Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays

We incorporate three distributed time delays into the model of pathogen dynamics with antibody and Cytotoxic T Lymphocyte (CTL) immune responses. We consider both actively and latently infected cells. The pathogen-target incidence rate, production/proliferation, and removal rates of the cells and pathogens are represented by general nonlinear functions. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive four threshold parameters that fully determine the existence and stability of the five steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations.