Global stability analysis of humoral immunity virus dynamics model including latently infected cells

Abstract

In this paper, we propose and analyse a virus dynamics model with humoral immune response including latently infected cells. The incidence rate is given by Beddington–DeAngelis functional response. We have derived two threshold parameters, the basic infection reproduction number and the humoral immune response activation number which completely determined the basic and global properties of the virus dynamics model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have proven that if , then the infection-free equilibrium is globally asymptotically stable (GAS), if , then the chronic-infection equilibrium without humoral immune response is GAS, and if , then the chronic-infection equilibrium with humoral immune response is globally asymptotically stable. These results are further illustrated by numerical simulations.