Hopf Bifurcation of an Age-Structured Hand–Foot–Mouth Disease Model in a Contaminated Environment

In this paper, we investigate an age-structured model of Hand–Foot–Mouth Disease (HFMD) in a contaminated environment. This paper characterizes both age structure and contaminated environment in the HFMD model and discusses their effects on the time delay in the conversion from exposed to infected individuals. By transforming the original model to an abstract nondensely defined Cauchy problem and utilizing the integrated semi-group theory, we establish the well-posedness of solutions. Then the existence and stability of equilibria are obtained on the basis of the basic reproduction number [Formula: see text]. It is proved that the disease-free equilibrium is globally asymptotically stable if [Formula: see text]. Meanwhile, the endemic equilibrium is locally asymptotically stable with time delay [Formula: see text]. Furthermore, Hopf bifurcation occurs at endemic equilibrium when [Formula: see text]. Finally, numerical simulations are performed to validate our theoretical results.