for the considered model in a bounded domain with arbitrary spatial dimensions, which extends the previous existing results. Then, we apply the global existence result to the case with a linear proliferation immune response and an incidence rate. We study the spatiotemporal dynamics about the three types of spatially homogeneous steady states: infection-free steady state S 0 , CTL-inactivated infection steady state S 1 , and CTL-activated infection steady state S ∗. Our analyses indicate that S 0 is globally asymptotically stable if the basic reproduction number R 0 is less than 1; if R 0 is between 1 and a threshold, then S 1 is globally asymptotically stable. However, if R 0 is larger than the threshold, then the chemoattraction and chemorepulsion can destabilize S ∗ , and thus, a spatiotemporal pattern forms as the chemotactic sensitivity crosses certain critical values. We obtain two kinds of important patterns, which are induced by chemotaxis: stationary Turing pattern and irregular oscillatory pattern. We also find that different chemotactic response functions can affect system's dynamics. Based on some empirical parameter values, numerical simulations are given to illustrate the effectiveness of the theoretical predications. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors of a multiple delayed HIV-1 infection model which describes the interactions of humoral, cytotoxic T lymphocyte (CTL) immune responses, and two modes of transmission that are the classical virus-to-cell infection and the direct cell-to-cell transmission are investigated. The model incorporates three delays, including the delays of cell infection, virus production and activation of immune response. We first prove the well-posedness of the model, and calculate the biological existence of equilibria and the reproduction numbers, which contain virus infection, humoral immune response, CTL immune response, CTL immune competition, and humoral immune competition. Further, the threshold conditions for the local and global stability of the equilibria for infection-free, immune-free, antibody response, CTL response, and interior are established by utilizing linearization method and the Lyapunov functionals. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is investigated by using the bifurcation theory. Numerical simulations are carried out to illustrate the theoretical results and reveal the effects of some key parameters on viral dynamics. [ABSTRACT FROM AUTHOR]

In the course of reverse transcription, drug-sensitive strain can mutate to a drug-resistant one. Cell-to-cell transmission is proved to be more efficient than virus-to-cell infection. The population of Cytotoxic T Lymphocytes (CTLs) can be divided into CTL precursors and CTL effectors. Naive CTL precursors are those that never have contacted antigen, circulating around the body. Once the host is infected, CTL precursors (CTLp) begin to proliferate and differentiate into CTL effectors (CTLe), which have antiviral activity. In this paper, we study an HIV model with drug-sensitive and drug-resistant mixed strains, CTLp and CTLe, both viral and cellular infections. The basic reproduction ratios for each strain are derived and the stability of each feasible equilibrium is analyzed by using Routh–Hurwitz criteria. The periodic solutions may occur near the equilibrium with CTL immune response via Hopf bifurcation. By using normal form theory, we find more information about the limit cycles, such as the amplitude, phase and stability. [ABSTRACT FROM AUTHOR]

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 4 + T 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 4 + T 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 4 + T cells for some fixed immune impairment gradually decreases with increasing noise intensity and follows the power law. [ABSTRACT FROM AUTHOR]

Individuals infected by human immunodeficiency virus (HIV) are under oxidative stress due to the imbalance between reactive oxygen species (ROS) production and elimination. This paper presents a mathematical model with the cytotoxic T lymphocytes (CTL) immune response to examine the role of ROS in the dynamics of HIV infection. We classify the equilibria of the model and study the stability of these equilibria. Numerical simulations show that incorporating ROS and CTL immune response into the model leads to very rich dynamics, including bistable phenomena and periodic solutions. Although the current antiretroviral therapy can suppress viral load to the undetectable level, it cannot eradicate the virus. A high level of ROS may be a factor for HIV persistence in patients despite suppressive therapy. These results suggest that oxidative damage and anti-oxidant therapy should be considered in the study of HIV infection and treatment. [ABSTRACT FROM AUTHOR]

Human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that infect the susceptible CD 4 + T cells. It is known that HIV and HTLV-I have in common a way of transmission through direct contact with certain body fluids related to infected individuals. Therefore, it is not surprising that a mono-infected person with one of these viruses can be co-infected with the other virus. In the literature, a great number of mathematical models has been presented to describe the within-host dynamics of HIV or HTLV-I mono-infection. However, the within-host dynamics of HIV/HTLV-I co-infection has not been modeled. In this paper, we develop a new within-host HIV/HTLV-I co-infection model. The model includes the impact of Cytotoxic T lymphocytes (CTLs) immune response, which is important to control the progression of viral co-infection. The model describes the interaction between susceptible CD 4 + T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. We first show the nonnegativity and boundedness of the model's solutions and then we calculate all possible equilibria. We derive the threshold parameters which govern the existence and stability of all equilibria of the model. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle's invariance principle. We have presented numerical simulations to illustrate the effectiveness of our main results. In addition, we discuss the effect of HTLV-I infection on the HIV-infected patients and vice versa. [ABSTRACT FROM AUTHOR]

In the literature, several mathematical models have been formulated and developed to describe the within-host dynamics of either human immunodeficiency virus (HIV) or human T-lymphotropic virus type I (HTLV-I) monoinfections. In this paper, we formulate and analyze a novel within-host dynamics model of HTLV-HIV coinfection taking into consideration the response of cytotoxic T lymphocytes (CTLs). The uninfected CD 4 + T cells can be infected via HIV by two mechanisms, free-to-cell and infected-to-cell. On the other hand, the HTLV-I has two modes for transmission, (i) horizontal, via direct infected-to-cell touch, and (ii) vertical, by mitotic division of active HTLV-infected cells. It is well known that the intracellular time delays play an important role in within-host virus dynamics. In this work, we consider six types of distributed-time delays. We investigate the fundamental properties of solutions. Then, we calculate the steady states of the model in terms of threshold parameters. Moreover, we study the global stability of the steady states by using the Lyapunov method. We conduct numerical simulations to illustrate and support our theoretical results. In addition, we discuss the effect of multiple time delays on stability of the steady states of the system. [ABSTRACT FROM AUTHOR]

In this paper, a periodic stochastic human immunodeficiency virus (HIV) model with distributed delay and cytotoxic T lymphocytes (CTL) immune response is investigated. First, by It ô's formula, we show that the solution with any positive initial value is global and positive. Then, by the stochastic comparison theorem, we obtain the sufficient conditions guaranteeing the existence and global attractivity of infection‐free periodic solution. Furthermore, we discuss the existence of the infective periodic solution by Has'minskii theory. Finally, numerical examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes a CTL-mediated HIV infection model. The model describes the interaction between healthy CD4+T cells, silent infected cells, active infected cells, free HIV particles, and cytotoxic T lymphocytes (CTLs). The healthy CD4+T cells can be infected when contacted by one of the following: (i) free HIV particles, (ii) silent infected cells, and (iii) active infected cells. The incidence rates of the healthy CD4+T cells with free HIV particles, silent infected cells, and active infected cells are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the incidence between the silent infected cells and healthy CD4+T cells. We first show that the model is well posed. The proposed model has three equilibria and their existence is governed by derived two threshold parameters: the basic HIV reproduction number ℜ 0 and the HIV-specific CTL-mediated immunity reproduction number ℜ 1 . Under a set of conditions on the general functions and the parameters ℜ 0 and ℜ 1 , we have proven the global asymptotic stability of all equilibria by using Lyapunov method. We have illustrated the theoretical results via numerical simulations. We have studied the effect of cell-to-cell (CTC) transmission on the dynamical behavior of the system. We have shown that inclusion of CTC transmission decreases the concentration of healthy CD4+T cells and increases the concentrations of infected cells and free HIV particles. [ABSTRACT FROM AUTHOR]

In this paper, we incorporate immune systems into an HIV model, which considers both logistic target-cell proliferation and viral cell-to-cell transmission. We study the dynamics of this model including the existence and stability of equilibria. Based on the existence of equilibria, we focus on the backward bifurcation and forward bifurcation. Considering the stability of equilibria, Hopf bifurcation is discussed by identifying the basic reproduction number R 0 as bifurcation parameter. The direction and stability of Hopf bifurcation are investigated by computing the first Lyapunov exponent. Specially, the effects of immune response on the basic reproduction number R 0 and viral dynamics are addressed by deriving the sensitivity analysis. As a result, we find that the removal rate of infected cells by cytotoxic T lymphocytes (CTLs), γ 1 , is the predominant factor of R 0 . However, we conclude from numerical results that it is unfeasible to decrease R 0 by increasing the value of γ 1 constantly. Numerical simulation is also presented to demonstrate the applicability of the theoretical predictions. These dynamics are investigated by the proposed model to point out the importance and complexity of immune responses in fighting HIV replication. [ABSTRACT FROM AUTHOR]

The dynamics of a model describing the human immunodeficiency virus (HIV) infection with cytotoxic T-lymphocyte (CTL), antibodies and two saturated rates is investigated and studied in this paper. The model includes five nonlinear differential equations describing the evolution of uninfected cells, infected ones, free HIV viruses, CTL immune response and antibodies. This model includes also two treatments that represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence, positivity and boundedness of solutions are given. Existence of the optimal control pair is established and the Pontryagin's maximum principle is used to find an optimal treatment strategy that maximizes the number of uninfected CD4+ T cells as well as cytotoxic T-lymphocyte and antibody immune responses. Finally, the optimality system is derived and solved numerically. Results show that administrating good therapy maximizes the amount of healthy CD4+ T cells and deceases considerably the viral load and the infected cells. [ABSTRACT FROM AUTHOR]

In this paper, a delayed human immunodeficiency virus (HIV) model with apoptosis of cells has been studied. Both immunological and intracellular delay have been incorporated to make the model more relevant. Firstly, the model has been investigated using local stability analysis. Next, the global stability analysis of steady states has been performed. The stability switch criteria taking the delay as the bifurcating parameter, leading to Hopf bifurcation has been studied. The transition of the system from order to chaos has been explored, and the analytical results have been verified by numerical simulations. The results thus can be used to describe the extensive dynamics exhibited by the model introduced in this article. The effects of apoptosis on viral load has been studied in the model numerically. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study the threshold dynamics of an HIV-1 viral infection model with cell-mediated immune responses and direct cell-to-cell transmission mechanism. The model demonstrates global threshold dynamics with respect to the reproductive numbers for viral infection ℜ 0 and for CTL immune response ℜ 1 . The proofs of main results come from suitable uses of analyzing the characteristic equation and constructing Lyapunov functionals. Specifically, if ℜ 0 < 1, the infection-free equilibrium E 0 is locally and globally asymptotically stable, and the viruses are cleared. If ℜ 1 < 1 < ℜ 0 , the CTL-inactivated equilibrium E 1 is locally and globally asymptotically stable, and the infection becomes chronic but without persistent CTLs response. If ℜ 1 > 1, the CTL-activated equilibrium E 2 is locally and globally asymptotically stable, and the infection is chronic with persistent CTLs response. Numerical simulations are performed to support our results. [ABSTRACT FROM AUTHOR]

Recently, hematopoietic stem cell (HSC) based therapy is being discussed as a possible treatment for HIV infection. The main advantage of this approach is that it limits the immune impairing effect of infection by introducing an independent influx of antigen-specific cytotoxic T lymphocytes (CTL). In this paper, we present a mathematical approach to predict the dynamics of HSC based therapy. We use a modification of a basic mathematical model for virus induced impairment of help to study how virus – immune system dynamics can be influenced by a single injection of CD8+ T lymphocytes derived from hematopoietic stem cells. Our mathematical and numerical results indicate that a single, large enough dose of genetically derived CTL may lead to restoration of the cellular immune response and result in long-term control of infection. [ABSTRACT FROM AUTHOR]

During early human immunodeficiency virus (HIV) infection multiple CD8+ T cell responses are elicited almost simultaneously. These responses exert strong selective pressures on different parts of HIV’s genome, and select for mutations that escape recognition and are thus beneficial to the virus. Some studies reveal that the later these escape mutations emerge, the more slowly they go to fixation. This pattern of escape rate decrease(ERD) can arise by distinct mechanisms. In particular, in large populations with high beneficial mutation rates interference among different escape strains –an effect that can emerge in evolution with asexual reproduction and results in delayed fixation times of beneficial mutations compared to sexual reproduction– could significantly impact the escape rates of mutations. In this paper, we investigated how interference between these concurrent escape mutations affects their escape rates in systems with multiple epitopes, and whether it could be a source of the ERD pattern. To address these issues, we developed a multilocus Wright-Fisher model of HIV dynamics with selection, mutation and recombination, serving as a null-model for interference. We also derived an interference-free null model assuming initial neutral evolution before immune response elicitation. We found that interference between several equally selectively advantageous mutations can generate the observed ERD pattern. We also found that the number of loci, as well as recombination rates substantially affect ERD. These effects can be explained by the underexponential decline of escape rates over time. Lastly, we found that the observed ERD pattern in HIV infected individuals is consistent with both independent, interference-free mutations as well as interference effects. Our results confirm that interference effects should be considered when analyzing HIV escape mutations. The challenge in estimating escape rates and mutation-associated selective coefficients posed by interference effects cannot simply be overcome by improved sampling frequencies or sizes. This problem is a consequence of the fundamental shortcomings of current estimation techniques under interference regimes. Hence, accounting for the stochastic nature of competition between mutations demands novel estimation methodologies based on the analysis of HIV strains, rather than mutation frequencies. [ABSTRACT FROM AUTHOR]

• A new HIV/HTLV-I co-infection model with latency and Cytotoxic T lymphocytes (CTLs) immune response is developed and rigorously analyzed. • Both silent and active infected cells have been considered. • Well-possedness of the model and existence of equilibria are established. • Global stability of the equilibria are established by means of Lyapunov functions. • We have presented numerical simulations to illustrate the effectiveness of our main results. Human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that attack the immune cells and impair their functions. Both HIV and HTLV-I can be transmitted between individuals through direct contact with certain body fluids from infected individuals. Therefore, a person can be co-infected with both viruses. HIV causes acquired immunodeficiency syndrome, while HTLV-I is the causative agent for adult T-cell leukemia and HTLV-I-associated myelopathy/tropical spastic paraparesis. Several mathematical models have been developed in the literature to describe the within-host dynamics of HIV and HTLV-I mono-infections. However, modeling a within-host dynamics of HIV/HTLV-I co-infection has not been involved. In the present paper, we are concerned to formulate and analyze a new HIV/HTLV co-infection model under the effect of Cytotoxic T lymphocytes (CTLs) immune response. The model describes the interaction between susceptible CD4+T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. The HIV can spread by two routes of transmission, virus-to-cell and cell-to-cell. On the other side, HTLV-I has two modes of transmission, (i) horizontal transmission via direct cell-to-cell contact, and (ii) vertical transmission through mitotic division of Tax-expressing HTLV-infected cells. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We define a set of threshold parameters which govern the existence and stability of all equilibria of the model. We explore the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle's invariance principle. We have presented numerical simulations to justify the applicability and effectiveness of the theoretical results. In addition, we evaluate the effect of HTLV-I infection on the HIV dynamics and vice versa. [ABSTRACT FROM AUTHOR]

Human T-lymphotropic virus type I (HTLV-I) and human immunodeficiency virus (HIV) are two famous retroviruses that share similarities in their genomic organization, and differ in their life cycle as well. It is known that HTLV-I and HIV have in common a way of transmission via direct contact with certain body fluids related to infected patients. Thus, it is not surprising that a single-infected person with one of these viruses can be dually infected with the other virus. In the literature, many researchers have devoted significant efforts for modeling and analysis of HTLV or HIV single infection. However, the dynamics of HTLV/HIV dual infection has not been formulated. In the present paper, we formulate an HTLV/HIV dual infection model. The model includes the impact of the Cytotoxic T lymphocyte (CTLs) immune response, which is important to control the dual infection. The model describes the interaction between uninfected CD 4 + T cells, HIV-infected cells, HTLV-infected cells, free HIV particles, HIV-specific CTLs, and HTLV-specific CTLs. We establish that the solutions of the model are non-negative and bounded. We calculate all steady states of the model and deduce the threshold parameters which determine the existence and stability of the steady states. We prove the global asymptotic stability of all steady states by utilizing the Lyapunov function and Lyapunov–LaSalle asymptotic stability theorem. We solve the system numerically to illustrate the our main results. In addition, we compared between the dynamics of single and dual infections. [ABSTRACT FROM AUTHOR]