Global Properties of General Viral Infection Models with Humoral Immune Response

Abstract

In this paper, we study the global properties of two general models for viral infection with humoral immune response. The incidence rate of infection, the removal rate of infected cells, the production and neutralize rates of viruses and the activation and removal rates of B cells are given by more general nonlinear functions. The second model generalizes the first one by taking into account the latently infected cells. We assume that the latent-to-active conversion rate is also given by a more general nonlinear function. For both models, we derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. By using suitable Lyapunov functions and LaSalle’s invariance principle, we prove the global asymptotic stability of all equilibria of the models.