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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]

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 investigate the global dynamics in an HIV virus infection model with saturated incidence. The model includes two viral strains, one is wild-type (i.e. drug sensitive) and another is drug-resistant. The wild-type strain can mutate and become drug-resistant during the process of reverse transcription. The nonnegativity and boundedness of solutions are established. The basic reproduction numbers of two strains and the existence of equilibria are also obtained. The threshold criteria on the local and global stability of equilibria and the uniform persistence of the model are established by using the linearization method, constructing suitable Lyapunov functions and the theory of persistence in dynamical systems. Moreover, the mathematical analysis and numerical examples show that model may have a positive equilibrium which is globally asymptotically stable. [ABSTRACT FROM AUTHOR]

In this paper, we propose a within-host HIV-1 epidemic model with cell-to-virus and cell-to-cell transmission. By mathematical analysis, we obtain the basic reproduction number $\mathcal {R}_{0}$ , which determines the viral persistence and the basic reproduction number $\mathcal {R}_{0}^{\mathrm{cc}}$ with respect to cell-to-cell transmission which is not strong enough, i.e., it is less than 1. If the basic reproduction number is less than 1, then the viral-free steady state $E_{0}$ is globally asymptotically stable, which is proved by fluctuation lemma and comparison method; if $\mathcal {R}_{0}>1$ is greater than 1, the endemic steady state $E^{*}$ is globally asymptotically stable, which is proved by constructing the Lyapunov functional. Antiretoviral therapy is implemented to suppress the viral replication. Protease inhibitors for cell-to-cell transmission play an important role in controlling cell-to-cell infection. Under some circumstances, the effects of the cell-to-cell infection process are more sensitive than those of cell-to-virus transmission. [ABSTRACT FROM AUTHOR]

In this paper, we construct an HIV infection model which includes latent infection, logistic growth for healthy CD4 T-cells, and antiretroviral therapy. We obtain the global asymptotic stability of the uninfected equilibrium by constructing a Lyapunov function, and we give a sufficient condition for the local asymptotic stability of the infected equilibrium. We also use the latin hypercube sampling technique to identify the key parameters in determining the stability of the infected equilibrium. By numerical simulations, we observe that the model without logistic growth would underestimate the number of infectious virions, while the model without latent infection would overestimate the number of infectious virions. [ABSTRACT FROM AUTHOR]

The main goal of this article is to exhibit the importance of awareness programs and travel-blocking operations, in the prevention of HIV/AIDS outbreaks, based on a multi-domains SIR epidemic model. The model devised describes the spatial-temporal spread of HIV/AIDS, in p neighboring domains, taking into account the epidemiological diversity of their populations. For a first case of the study, we focus on discussing the benefits of awareness campaigns that aim to raise public consciousness among susceptible people, about the danger of HIV/AIDS. Thus, for the reason that intra-domains interventions are not always sufficient to prevent people belonging to a domain (neighborhood, town or city for example), from a rapid expansion of HIV/AIDS, we propose the travel-blocking strategy, as a second approach presenting inter-domains interventions that health-policy makers could follow, by restricting the number of suspicious people that can participate in spreading HIV/AIDS via travel, coming from domains at high-risk of infection to enter domains with lower risk. The optimal control theory, based on Pontryagin's maximum principle, is applied twice in this paper, for the characterizations of the awareness and travel-blocking controls. The numerical results associated to the multi-points boundary value problems are obtained based on the Forward-Backward Sweep Method combined with progressive-regressive Runge-Kutta fourth-order schemes. [ABSTRACT FROM AUTHOR]

In this paper, local stability and Hopf bifurcation of a delayed heroin model with saturated treatment function are discussed. First of all, sufficient conditions for local stability and existence of Hopf bifurcation are obtained by regarding the time delay as a bifurcation parameter and analyzing the distribution of the roots of the associated characteristic equation. Directly afterward, properties of the Hopf bifurcation, such as the direction and stability, are investigated with the aid of the normal form theory and the manifold center theorem. Finally, numerical simulations are presented to justify the obtained theoretical results, and some suggestions are offered for controlling heroin abuse in populations. [ABSTRACT FROM AUTHOR]

This paper studies the global stability of two discrete-time HIV infection models. The models integrate (i) latently infected cells, (ii) long-lived chronically infected cells and (iii) short-lived infected cells. The second model generalizes the first one by assuming that the incidence rate of infection as well as the production and removal rates of the HIV particles and cells are modeled by general nonlinear functions. We discretize the continuous-time models by using a nonstandard finite difference scheme. The positivity and boundedness of solutions are established. The basic reproduction number is derived. By using the Lyapunov method, we prove the global stability of the models. Numerical simulations are presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the qualitative behavior of HIV dynamics models with immune impairment. The HIV particles infect both CD4+ T cells and macrophages. Both latently and actively infected cells are incorporated into the models. The models consider multiple discrete or distributed delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The existence and global stability of the steady states are determined by the basic reproduction number. The global stability analysis of the steady states is performed using Lyapunov method. We solve the system of delay differential equations numerically to support the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a dynamic compartmental model is constructed for the transmission of HIV/AIDS receiving drug treatment and knowledge from effective awareness programs through media. Using stability theory of differential equations the model is analyzed qualitatively. The equilibrium points in the local and global stability proof are found to be stable under certain conditions. Further, we use Pontryagin’s Minimum Principle in the time-dependent constant control case to derive necessary conditions for the optimal control of the disease. Sensitivity analysis is also performed to check the robustness of the model with respect to small changes in parametric values of the system. In order to predict the long term dynamics of the disease, projections are made. These studies reveal that HIV incidence could be substantially reduced by improving the test-and-treat strategy and implication of media awareness.

Novel switched HIV/AIDS (human immunodeficiency virus/acquired immune deficiency syndrome) epidemic models with distributed time delay and bounded noise and Gaussian white noise are developed and investigated using stochastic Itô's lemma and the Lyapunov–Razumikhin method. New criteria depending on these factors are established to confirm that the disease-free equilibrium of the model is stochastically asymptotically stable as the threshold parameter is less than unity, which implies that the disease eventually disappears theoretically. Otherwise, the disease persists weakly. Further, the main results show that the threshold values are related to two types of noise and time delay. Pulse control strategies are then applied to two types of the infected population, the susceptible population, and the infected population, respectively. More precisely, the effects of each control strategy on the stochastic solution of the model are evaluated to justify the relation between control parameters and threshold parameters of the model. In comparison with the basic reproduction number of the model with pulse control, it is easily found that the main results in these references are improved and extended. Finally, four examples are presented to support the main results, and one future research direction is suggested. [ABSTRACT FROM AUTHOR]

In this article, we study a fractional order HIV/AIDS infection model with ABC-fractional derivative. The model is based on four classes of a population. The study includes the existence and uniqueness of solution, the stability analysis, and simulations. We utilize the fixed point technique for the existence and uniqueness analysis. The stability of the fractional order model is derived with the help of existing literature for the Hyers–Ulam stability. For the numerical computations, the Lagrange interpolation is utilized, and the simulations are obtained for specific parameters. The results are closer to the classical results for different orders. [ABSTRACT FROM AUTHOR]

Research reveals that most HIV infections come from undiagnosed people and untreated people, but principally from unaware people. Human awareness results in the reduction of susceptibility to infection, naturally, in the epidemiological study this factor should be included. Researchers have produced a wealth of information about the disease, including a number of critical tools and interventions to diagnose, prevent and treat HIV. Broadcast media have tremendous reach and influence, particularly with young people, so in this study, we incorporate the influence of media and investigate the effect of awareness program in disease outbreaks. We divided the whole susceptible and infected populations into two sub-classes: 'unaware class' and 'aware class'. A detailed mathematical analysis has been carried out and numerical simulations have been performed to show the role of some of the important model parameters. [ABSTRACT FROM AUTHOR]

In this manuscript, we investigate a nonlinear delayed model to study the dynamics of human-immunodeficiency-virus in the population. For analysis, we find the equilibria of a susceptible–infectious–immune system with a delay term. The well-established tools such as the Routh–Hurwitz criterion, Volterra–Lyapunov function, and Lasalle invariance principle are presented to investigate the stability of the model. The reproduction number and sensitivity of parameters are investigated. If the delay tactics are decreased, then the disease is endemic. On the other hand, if the delay tactics are increased then the disease is controlled in the population. The effect of the delay tactics with subpopulations is investigated. More precisely, all parameters are dependent on delay terms. In the end, to give the strength to a theoretical analysis of the model, a computer simulation is presented. [ABSTRACT FROM AUTHOR]

In this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana–Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard–Lindelöf has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane R + 3 is a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic. [ABSTRACT FROM AUTHOR]