An age-structured hand, foot and mouth disease model with partial immunity

Hand-foot-mouth disease (HFMD) is an infectious disease caused by enteroviruses common in everyone and reinfection can occur. In order to investigate the impact of covert infection and temporary immunity on the transmission of HFMD, we establish an age-structured model, which is based on a system of partial differential equations, describing the interactions among susceptible individuals, latently infected individuals, and temporarily immune individuals. At first, a careful analysis of the existence and local stability of equilibrium states shows the disease-free equilibrium is globally asymptotically stable for R 0 1 , the endemic equilibrium is unstable for R 0 > 1 , by means of reformulating the model as an abstract Cauchy problem. Then, an application of the Lyapunov–Schmidt approach reveals the conditions for the occurrence of backward bifurcation, and the numerical simulations of obtained conclusions are examined.