Global stability of discrete virus dynamics models with humoural immunity and latency

Abstract

This paper studies the global stability of discrete-time viral infection models with humoural immunity. We consider both latently and actively infected cells. We study also a model with general production and clearance rates of all compartments as well as general incidence rate of infection. We use nonstandard finite difference method to discretize the continuous-time models. The positivity and boundedness of solutions of the discrete models are established. We establish by using Lyapunov method, the global stability of equilibria in terms of the basic reproduction number (Formula presented.) and the humoural immune response activation number (Formula presented.). The results signify that the infection dies out if (Formula presented.). Moreover, the infection persists with inactive immune response if (Formula presented.) and with active immune response if (Formula presented.). We illustrate our theoretical results by using numerical simulations.