Considering the influence of media reports and environmental transmission on disease transmission,a SEVIQBR infectious disease model is established.Firstly,the basic reproduction number R0 of the model is obtained by the next generation matrix method.Based on the basic reproduction number,the existence of disease-free equilibrium and endemic equilibrium of the model is discussed.Then,the local stability of disease-free equilibrium is studied by means of Hurwitz criterion,and the global asymptotic stability of disease-free equilibrium is studied by constructing an appropriate Lyapunov function.The results show that when the basic reproduction number R0＜1,the disease-free equilibrium of the model is globally asymptotically stable.When R0 satisfies certain conditions,the endemic equilibrium of the model exists.Finally,we give some numerical simulations to explain the theoretical results.
关键词
基本再生数/稳定性/Lyapunov函数/媒体报道/SEVIQBR模型
Key words
basic reproduction number/stability/Lyapunov function/media coverage/SEVIQBR model
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