Global Stability of General Pathogen Models With CTL Impairment and Distributed Delays

This paper presents a pathogen dynamics models with impaired of cytotoxic T lymphocytes (CTLs) function. The models includes both pathogen-to-cell and cell-to-cell modes of transmission which are represented by general nonlinear functions. The basic reproduction number R0 is determined and two equilibrium points are calculated. Nonnegativity and boundedness of the solution are proved. Lyapunov function and LaSalle’s invariance principle are used to prove the global stability of each equilibria. Simulations are used to illustrate the theoretical results. A study is conducted on the effect of impaired CTL-cell functions and time delays on pathogen dynamics. Finally, we have observed that increasing of time delay will suppress the pathogen replication.