主题：Bifurcation analysis of epidemic model on networks
主讲人：靳祯（Jin Zhen） 教授
Shanxi University Professor , Director of Shanxi Mathematics Association, Deputy Director of the Chinese Biological Mathematics Association
报告摘要：The bifurcation of most epidemic models on complex networks leading from a disease free equilibrium to an endemic equilibrium is forward. Gross et al. established a pair-approximation epidemic model for the spreading of infections on an adaptive network based on the well-known SIS model, and numerical studies have figured out that the rewiring mechanism can lead to backward bifurcation and Hopf bifurcation. However, they have not presented a strict mathematical proof of their conclusion in the literature. In this talk, we give the basic reproduction number and the critical conditions of the bifurcations occur analytically. Furthermore, we give a detailed analysis for these rich dynamical behaviors, such as bistability and periodicity.