江苏省应用数学（中国矿业大学）中心系列学术报告
题目： Threshold dynamics in an SEIRS model with latency and temporary immunity
报告人：袁沅 教授 单位： 纽芬兰纪念大学
时 间：2023年9月7日（周四）下午 14:00-15：00
地点： 数学院A321
报告内容简介：A disease transmission model of SEIRS type with distributed delays in latent and temporary immune periods is discussed. With general/particular probability distributions in both of these periods, we address the threshold property of the basic reproduction number R0 and the dynamical properties of the disease-free/endemic equilibrium points present in the model. More specifically, we show the dependence of R0 on the probability distribution in the latent period and the independence of R0 from the distribution of the temporary immunity,prove that the disease free equilibrium is always globally asymptotically stable when R0 < 1, and according to the choice of probability functions in the latent and temporary immune periods, establish that the disease always persists when R0 > 1 and an endemic equilibrium exists with different stability properties. In particular, the endemic steady state is at least locally asymptotically stable if the probability distribution in the temporary immunity is a decreasing exponential function when the duration of the latency stage is fixed or exponentially decreasing. It may become oscillatory under certain conditions when there exists a constant delay in the temporary immunity period. Numerical simulations are given to verify the theoretical predictions.
个人简介：袁沅教授 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（University of Western Ontario）获得博士学位。2002年荣获NSERC（加拿大国家自然科学基金）资助在滑铁卢大学(University of Waterloo)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（Memorial University of Newfoundland）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 Applications, SIAM Journal on Applied Dynamical Systems等主要应用数学及生物数学杂志发表论文六十多篇。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。