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Threshold dynamics for a HFMD epidemic model with periodic transmission rate. (English) Zbl 1280.92062

Summary: In this paper, a periodic epidemic model is proposed in order to simulate the dynamics of HFMD transmission. We consider the effects of quarantine in the children population. We obtain a threshold value which determines the extinction and uniform persistence of the disease. Our results show that the disease-free equilibrium is globally asymptotically stable if the threshold value is less than unity. Otherwise, the system has a positive periodic solution and the disease persists. Numerical simulations show that quarantine has a positive impact on the spread of disease, i.e., quarantine is beneficial to the intervention and control of the disease outbreak in the children population.

MSC:

92D30 Epidemiology
34C25 Periodic solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
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References:

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