接种率受媒体报道影响的手足口病模型的分析

Analysis of a Model of Hand-Foot-Mouth Disease with Vaccination Rate Related to Media Coverage

摘要: 为研究媒体报道对手足口病的影响，建立了一类接种率受媒体报道影响的SEI₁I₂R手足口病常微分方程组模型。文中通过再生矩阵的方法计算出模型的基本再生数R₀，结果表明，当R₀<1时，模型始终存在无病平衡点；当R₀>1时，模型存在唯一的地方病衡点。通过Hurwitz判据分析得出无病平衡点的局部渐近稳定性，然后构造适当的Lyapunov函数得出无病平衡点的全局渐近稳定性，最后利用数值模拟说明了地方病平衡点的稳定性。

Abstract: In this paper, to study the influence of media coverage on hand-foot-mouth disease (HFMD), a kind of SEI₁I₂R epidemic model with vaccination rate related to media coverage has been established. The basic reproduction number R₀ of the system has been calculated by the method of the next generation Matrix. The results show that the model always has a disease-free equilibrium when R₀<1 , and there is a unique endemic equilibrium when R₀>1 . First, the local asymptotic stability of the disease-free equilibrium is obtained by the Hurwitz criterion analysis, and then the global stability of disease-free equilibrium is obtained by constructing the appropriate Lyapunov function. Finally, the stability of the endemic equilibrium is verified by the numerical simulation.