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Stability analysis and optimal control of a hand-foot-mouth disease (HFMD) model. (English) Zbl 1300.34118

Summary: In this paper, we propose a system of ordinary differential equations to model the hand-foot-mouth disease (HFMD). We derive the expression of the basic reproduction number \(\mathcal R_0\). When \(\mathcal R_0<1\), the system only has the disease free equilibrium, which is globally asymptotically stable; otherwise, the system is persistent. By sensitivity analysis, we identify the control parameters. Then we formulate an optimal control problem to find the optimal control strategy. These results are applied to the spread of HFMD in Mainland China. The basic reproduction number tells us that it is outbreak in China.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
92D30 Epidemiology
49J15 Existence theories for optimal control problems involving ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
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