报告题目：Functional Differential Equations and Applications in Mathematical Biology

报 告 人：Yuan Yuan（袁沅） 教授（Memorial University of Newfoundland）

负 责 人：王小利

报告时间：2026年05月21日（星期四）上午10:00－11:00

报告地点：数学大楼912报告厅

参加人员：教师、研究生、本科生

摘要：Functional differential equations provide a powerful framework for modeling complex dynamical processes in mathematical biology, particularly in systems involving time delays, age structure, or stage structure. In this talk, we present several biologically motivated models formulated within this framework, including an age-structured HIV infection model with immune response, a predator–prey system with nonlocal competition and cannibalism, and a stage-structured fish population model with harvesting.

We focus on the qualitative analysis of these models, emphasizing the derivation of threshold quantities such as reproduction numbers, and the investigation of local and global stability of equilibria. By employing analytical techniques such as characteristic equations, Lyapunov functionals, persistence theory, and bifurcation analysis, we establish conditions for disease eradication or persistence, population survival, and the impact of key factors such as treatment strategies, intra-species interactions and harvesting policies.

These results demonstrate how functional differential equations provide a unified and powerful framework for understanding complex biological dynamics and offer insights into applications such as disease control and resource management.

报告人简介：袁沅，加拿大纽芬兰纪念大学数学与统计系终身正教授、博士生导师。主要研究方向包括非线性动力系统的稳定性及分支分析、时滞微分方程及其在生物/生态数学、传染病传播与控制、神经网络等的应用、微分方程的符号及数值计算方法。在SIAM Journal on Applied Mathematics, Journal of Mathematical Biology, Journal of Differential Equations, Nonlinear Analysis: Real World Applications, SIAM Journal on Applied Dynamical Systems 等主要应用数学及生物数学杂志发表论文六十多篇。