Global stability of discrete pathogen infection model with humoral immunity and cell-to-cell transmission

Abstract

Abstract This paper investigates the global stability of discrete-time pathogen infection model with pathogen-to-cell and cell-to-cell transmissions and humoral immunity. We consider both latently and actively infected cells. The model incorporates three types of intracellular time delays. We use nonstandard finite difference method to discretize the continuous-time model. We establish by using Lyapunov method, the global stability of equilibria in terms of the basic reproduction number R 0 and the humoral immune response activation number R 1 . We have proven that if R 0 ≤ 1 , then the pathogen-free equilibrium Q0 is globally asymptotically stable, if R 1 ≤ 1 R 0 , then the persistent pathogen equilibrium without immune response Q* is globally asymptotically stable, and if R 1 > 1 , then the persistent pathogen equilibrium with immune response Q ¯ is globally asymptotically stable. We illustrate our theoretical results by using numerical simulations. The effect of time delay on the pathogen dynamics is also studied. We have shown that the time delay has similar effect as the drug therapy. This gives some impression to develop new class of treatment to increase the delay period and then suppress the pathogen replication.