受国际合作处资助，应数学系苏颖副教授邀请，加拿大西安大略大学邹幸福教授将于6月1至8日访问公司数学系，访问期间将做如下四个学术报告。

报告1-2时间：2018年6月5日下午14:30-17:30

报告3-4时间：2018年6月7日下午14:30-17:30

报告地点：格物楼503

报告1题目：On a diffusive host-pathogen system with different dispersal rates and spatial heterogeneity

摘要：In this talk, I will report some recent results on a diffusive host-pathogen model with spatially heterogeneous parameters and distinct dispersal rate for the susceptible and infected hosts. In addition to global existence of solution, existence of a global attractor, we also discuss the threshold dynamics in terms of the basic reproduction number R0 which is identified as the spectral radius of a linear operator in the appropriate functions space.We show that if R0<1, the pathogen free equilibrium is globally stable, and if R0>1, the solution of the model is uniformly persistent and there exists a positive steady state.In the latter case, we also explore the asymptotic profiles of the endemic steady state  as the dispersal rate of the susceptible or infected hosts approaches zero. The results reveal some difference between the roles that the diffusions of susceptible and infectious hosts can play. This is a joint work with Dr. Yixiang Wu (Vanderbilt University).

报告2题目：Modeling the role of white-tailed deer in geographic spread of the black-legged tick Ixodes scapularis by a spatially nonlocal model.

摘要：Lyme disease is transmitted via blacklegged ticks,the spatial spread of which is believed to be primarily via transport on white-tailed deer. In this talk, I will present a mathematical model to describe the spatial spread of blacklegged ticks due to deer dispersal. The model turns out to be a system of differential equations with a spatially non-local term accounting for the phenomenon thata questing female adult tick that attaches to a deer at one location maylater drop to the ground, fully fed, at another location. After justifying the well-posedness of the model and analyzing the stability of its steady states, we will explore the existence of traveling wave fronts connecting the extinction equilibriumwith the positive equilibrium for the system. We derive an algebraic equation that determines a critical value $c^*$ which turns out to be the minimum wave speed and the actual spread speed of the tick population. We then present some numerical simulation results to demonstrate the above results. We also explore the dependence of $c^*$ on the dispersion rate of the white tailed deer,by which one may evaluate the role of the deer's dispersion in the geographical spread of the ticks. This is a joint work with Stephen Gourley and Xiulan Lai et al.

报告3题目：Coexistence of competing species for intermediate dispersal rates in a reaction-diffusion chemostat model

摘要：In this talk, I will revisit a diffusive chemostat model with two competing species and one nutrient. We show that for large diffusion rate, both species will be washed out, while for small diffusion rate, competition exclusion will occur. This implies that a stable coexistence can only occurs at intermediate diffusion rate. We present an explicit way of determining parameter range which supports a stable coexistence steady state.

报告4题目：A DDE model modelling the fear effect in predator-prey interactions with adaptive avoidance of predators

摘要：Recent field experiment of vertebrates showed that mere presence of a predator would cause a dramatic change of a prey's demography. Fear of predators increases prey's survival probability but leads to a cost in prey's reproduction. Based on the experimental findings, we propose an age structured predator-prey model with the cost of fear and adaptive avoidance of predators. Mathematical analyses show that maturation delay between juvenile prey and adult prey can induce stability change of an equilibrium. Particularly,the positive equilibrium may lose its stability with a relatively large value of delay and regain stability if the delay is  further larger. Numerical simulations show that either strong adaptation of adult prey or large cost of fear have destabilizing effect while large population of predators has a stabilizing effect on the predator-prey interactions under consideration. Numerical simulations also indicate that adult prey needs stronger anti-predator respponse if population of predators is larger and needs weaker anti-predator response if the cost of fear is larger.

报告人简介：邹幸福于1983和1989年在中山大学数学系和湖南大学数学系分别获学士和硕士学位。1993-1997年就读于加拿大约克大学并获博士学位，继而在加拿大维多利亚大学和美国乔治亚理工学院动力系统与非线性研究中心做博士后。1999.1-2004.1在加拿大纽芬兰纪念大学先后任助理教授和副教授（终身教职），2004年开始在加拿大西安大略大学应用数学系任正教授（终身教职），2012年入选湖南省“百人计划”专家并在中南大学担任特聘教授。邹幸福教授是北美地区在微分方程与动力系统及应用的研究领域中的最活跃的学者之一。近年来主要从事偏泛函微分方程、应用动力系统、生物生态模型和神经网络模型的动力性态特性研究，取得了一系列有影响的成果，在J. Diff. Eqns.、SIAM J. Appl. Math.、SIAM J. Math. Anal.等著名杂志发表有影响的研究论文100余篇，担任Applicable Analysis、Journal of Computational and Applied Mathematics、Communications on Pure and Applied Analysis等SCI收录杂志的编委，曾获加拿大国家自然科学和工程基金博士后奖，Petro-Canada青年研究创新奖，安大略省长杰出研究奖。