一类具有媒体报道和环境传播的SEVIQBR传染病模型的动力学分析

Dynamic Analysis of a SEVIQBR Infectious Disease Model with Media Coverage and Environmental Transmission

考虑媒体报道以及环境传播对疾病传播的影响,建立了一类受媒体报道和环境传播影响的SEVIQBR传染病模型.首先,通过下一代矩阵的方法得到了模型的基本再生数R0,基于基本再生数讨论模型无病平衡点以及地方病平衡点的存在性.接着,借助Hurwitz判据研究了无病平衡点的局部稳定性,并构造适当的Lyapunov函数证明无病平衡点的全局渐近稳定性.结果表明:当基本再生数R0<1时,模型的无病平衡点是全局渐近稳定的,当R0满足一定条件时,模型的地方病平衡点是存在的.最后,通过数值模拟验证了理论结果.

Considering the influence of media reports and environmental transmission on disease transmission,a SEVIQBR infectious disease model is established.Firstly,the basic reproduction number R_(0) 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 R_(0)<1,the disease-free equilibrium of the model is globally asymptotically stable.When R_(0) satisfies certain conditions,the endemic equilibrium of the model exists.Finally,we give some numerical simulations to explain the theoretical results.