报告题目： Threshold dynamics in an SEIRS model with latency and temporary immunity

报 告 人：Prof. Yuan Yuan Memorial University of Newfoundland, Canada

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邀 请 人：白振国

报告时间：2020年11月27日（周五） 19：30-21：30

报告地点：腾讯会议ID：860 501 286

报告人简介：袁沅，加拿大纽芬兰纪念大学数学与统计系教授。本科毕业于武汉大学，后于中南大学、西安大略大学获得硕士和博士学位，之后在滑铁卢大学从事博士后研究。袁教授主要研究领域为数学生物学、数学生态学、非线性动力系统、时滞微分方程等；已在SIAM J. Appl. Math., SIAM J. Appl. Dyn. Syst., J. Math. BIol., J. Differential Equations等国际著名学术期刊上发表高水平学术论文50余篇，并兼任多个国际期刊编委、特邀编辑等。

报告摘要： In this talk, we discuss a disease transmission model of SEIRS type with distributed delays in latent and temporary immune periods. 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, 1. 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, 2. prove that the disease free equilibrium is always globally asymptotically stable when R0 < 1, and 3. 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.