报告题目：The Linear Stability and Basic Reproduction Numbers for Autonomous FDEs

报告人：赵晓强 教授 加拿大纽芬兰纪念大学

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邀请人：白振国

报告时间：2023年4月4日19：30-22：30

腾讯会议ID：977-613-843

报告人简介：赵晓强，加拿大纽芬兰纪念大学数学与统计系教授，该校University Research Professorship荣誉获得者。赵教授先后于1983年和1986年在西北大学数学系获学士和硕士学位，1990年在中国科学院应用数学研究所获博士学位。赵教授长期从事动力系统、微分方程和生物数学相关领域的研究，在单调动力学、一致持久性、行波解和渐近传播速度、主特征值、基本再生数的理论及应用等方面的系列工作受到同行的广泛关注和引用。迄今为止，他已在“Comm. Pure Appl. Math.、J. Eur. Math. Soc.、J. reine angew. Math.、J. Math. Pures Appl.、Trans. Amer. Math. Soc.、SIAM J. Math. Anal.”等国际知名期刊上发表论文180余篇，并在Springer出版专著“Dynamical Systems in Population Biology”。赵教授个人主页：https://www.math.mun.ca/~zhao/

报告摘要：The basic reproduction number R0 is an important concept in population biology. As a threshold quantity for population dynamics, it is unquestionably one of the most valuable mathematical ideas brought to theoretical ecology and epidemiology. In this talk, I will report our recent research on the linear stability and R0 for autonomous and cooperative functional differential equations (FDEs). In particular, we will give a general formula of R0 for autonomous andcompartmental FDE models, where both the production (infection) and the internal transition havetime delays. We also extend this theory to abstract autonomous FDEs on an ordered Banach space so that it can be applied to time-delayed reaction-diffusion systems. As an illustrative example, we establish the threshold dynamics for a time-delayed population model of black-legged ticks in terms of R0.