GLOBAL STABILITY OF A GENERAL VIRUS DYNAMICS MODEL WITH MULTI-STAGED INFECTED PROGRESSION AND HUMORAL IMMUNITY

Abstract

In this paper, we propose an [Formula: see text]-dimensional nonlinear virus dynamics model that describes the interactions of the virus, uninfected target cells, [Formula: see text]-stages of infected cells and B cells. We assume that the incidence rate of infection, the generation and removal rates of all compartments are given by general nonlinear functions. We derive two threshold parameters, the basic reproduction number, [Formula: see text] and the humoral immunity number, [Formula: see text] and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the model. Utilizing Lyapunov functions and LaSalle’s invariance principle, the global asymptotic stability of all steady states of the model is proved. Numerical simulations are conducted for specific forms of the general functions in order to illustrate the dynamical behavior.