Stability of a Discrete-Time Pathogen Infection Model with Adaptive Immune Response

This paper studies the global stability of a discrete-time pathogen dynamic model with both cell-mediated and antibody immune responses. Both latently and actively infected cells are incorporated into the model. We discretize the continuous-time model by using the nonstandard finite difference (NSFD) method. We establish that NSFD preserves the nonnegativity and boundedness of the solutions of the model. We derive four threshold parameters which govern the existence and stability of the steady states. We establish by using the Lyapunov method, the global stability of the five steady states of the model. We illustrate our theoretical results by using numerical simulations