报告人：陈玉明 教授

Wilfrid Laurier University, Canada

题目1：A delayed model on biological control with natural enemy migration

题目2：Imitation dynamics of vaccine decision

making behaviors based on the game theory

时间：5月29日，10:00-11:00，下午2:00-3:00

地点：数学系致远楼102

欢迎各位老师和同学参加！

陈玉明教授， 分别于1991年和1994年从北京大学获应用数学学士学位和硕士学位，并于2000年从加拿大约克大学（York University）获理学博士学位，2000年9月至2001年6月在加拿大阿尔伯塔大学（University of Alberta）做博士后。从20001年7月起，一直任教于加拿大罗瑞尔大学(Wilfrid Laurier University)。现为该校数学系正教授、博士生导师。主要研究兴趣为动力系统和泛函微分方程理论及其在生物数学和神经网络中的应用。已在包括 SIAM Journal on Mathematical Analysis, Nonlinearity, Journal of Differential Equations, Physica D, Proceedings of the American Mathematical Society， Mathematical Biosciences, Neural Networks等国际著名刊物发表论文80余篇，其成果被同行广泛引用，曾获安大略省科技与创新部早期研究者奖。主持了4项加拿大国家自然科学与工程理事会(NSERC)科研基金项目，参与了3项中国国家自然科学基金面上项目。积极参与高质量人才如硕士生、博士生、博士后的培养。陈教授与中国学者有广泛交流与合作。

报告摘要

Abstract 1: Biological control is an environmentally sound and effective means of reducing or mitigating pests and pest effects through the use of natural enemies. In this talk, we propose and analyze a model on biological control, which is based on the abundance of pest and a simple predator-prey model. We first study the existence and stability of equilibria. It turns out that backward bifurcation occurs with the migration rate as the bifurcation parameter. The stability of the trivial equilibrium and the boundary equilibrium is delay-independent. However, the stability of the positive equilibrium may be delay-dependent. Moreover, delay can switch the stability of the positive equilibrium. When the positive equilibrium loses stability, Hopf bifurcation can occur. The direction and stability of Hopf bifurcation is derived by applying the center manifold method and the normal form theory. The main theoretical results are illustrated with numerical simulations. This is a joint work with Professor Fengqin Zhang.

Abstract 2:To investigate the imitation dynamics of vaccine uptake, an age structured epidemic model based on game theory is proposed. The model is derived under the assumption that the potential infection risk depends on the infection age. The existence and local stability of equilibria are analyzed. A Hopf bifurcation may occur from the endemic and vaccinator equilibrium. Our study shows that imitation behavior is not the only reason to destabilize the system and bring about oscillations. Infection age is another factor to produce the limit cycles. The results show how the prevalence of the infection changes with respect to the infection age. This is a joint work with Dr. Yang and Prof. Marcheva.