Abstract：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.



报告人简介：靳 祯，山西大学教授。现任山西省数学会理事长，中国生物数学学会副理事长，《Plos One》等编委。曾获教育部新世纪优秀人才，山西省教学名师，全国优秀教师等荣誉，享受国务院政府特殊津贴。目前也是山西省科技创新团队,国家自然科学奖及国家基金数理学部的会审专家。主要从事生物数学及复杂网络研究工作，先后主持国家自然基金项目5 项，其中国家基金重点项目1 项。作为第一完成人，2010 年获得山西省科学技术奖（自然科学类）一等奖，2014 年获得教育部高等学校优秀成果二等奖奖（自然科学类）。

主持人：傅显隆 教授