Global stability of a delayed adaptive immunity viral infection with two routes of infection and multi-stages of infected cells

Abstract

This paper proposes and analyzes a viral infection model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, B cells and CTL cells. We consider both virus-to-cell and cell-to-cell transmissions and n+1 intracellular distributed time delays. The incidence rate of infection as well as the generation and removal rates of all compartments are described by general nonlinear functions. We derive five threshold parameters which determine the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established which is sufficient to investigate the global stability of the five equilibria of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle’s invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions. Effect of antiviral treatment, time delays and cellular infection on the dynamical behavior of the system is addressed.