报告题目： Asymptotic behavior of the basic reproduction ratio for periodic reaction-diffusion systems

报 告 人：张磊 博士 哈尔滨工业大学（威海）

照    片：

邀 请 人：白振国

报告时间：2020年11月2日（周一） 19：00-21：00

报告地点：腾讯会议ID：580 136 954

报告人简介：张磊, 2012年本科毕业于河北大学，2018年获得中国科学技术大学理学博士学位，2015年至2017年在加拿大纽芬兰纪念大学联合培养。现为哈尔滨工业大学（威海）讲师，于加拿大纽芬兰纪念大学从事博士后研究。主要研究领域为微分方程的动力学，部分成果发表在SIAM JMA、JDDE、JDE、EJAM等期刊。

报告摘要： In this talk, I will present the asymptotic behavior of the basic reproduction ratio for periodic reaction-diffusion systems in the case of small and large diffusion coefficients. We first establish the continuity of the basic reproduction ratio with respect to parameters by developing the theory of resolvent positive operators. Then we investigate the limiting profile of the principal eigenvalue of an associated periodic eigenvalue problem for large diffusion coefficients. We further obtain the asymptotic behavior of the basic reproduction ratio as the diffusion coefficients go to zero and infinity, respectively. We also investigate the limiting behavior of positive periodic solution for periodic and cooperative reaction-diffusion systems with the Neumann boundary condition when the diffusion coefficients are large enough. Finally, we apply these results to reaction-diffusion model of Zika virus transmission.