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This paper studies the stability of a mathematical model for within-host Chikungunya virus (CHIKV) infection. The model incorporates (i) two types of infected monocytes, latently infected monocytes which do not generate CHIKV until they have been activated and actively infected monocytes, (ii) antibody immune response, and (iii) saturated incidence rate. We derive a biological threshold number R0. Using the method of Lyapunov function, we established the global stability of the steady states of the model. We have proven that, when R0 ≤ 1, then Q0 is globally asymptotically stable and when R0 > 1, the endemic equilibrium Q1 is globally asymptotically stable. The theoretical results have been supported by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies the stability of a mathematical model for within-host Chikungunya virus (CHIKV) infection. The model incorporates (i) two types of infected monocytes, latently infected monocytes which do not generate CHIKV until they have been activated and actively infected monocytes, (ii) antibody immune response, and (iii) saturated incidence rate. We derive a biological threshold number R0. Using the method of Lyapunov function, we established the global stability of the steady states of the model. We have proven that, when R0 ≤ 1, then Q0 is globally asymptotically stable and when R0 > 1, the endemic equilibrium Q1 is globally asymptotically stable. The theoretical results have been supported by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability analysis of a virus dynamics model with CTL immune response and with both cell-to-cell and virus-to-cell transmissions. The model contains three types of distributed time delays. The existence and global stability of all steady states of the model are determined by two parameters, the basic reproduction number (R0) and the CTL immune response activation number (R1). By using suitable Lyapunov functionals, we show that if R0 ≤ 1, then the infection-free steady state E0 is globally asymptotically stable; if R1 ≤ 1 < R0, then the CTL-inactivated infection steady state E1 is globally asymptotically stable; if R1 > 1, then the CTL-activated infection steady state E2 is globally asymptotically stable. Numerical simulations are conducted to support the theoretical results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the effect of the cytotoxic T lymphocytes (CTLs) on an HIV-1 dynamics. The model considers that the virus infects the macrophages in addition to the CD4+ T cells. The role of the CTLs is to kill the infected macrophages and CD4+ T cells. The time delay which accounts the time of infection and the time of producing new active HIV-1 is modeled. The HIV-1 dynamics is modeled as a 6-dimensional nonlinear delay differential equations. The incidence rate of infection and killer rate of infected cells are given by general nonlinear functions. We study the qualitative behavior of the system. The global stability analysis has been established using Lyapunov method and LaSalle invariance principle. We present an example and perform numerical simulations to emphasize our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze an HIV dynamics model. The model can be seen as a generalization of many HIV dynamics models presented in the literature since it incorporates (i) two classes of target cells, CD4+ T cells and macrophages, (ii) two types of infected cells, short-lived infected cells and the long-lived chronically infected cells, (iii) intracellular discrete delays, (iv) reverse transcriptase inhibitors (RTIs) drugs with different drug efficacies on CD4+T cells and macrophages. The incidence rate of infection is represented by a general function. A bifurcation parameter, known as the basic reproduction number, R0 is derived. We established a set of conditions on the general function which are sufficient to determine the global dynamics of the model. Using Lyapunov functionals and LaSalle's invariance principle, the global asymptotic stability of the two equilibria of the model is obtained. An example is presented and some numerical simulations are conducted in order to illustrate the dynamical behavior. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamical behavior of a nonlinear model for viral infection with Cytotoxic T Lymphocyte (CTL) immune response. The model is a generalization of several models presented in the literature by considering more general functions for the: (i) intrinsic growth rate of uninfected cells; (ii) incidence rate of infection; (iii) natural death rate of infected cells; (iv) rate at which the infected cells are killed by CTL cells; (v) production and removal rates of viruses; (vi) activation and natural death rates of CTLs. We derive two threshold parameters R0 (the basic infection reproduction number) and R1 (the CTL immune response activation number) and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the model. By using suitable Lyapunov functions and LaSalle's invariance principle, we prove the global asymptotic stability of all equilibria of the model. [ABSTRACT FROM AUTHOR]

In this paper, we study the global stability of a mathematical model that describes the virus dynamics under the e¤ect of antibody immune response. The model is a modi?cation of some of the existing virus dynamics models by considering the latently infected cells and nonlinear incidence rate for virus infections. We show that the global dynamics of the model is completely determined by two threshold values R0, the corresponding reproductive number of viral infection and R1, the corresponding reproductive number of antibody immune response, respectively. Using Lyapunov method, we have proven that, if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable (GAS), if R1 ≤ 1 < R0, then the infected steady state without antibody immune response is GAS, and if R1 > 1, then the infected steady state with antibody immune response is GAS. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a viral infection model with humoral immunity. The incidence rate is given by Hill type infection rate. We have derived two threshold parameters, R0 and R1 which completely determined the global properties of the model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have established the global asymptotic stability of all steady states of the model. We have proven that, if R0 ⩽ 1, then the infection-free steady state is globally asymptotically stable (GAS), if R1 ⩽ 1 < R0, then the chronic-infection steady state without humoral immune response is GAS, and if R1 > 1, then the chronic-infection steady state with humoral immune response is GAS. [ABSTRACT FROM AUTHOR]

In this paper, we study the global dynamics of a viral infection model with antibody immune response. The incidence rate is given by a general function of the population of the uninfected target cells, infected cells and free viruses. We have established a set of conditions on the general incidence rate function and determined two threshold parameters R0 (the basic infection reproduction number) and R1 (the antibody immune response activation number) which are su¢ cient to determine the global behavior of the model. The global asymptotic stability of the equilibria of the model has been proven by using direct Lyapunov method and applying LaSalle's invariance principle. [ABSTRACT FROM AUTHOR]

In this paper, we study the global properties of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model contains two types of intracellular discrete time delays to describe the time required for viral contacting an uninfected target cell and viral emission. We have established a set of conditions on the general incidence rate function and determined two threshold parameters R0 (the basic infection reproduction number) and R1 (the antibody immune response activation number) which are sufficient to determine the global behavior of the model. The global asymptotic stability of the equilibria of the model has been proven by using direct Lyapunov method and applying LaSalle's invariance principle. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a viral infection model with humoral immunity. The incidence rate is given by Hill type infection rate. We have derived two threshold parameters, R0 and R1 which completely determined the global properties of the model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have established the global asymptotic stability of all steady states of the model. We have proven that, if R0 ≤ 1, then the infection-free steady state is globally asymptotically stable (GAS), if R1 ≤ 1 < R0, then the chronic-infection steady state without humoral immune response is GAS, and if R1 > 1, then the chronic-infection steady state with humoral immune response is GAS. [ABSTRACT FROM AUTHOR]

In this paper, we study the global properties of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model contains two types of intracellular discrete time delays to describe the time required for viral contacting an uninfected target cell and viral emission. We have established a set of conditions on the general incidence rate function and determined two threshold parameters R0 (the basic infection reproduction number) and R1 (the antibody immune response activation number) which are sufficient to determine the global behavior of the model. The global asymptotic stability of the equilibria of the model has been proven by using direct Lyapunov method and applying LaSalle's invariance principle. [ABSTRACT FROM AUTHOR]