In this talk, we propose a class of epidemic models in which infected individuals have a discrete set of states of infectivity and can switch among different states. The models also incorporate general incidence forms 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 transmission-transfer network is strongly connected, adapting the improved graph-theoretical approach, we establish that the basic reproduction number R0 is a sharp threshold parameter. We will also discuss combining a simplified model and reported infected data of SARS-CoV-2 variants with Physical Information Neural Networks (PINNs) to simulate observed or unobserved dynamics, facilitate time-dependent parameter inferences, and make short-term predictions.