Threshold Dynamics in an SEIRS Model with Latency and Temporary Immunity


主讲人:Professor Yuan Yuan,纽芬兰纪念大学




主讲人介绍:纽芬兰纪念大学数学与统计系教授。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University of Western  Ontario获得博士学位,之后在University of Waterloo做短暂博士后研究,2002年9月起受聘于Memorial University  of Newfoundland至今。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,在SIAM J. Appl. Math., SIAM  J. Appl. Dyn. Syst., J. Differential Equations, J. Math.  BIol.等国际著名学术期刊上发表论文近60篇,并兼任多个国际期刊编委。

内容介绍: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 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.