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

报 告 人：袁沅教授（纽芬兰纪念大学）

报告时间：2026年6月9日上午10:30-12:30

报告地点：数学院一楼135报告厅

报告摘要：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.

个人简历：袁沅，1984年于武汉⼤学获得学⼠学位，1988 年于中南⼤学获得硕⼠学位，2002年于加拿⼤⻄安⼤略⼤学（University of Western Ontario）获得博⼠学位。同年年荣获NSERC（加拿⼤国家⾃然科学基⾦）资助在滑铁卢⼤学(University of Waterloo)做短暂博⼠后研究，随后于2002年9⽉起受聘于加拿⼤纽芬兰纪念⼤学（Memorial University of Newfoundland）⾄今，现为该校数学与统计系终⾝正教授和博⼠⽣导师。袁教授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。现已在《SIAM Journal of Applied Mathematics》,《Journal of Mathematical Biology》, 《Journal of Mathematical Analysis and Applications》, 《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⼋⼗多篇。研究成果深受同⾏好评及引⽤，研究⼀直受到加拿⼤国家⾃然科学基⾦的资助。与中国多所⾼校同⾏有科研合作。袁教授参与了多国国家科研基⾦的评审，是⼏个应⽤数学杂志的编委及多个动⼒系统与应⽤数学杂志的评审⼈。组织了多个国际，国内学术会议，培养了各类⻘年学⽣，学者三⼗多名。