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In this paper we propose and analyze a pathogen dynamics model with antibody and Cytotoxic T Lymphocyte (CTL) immune responses. We incorporate latently infected cells and three distributed time delays into the model. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive four threshold parameters which 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. [ABSTRACT FROM AUTHOR]