数统学院讲座预告

报告承办单位: 数学与统计学院

报告题目: Exact multiplicity, bifurcation curves, and asymptotic profiles of endemic equilibria of a cross-diffusive epidemic model

报告摘要：This study examines the global structure of endemic equilibrium (EE) solutions of a cross-diffusive epidemic model which incorporates the repulsive movement of the susceptible population away from the infected population. We show that the basic reproduction number alone cannot determine the existence of the EEs and the model may have multiple EEs when the repulsive movement rate is large. We prove that the set of EEs forms a simple and unbounded curve bifurcating from the curve of disease free equilibria at as varies from zero to infinity, where the bifurcation curve can be forward or backward. We find conditions under which a forward bifurcation curve is of S-shaped and show that a large tends to induce backward bifurcation curves. Results on the asymptotic profiles of the EEs are obtained as the repulsive movement rate is large or the random movement rates are small. Finally, we perform numerical simulations to illustrate the results.

报告人姓名: 吴毅湘

报告人所在单位: 美国中田纳西州立大学

报告人职称: 助理教授

报告时间: 2025年5月30日（星期五）下午16:00--18:30

报告地点: 理科楼A419

报告人简介：吴毅湘，于2010年在中南大学获得理学学士学位，于2015年在美国路易斯安那大学获得理学博士学位。2015年7月至2016年8月在加拿大西安大略大学从事博士后研究。2016年9月至2019年7月，任美国范德堡大学助理教授 (non-tenure track)。2019年8月，任美国中田纳西州立大学助理教授 (tenure track)。研究兴趣主要是反应扩散方程和生物数学。其研究成果已在SIAM Journal on Mathematical Analysis、 Nonlinearity、SIAM Journal on Applied Mathematics、Journal of Mathematical Biology、Journal of Differential Equations等国际数学杂志上发表论文40余篇。