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This paper investigates an adaptive immunity HIV infection model with three types of distributed time delays. The model describes the interaction between healthy CD4+T cells, silent infected cells, active infected cells, free HIV particles, Cytotoxic T lymphocytes (CTLs) and antibodies. The healthy CD4+T cells can be infected when they contacted by free HIV particles or silent infected cells or 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 the virus and cells are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the infection due to the incidence between the silent infected cells and healthy CD4+T cells. We show that the model is well posed and it has five equilibria and their existence are governed by five threshold parameters. Under a set of conditions on the general functions and the threshold parameters, 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 and time delays on the dynamical behavior of the system. We have shown that the inclusion of time delay can significantly increase the concentration of the healthy CD4+ T cells and reduce the concentrations of the infected cells and free HIV particles. While the inclusion of CTC transmission decreases the concentration of the healthy CD4+ T cells and increases the concentrations of the infected cells and free HIV particles.

This paper studies an (n + 4)-dimensional nonlinear viral infection model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, CTL cells and B cells. Both viral and cellular infections have been incorporated into the model. The well-posedness of the model is justified. The model admits five equilibria which are determined by five threshold parameters. The global stability of each equilibrium is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations.

Abstract This paper studies the global dynamics of a general diffusive hepatitis B virus (HBV) infection model. The model includes both enveloped viruses and DNA containing capsids. Two immune responses are recruited to attack the virus and infected hepatocytes. These are the cytotoxic T-lymphocytes (CTL) which kill the infected liver cells, and B cells which send antibodies to attack the virus. The non-negativity and boundedness of the solutions are discussed. The existence of spatially homogeneous equilibrium points is examined. The global stability of all possible equilibrium points is proved by choosing suitable Lyapunov functionals. Some numerical simulations are performed to enhance the theoretical results and present the behavior of solutions in space and time.

The objective of this paper is to investigate a mathematical model describing the infection of hepatitis B virus (HBV) in intrahepatic and extrahepatic tissues. Additionally, the model includes the effect of the cytotoxic T cell (CTL) immunity, which is described by a linear activation rate by infected cells. The positivity and boundedness of solutions for non-negative initial data are proven, which is consistent with the biological studies. The local stability of the equilibrium is established. In addition to this, the global stability of the disease-free equilibrium and the endemic equilibrium is fulfilled by using appropriate Lyapanov functions. Finally, numerical simulations are performed to support our theoretical findings. It has been revealed that the fractional-order derivatives have no influence on the stability but only on the speed of convergence toward the equilibria.