江蘇省應用數學（中國礦業大學）中心系列學術報告
題目： Threshold dynamics in an SEIRS model with latency and temporary immunity
報告人：袁沅 教授 單位： 紐芬蘭紀念大學
時 間：2023年9月7日（周四）下午 14:00-15：00
地點： 數學院A321
報告内容簡介：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.
個人簡介：袁沅教授 1984年于武漢大學獲得學士學位，1988年于中南大學獲得碩士學位，2002年于加拿大西安大略大學（University of Western Ontario）獲得博士學位。2002年榮獲NSERC（加拿大國家自然科學基金）資助在滑鐵盧大學(University of Waterloo)做短暫博士後研究，随後于2002年9月起受聘于加拿大紐芬蘭紀念大學（Memorial University of Newfoundland）至今，現為該校數學與統計系終身正教授和博士生導師。袁教授主要研究方向包括非線性動力系統的穩定性及分支分析、時滞微分方程及其在神經網絡和生物數學等的應用、微分方程的符号及數值計算方法。現已在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等主要應用數學及生物數學雜志發表論文六十多篇。研究成果深受同行好評及引用，研究一直受到加拿大NSERC的資助。