數統學院講座預告
報告承辦單位: 數學與統計學院
報告題目: Exact multiplicity, bifurcation curves, and asymptotic profiles of endemic equilibria of a cross-diffusive epidemic model
報告摘要：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.
報告人姓名: 吳毅湘
報告人所在單位: 美國中田納西州立大學
報告人職稱: 助理教授
報告時間: 2025年5月30日（星期五）下午16:00--18:30
報告地點: 理科樓A419
報告人簡介：吳毅湘，于2010年在中南大學獲得理學學士學位，于2015年在美國路易斯安那大學獲得理學博士學位。2015年7月至2016年8月在加拿大西安大略大學從事博士后研究。2016年9月至2019年7月，任美國范德堡大學助理教授 (non-tenure track)。2019年8月，任美國中田納西州立大學助理教授 (tenure track)。研究興趣主要是反應擴散方程和生物數學。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等國際數學雜志上發表論文40余篇。