The state of an infectious disease can represent the degree of infectivity of infected individuals, or susceptibility of susceptible individuals, or immunity of recovered individuals, or a combination of these measures . When the disease progression is long such as for HIV, individuals often experience switches among different states . We derive an epidemic model in which infected individuals have a discrete set of states of infectivity and can switch among different states . The model also incorporates a general incidence form in which new infections are distributed among different disease states . We discuss the importance of the transmission-transfer network for infectious diseases . Under the assumption that the tranmission-transfer network is strongly connected, we establish that the basic reproduction number R0 is a sharp threshold parameter: if R0≤1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out; if R0> 1, the disease-free equilibrium is unstable, the system is uniformly persistent and initial outbreaks lead to persistent disease infection . For a restricted class of incidence functions, we prove that there is a unique endemic equilibrium and it is globally asymptotically stable when R0> 1 . Furthermore, we discuss the impact of different state structures on R0, on the distribution of the disease states at the unique endemic equilibrium, and on disease control and preventions . Implications to the COVID-19 pandemic are also discussed.