一类受媒体影响的传染病模型的动力学分析

Analysis for the Dynamics of an Epidemic Model with the Impact of Media

建立并研究了一类受媒体影响的传染病模型。通过数学分析,得到了基本再生数并证明了地方病平衡点的存在性,分析模型的前向和后向分支以及Hopf分支出现的条件。模型显示:当R_0<1时,无病平衡点是局部渐近稳定的;当R_0> 1时,无病平衡点是不稳定的。通过数值模拟对R_0、γ、β、α和δ之间的关系进行了参数分析。

In this paper,an epidemic model with the impact of media is formulated and studied.By mathematical analysis,we obtained the basic reproduction number and prove the existence of endemic equilibrium.The model is shown that the disease-free equilibrium is locally asymptotically stable if R0<1;when R0>1,the disease-free equilibrium is unstable.Numerical simulations are performed on the relationship between R0,γ,β,αandδ.