报告题目：Global Dynamics of a Time-delayed Nonlocal Reaction-Diffusion Model of Within-host Viral Infections

报 告 人： Xiaoqiang Zhao, Memorial University of Newfoundland

报告时间：2024年5月27日，8：30—9：30

报告地点：数学楼2-2

摘要：In this talk, I will report our recent research on a time-delayed nonlocal reaction-diffusion model of within-host viral infections. We introduce the basic reproduction number R0 and show that the infection-free steady state is globally asymptotically stable when R0 is less than or equals one, while the disease is uniformly persistent when R0 is greater than one. In the case where all coefficients and reaction terms are spatially homogeneous, we obtain an explicit formula of R0 and the global attractivity of the positive constant steady state. Numerically, we illustrate the analytical results and investigate the impact of drugs on curtailing the spread of the virus.

报告人简介：赵晓强，加拿大纽芬兰纪念大学数学与统计系教授，该校University Research Professorship荣誉获得者。赵教授先后于1983年和1986年在西北大学数学系获学士和硕士学位，1990年在中国科学院应用数学研究所获博士学位。赵教授长期从事动力系统、微分方程和生物数学相关领域的研究，在单调动力学、一致持久性、行波解和渐近传播速度、主特征值、基本再生数的理论及应用等方面的系列工作受到同行的广泛关注和引用。迄今为止，他已在“Comm. Pure Appl. Math.、 J. Eur. Math. Soc.、 J. reine angew. Math.、 J. Math. Pures Appl.、Trans. Amer. Math. Soc.、SIAM J. Math. Anal.” 等国际知名期刊上发表论文180余篇，并在Springer出版专著“Dynamical Systems  in Population Biology”。赵教授个人主页：https://www.math.mun.ca/~zhao/

报告题目：Invariance Principle for Hybrid Dynamical Systems with Applications to Epidemic Models

报 告 人：Liu Xinzhi, Department of Applied Mathematics, University of Waterloo

报告时间： 2024年5月28日，下午2：30—3：30

报告地点： 数学楼2-3

摘要：There has been a growing interest in hybrid dynamical systems in recent years. Such systems often undergo vector field switching and/or state jumps due to sudden changes in model characteristics. By introducing the notions of persistent limit set and persistent mode, we extend the classical LaSalle's invariance principle to hybrid systems exhibiting both impulses and switching. A weak invariance principle is established for such systems, under a weak dwell-time condition on the impulsive and switching signals. This weak invariance principle is then applied to derive asymptotic stability criteria for impulsive switched systems. As an application, we investigate a switched SEIR epidemic model with pulse treatment and establish sufficient conditions for the global asymptotic stability of the disease-free solution under weak dwell-time signals.

报告人简介：刘新芝现任加拿大滑铁卢大学应用数学系教授。1988年在美国德克萨斯大学阿灵顿分校获博士学位。于1990年受聘滑铁卢大学并于1994年被聘为该校终身教授。刘新芝教授是国家级领军人才，于2001年受聘于华中科技大学。刘教授的研究方向包括：混合动力系统，非线性系统控制及稳定性，复杂网络的同步，保密通讯，传染病模型等。已发表学术论文400余篇，学术专著6部, 学术编著20余部。