报 告 题 目：Stochastic dynamics of an SIS epidemic on networks

主 讲 人：刘 桂 荣

单 位：山西大学

时 间：5月12日14:30

腾讯 ID：459-999-086

摘 要：

We derive a stochastic SIS pairwise model by considering the change of the variables of this system caused by an event. Based on approximations, we construct a low-dimensional deterministic system that can be used to describe the epidemic spread on a regular network. The mathematical treatment of the model yields explicit expressions for the variances of each variable at equilibrium. Then a comparison between the stochastic pairwise model and the stochastic mean-field SIS model is performed to indicate the effect of network structure. We find that the variances of the prevalence of infection for these two models are almost equal when the number of neighbors of every individual is large. Furthermore, approximations for the quasi-stationary distribution of the number of infected individuals and the expected time to extinction starting in quasi-stationary are derived. We analyze the approximations for the critical number of neighbors and the persistence threshold based on the stochastic model. The approximate performance is then examined by numerical and stochastic simulations. Moreover, during the early development phase, the temporal variance of the infection is also obtained. The simulations show that our analytical results are asymptotically accurate and reasonable.

简 介：

刘桂荣，山西大学教授，博士生导师。2007年毕业于山西大学，获博士学位。主要从事微分方程与生物数学方向的研究工作。主持国家自然科学基金4项、人社部留学回国人员科技活动择优资助项目(优秀类)1项、省级项目5项。2010年，以第一完成人获得山西省教学成果一等奖；2011年，入选山西大学青年英才计划；2012年，入选山西省高等学校优秀青年学术带头人支持计划；2015年，以第一完成人获山西省科学技术奖 (自然科学类) 二等奖。