Threshold Dynamics for A Hand, Foot and Mouth Disease Model

We established an epidemic model of HFMD, which detailed the interaction of the children and the adults in transmitting the HFMD disease. We obtained the basic reproduction number which governs the stability of the disease-free equilibrium and the endemic equilibria. Applying Routh-Hurwitz criteria and LaSalle-Lyapunov Theorem, we obtained the global stability of the disease-free equilibrium and the endemic equilibria, meanwhile we obtained the existence of the periodic solutions arising by Hopf bifurcation around these endemic equilibria, which revealed that the exposed adults who are infected by HFMD virus whereas remaining asymptomatic also have significant effects on disease transmission.