In this paper, we investigate the global properties of two general models of pathogen infection with immune deficiency. Both pathogen-to-cell and cell-to-cell transmissions are considered. Latently infected cells are included in the second model. We show that the solutions are nonnegative and bounded. Lyapunov functions are organized to prove the global asymptotic stability for uninfected and infected steady states of the models. Analytical expressions for the basic reproduction number R0 and the necessary condition under which the uninfected and infected steady states are globally asymptotically stable are established. We prove that if R0< 1 then the uninfected steady state is globally asymptotically stable (GAS), and if R0> 1 then the infected steady state is GAS. Numerical simulations are performed and used to support the analytical results.