报告题目1：Dynamical analysis of a spatially heterogeneous disease model with degenerate structure

报告人：吴毅湘教授，美国Middle Tennessee State University

报告时间：2026年1月8日（周四）9:00

报告地点：腾讯会议（会议号：439-396-875）

报告摘要：In this article, we analyze a reaction-diffusion model for cocoa black pod disease with space-dependent parameters and partial degradation, which assumes that susceptible and infected cocoa pods remain immobile within the region. Spores produced by infected pods, which drive both direct and indirect infections, are assumed to disperse at distinct rates depending on their mode of transmission. Firstly, we establish the well-posedness of the model, including the boundedness and global existence of solutions. Additionally, to address the lack of compactness of solution semiflow, we establish the asymptotic smoothness of the semiflow generated by the model. Subsequently, we define the basic reproduction number (BRN) $\mathcal{R}_0$ by utilizing the standard next generation operator approach and derive some properties of $\mathcal{R}_0$. The BRN, $\mathcal{R}_0$, is shown as a threshold parameter for disease eradication versus uniform persistence: if $\mathcal{R}_0\leq1$, the disease will become extinct; if $\mathcal{R}_0>1$, the infection will persist. Moreover, when $\mathcal{R}_0>1$ and the diffusion rate of spores  responsible for direct or indirect transmission is zero, we further show that the model has a unique globally attractive positive steady state by constructing delicate Lyapunov functions.

报告人简介：吴毅湘，于2010年在中南大学获得理学学士学位，于2015年在美国路易斯安那大学获得理学博士学位。2015年7月至2016年8月，在加拿大西安大略大学从事博士后研究。2016年9月至2019年7月，任美国范德堡大学助理教授(non-tenure track)。2019年8月，任美国中田纳西州立大学助理教授(tenure track)。2025年8月，任美国中田纳西州立大学副教授。研究兴趣主要是反应扩散方程和生物数学。已在SIAM Journal on Mathematical Analysis、Nonlinearity、SIAM Journal on Applied Mathematics、Journal of Mathematical Biology、Journal of Differential Equations等国际数学期刊上发表论文40余篇。

报告题目2：On the ideal free distribution in time-periodic environments

报告人：林经洋教授，美国Ohio State University

报告时间：2026年1月8日（周四）10:00

报告地点：腾讯会议（会议号：439-396-875）

报告摘要：A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members have chosen a fixed spatial location in a way that optimizes its individual fitness, allowing for the effects of crowding. In this paper, we extend the idea of individual fitness associated with a specific location in space to account for the full path that an individual organism takes in space and time over a periodic cycle, and extend the mathematical formulation of an ideal free distribution to general time periodic environments. We show that such generalized ideal free distribution enables a population to be evolutionarily stable. A sharp criterion on the environmental functions is found to be necessary and sufficient for such ideal free distribution to be feasible. In the case the criterion is met, we showed that there exist dispersal strategies that can be identified as producing a time-periodic version of an ideal free distribution, and such strategies are evolutionarily steady and are neighborhood invaders from the viewpoint of adaptive dynamics. Our results extend previous works in which the environments are either temporally constant, or temporally periodic but the total carrying capacity is temporally constant. This is joint work with R.S. Cantrell and C. Cosner of Univ. Miami, and Hua Zhang of Shanghai Jiaotong Univ.

报告人简介：林经洋(King-Yeung Lam)，美国俄亥俄州立大学教授。法国Sorbonne Université及Institu Henri Poincaré访问教授。2006年本科毕业于香港中文大学数学系，2011年于美国明尼苏达大学获得博士学位，师从倪维明教授。此后在美国俄亥俄州立大学(OSU)Mathematical Bios Institute任Croucher Foundation博士后，并于数学系任Zassenhaus助理教授、副教授、教授，兼任OSU数学研究所主任，担任CPDE、JMB、SIAP等国际重要期刊的编委。研究领域为偏微分方程，特别是抛物椭圆方程(组)、Hamilton-Jacobi equations和自由边界问题，及其在生物学中的应用。已在SIAM J. Appl. Math.、SIAM J. Math. Anal.、J. Diff. Equations、Calc. Var、Partial Diff. Equations、J. Funct、Anal.、Mem. Amer. Math. Soc.、Indiana Univ. Math. J.、J. Math. Biol、Bul. Math. Biol.等国际著名SCI期刊上发表学术论文40多篇。

邀请人：无穷维动力系统和偏微分方程研究所