Stability of Virus Infection Models with Antibodies and Chronically Infected Cells

Abstract

Two virus infection models with antibody immune response and chronically infected cells are proposed and analyzed. Bilinear incidence rate is considered in the first model, while the incidence rate is given by a saturated functional response in the second one. One main feature of these models is that it includes both short-lived infected cells and chronically infected cells. The chronically infected cells produce much smaller amounts of virus than the short-lived infected cells and die at a much slower rate. Our mathematical analysis establishes that the global dynamics of the two models are determined by two threshold parameters $R_0$ and $R_1$. By constructing Lyapunov functions and using LaSalle's invariance principle, we have established the global asymptotic stability of all steady states of the models. We have proven that, the uninfected steady state is globally asymptotically stable (GAS) if , the infected steady state without antibody immune response exists and it is GAS if , and the infected steady state with antibody immune response exists and it is GAS if $R_1>1$. We check our theorems with numerical simulation in the end.