报告题目: Asymptotic Behavior of The Principal Eigenvalue and Basic Reproduction Ratio for Time-Periodic Reaction-Diffusion Systems with Time Delay

报告人：王其如教授 中山大学

邀请人：李善兵

报告时间：2023年06月14日（周三）9：00-10：00

报告地点：腾讯会议：714-228-256，密码：202306

报告人简介：王其如，中山大学数学学院教授、博士研究生导师，中国工业与应用数学学会理事、数学与国防创新委员会委员，广东省和广州工业与应用数学学会理事长、党支部书记。从事微分方程与动力系统、数学建模等方面的研究及应用，主持完成国家自然科学基金面上项目4项、在研1项，在国内外学术期刊J. Differential Equations、Nonlinear Anal. Real World Appl.、Discrete Contin. Dyn. Syst.、Fract. Calc. Appl. Anal.、中国科学数学（中、英文版）等发表相关学术论文130余篇。是德国《数学文摘》和美国《数学评论》的评论员等。

报告摘要：In this talk, we discuss the asymptotic behavior of the basic reproduction ratio for time-periodic and delay reaction-diffusion systems in the cases of small and large diffusion coefficients. First, we employ the generalized Kerin-Rutman theorem to establish the existence of the principal eigenvalue for periodic and cooperative reaction-diffusion systems with delay. Then, motivated by Kerin-Rutman theorem, we provide a method to estimate the upper and lower bounds of principal eigenvalues so as to obtain the asymptotic behavior of the principal eigenvalue. In view of the relationship between the basic reproduction ratio and the principal eigenvalue, we obtain the limiting profile of the basic reproduction ratio according to the asymptotic behavior of the principal eigenvalue.