主讲人:Professor Yuan Yuan,纽芬兰纪念大学
时间:2019年12月20日10:00
地点:3号楼332室
举办单位:数理学院
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 speci?cally, 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 di?erent 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 ?xed 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.