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

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 R₀ and the humoral immune response activation number R₁ 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 R₀ ≤ 1, then the infection-free equilibrium is globally asymptotically stable (GAS), if R₁ ≤ 1 < R₀, then the chronic-infection equilibrium without humoral immune response is GAS, and if R₁ > 1, then the chronic-infection equilibrium with humoral immune response is globally asymptotically stable. These results are further illustrated by numerical simulations.