报告题目1：Spatial dynamics of a pest population with stage-structure and control

报告人： 金瑜 教授， 美国内布拉斯加大学林肯分校

报告时间：2024年6月16日（周日）8：20—9：00

报告地点：20-404（第一会议室）

报告摘要： We study an integro-difference model for a pest population with stage structure and control on each stage. When the spatial domain is infinite, we establish the spreading speeds and existence of traveling waves; when the spatial domain is finite, we first establish threshold conditions in terms of the principal eigenvalue of an associated eigenvalue problem to determine population persistence and extinction, and then define the net reproductive rate and use it to develop equivalent threshold conditions for persistence and extinction. The cases where the reproduction function is monotone and nonmonotone are both investigated. Numerical simulations show that the larger the control effectiveness is the easier to eradicate the pest population and that the same control effectiveness on different stages may yield different population dynamics in the long-term.

报告题目2：Dynamics of classical solutions of a multi-strain diffusive epidemic model with mass-action transmission mechanism

报告人：  Rachidi Salako 教授， University of Nevada, USA

报告时间：2024年6月16日（周日）9：00—9：40

报告地点：20-404（第一会议室）

报告摘要：  We study a diffusive epidemic model and examine the spatial spreading dynamics of a multi-strain infectious disease. In particular, we address the questions of competition-exclusion or coexistence of the disease's strains. Our results indicate that if one strain has its local reproduction function spatially homogeneous, which either strictly minimizes or maximizes the basic reproduction numbers, then the phenomenon of competition-exclusion occurs. However, if all the local reproduction functions are spatially heterogeneous, several strains may coexist. In this case, we provide complete information on the large time behavior of classical solutions for the two-strain model when the diffusion rate is uniform within the population and the ratio of the local transmission rates is constant. Particularly, we prove the existence of two critical superimposed functions that serve as threshold values for the ratio of the transmission rates and that of the recovery rates. Furthermore, when the populations' diffusion rates are small, our results on the asymptotic profiles of coexistence endemic equilibria indicate a spatial segregation of infected populations. 

报告题目3：Stationary solutions of a chemotaxis system with singular sensitivity and logistic source

报告人：  薛书文教授， Northern Illinois University, USA

报告时间：2024年6月16日（周日）9：40—10：20

报告地点：20-404（第一会议室）

报告摘要：  Chemotaxis, the directed movement of cells or living organisms in response to the concentration gradient of chemical substances, plays a significant role in a large range of biological phenomena such as tumor growth, wound healing, and embryo development. In this talk, first, we will introduce the chemotaxis model. Then, we will talk about the stability and instability of the constant solution. Next, we will discuss the local and global bifurcation and spiky stationary solutions which can be used to model cell aggregation. Numerical simulations and some open questions will also be presented.

报告题目4：Population Dynamics in a Habitat with Protection Zones

报告人：  王金凤教授， 哈尔滨师范大学

报告时间：2024年6月16日（周日）10：40—11：20

报告地点：20-404（第一会议室）

报告摘要： In this talk, we will introduce two reaction diffusion equations with protection/control zones, one is about single species, the other one is about an SIS model. We investigate the exact starting point and length of protection zones to protect the survival of single species, or to establish the disease.,

报告题目5：On two stream species Lotka-Volterra competition patch models

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

报告时间：2024年6月16日（周日）11：20—12：00

报告地点：20-404（第一会议室）

报告摘要： We study the dynamics of two-species Lotka-Volterra competition patch models. The populations are supposed to live in a stream environment, where they are subject to both random dispersal and directed drift. We suppose that one species is a resident species and study the conditions on the parameters under which the other species can or cannot invade. We show that factors such as the magnitude of random dispersal rates and drift rates, the distribution of resources, and the convexity of the drift rates may significantly affect the competition outcomes of the species.

邀请人：非线性分析与PDE团队