一类具有媒体播报和时滞效应的传染病模型的稳定性分析

Stability Analysis on An Epidemic Model with the Effect of Media Coverage and Time Delay

本文研究了一类具有媒体播报和时滞的SIS_mM传染病模型.在模型中考虑了染病者康复后有一部分人仍然保持对疾病的防范意识,成为有意识的易感者,其余则成为无意识的易感者.给出了系统的基本再生数R_0,利用特征方程理论和阈值理论,证明了平衡点的稳定性和Hopf分支的存在性.结论表明染病者康复之后,成为无意识的易感者的比率越低,染病者的人数就会越少.

In this paper, we study a class of SISmM epidemic model incorporating media coverage and time delay. Some recovery people, who keep awareness of disease, will transfer to susceptible responsive, and the others will be susceptible non-responsive. The basic reproduction number R_0 is given. The stability of equilibria and the existence of Hopf bifurcation have been obtained by the theory of the characteristic equation and the threshold. The conclusions show that the number of infected population increases with the rate of translation from susceptible non-responsive to susceptible decreasing.