报告题目: Network Epidemic Model with Adaptive Rewiring

报告时间：9月18号（周三）下午2:30

报告地点: 理学院206

报 告 人: 袁沅

报告摘要:The adaptive rewiring mechanism is considered in two network epidemic models. Using the idea of age structure, we establish the non-Markovian SIR network model with fixed infectious period and preventive rewiring for each node and each link, then give the pairwise reproduction number and provide the formula for the final epidemic size by rigorous analysis and tedious computation. We realize that the rewiring process does not occur immediately, but takes some time. We therefore establish a delayed SIS network model with adaptive rewiring mechanism and discuss the effect of adaptive rewiring delay in the model. We found that with the rewiring time, there are infinite equilibria lie on a line in a high-dimensional state space, which is quite different from normal delayed model. The simulation results show that adaptive rewiring inhibits the spread of disease and decreases the size of disease outbreak for the network SIR model, while in the network SIS model, the system approaches to different steady state on the line under the same initial values and different rewiring delays, and the stable limit cycle can appear with the increase of rewiring delay. These surprising results may provide new insights into the study of delayed network epidemic model.

袁沅教授简介：袁沅，1984年于武汉大学获得学士学位，1988年于中南大学获得硕士学位，2002年于加拿大西安大略大学获得博士学位。2002年荣获加拿大国家自然科学基金资助在滑铁卢大学做短暂博士后研究，随后于2002年9月起受聘于加拿大纽芬兰纪念大学至今，现为该校数学与统计系终身正教授和博士生导师。袁教授主要研究方向包括非线性动力系统的稳定性及分支分析、时滞微分方程及其在神经网络和生物数学等的应用、微分方程的符号及数值计算方法。现已在SIAM Journal of Applied Mathematics, Journal of Mathematical Biology,Journal of Mathematical Analysis and Applications, Journal of Differential Equations, Nonlinear Analysis:Real World Applicaitons, SIAM Journal on Applied Dynamical Systems 等主要应用数学及生物数学杂志发表论文近六十篇。研究成果深受同行好评及引用，研究一直受到加拿大NSERC的资助。

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