The Global Dynamics of an Age-Structured Hand-Foot-Mouth Disease Model with Saturation Incidence and Time Delay

Abstract

The global dynamic behavior of an age-structured hand-foot-mouth disease (HFMD) model with saturation incidence and time delay is investigated in the work. The time delay occurs during the transition from latent to infectious individuals. Firstly, the model is expressed as an abstract Cauchy problem. The presence of equilibria is then pointed; meanwhile, we define the model’s basic reproduction number${\mathcal{R}}_0$. The conclusions show that a threshold of${\mathcal{R}}_0=1$can be used to evaluate whether the disease is on the verge of extinction or is still present. When${\mathcal{R}}_0<1$, the disease-free equilibrium is globally stable. While${\mathcal{R}}_0>1$, there exists an endemic equilibrium, and the global stability of the endemic equilibrium is also demonstrated. Finally, some numerical examples are given to demonstrate the obtained conclusions.