Impact of reinfection on dynamics of epidemic model with discrete two-state structure

This article investigates an infectious disease model with two-state and repeated infection in recovered populations. The state of an infected individual can switch between two possible states. Some suitable reproduction numbers like the classic basic reproduction number are introduced, which can determine the number of equilibrium points of the epidemic model, the stability of the healthy manifold and the strongly (weakly) endemic equilibrium. Based on different combinations of reproduction numbers and initial conditions, the dynamics of the epidemic model may present four different behaviors: (1) all states tend to a point in a disease-free manifold; (2) all states tend to a strongly (weakly) endemic equilibrium; (3) some states starting from the neighborhood of an unstable healthy submanifold approach a stable healthy submanifold; and (4) all states may approach a point in a disease-free manifold or (weakly) endemic equilibrium according to different initial conditions. Finally, three numerical examples and one actual data example are provided to demonstrate various possible behaviors and validate the theoretical findings.