We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio [Formula: see text] and the existence and uniqueness of an endemic equilibrium when [Formula: see text] . We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when [Formula: see text] . Our results encompass and generalize those of Hyman and Li (J Math Biol 50:626-644, 2005; Math Biosci Eng 3:89-100, 2006).