具有媒体饱和效应影响的时滞SIS模型研究

A Class of Delay SIS Model with Media Saturation

媒体报道对疾病的预防和控制有着重要的作用,其可以减少人们感染疾病的机会.通过建立具有媒体饱和的传染病时滞模型来刻画媒体报道对感染率的影响,首先计算出无病平衡点和当R_0>1时存在唯一的地方病平衡点;其次,分析了平衡点的稳定性,并得到当参数满足一定条件时,时滞τ超过临界值τ_0,地方病平衡点处会出现Hopf分支;最后,通过数值模拟来验证理论分析.

Media coverage plays an important role in the prevention and control of diseases, which can reduce the chances of people getting infected. In this paper a delayed infectious disease model with media saturation is established, and the disease-free equilibrium is calculated and when R0 〉 1 there exists a unique endemic equilibrium; Then the stability of the two equilibria is analyzed and obtained when the delay τ exceeds the critical valueτ0, and when the parameters satisfy certain conditions, the endemic equilibrium will appear the Hopf bifurcation; Finally, through numerical simulation the stability of equilibrium is verified.