学术报告一

题目：On a competition-diffusion-advection system from river ecology: mathematical analysis and numerical study

摘要：This paper is mainly concerned with a two-species competition model in open advective environments, where individuals cannot pass through the upstream boundary and do not return into the habitat after leaving the downstream end. By the theory of principal eigenvalue, we first obtain two critical curves ($\Gamma_1$ and $\Gamma_2$) in the plane of bifurcation parameters that sharply determine the local stability of the two semi-trivial steady states. Then under various conditions on given parameters, we discuss the global dynamics via different techniques including the comparison principle for eigenvalues and perturbation and compactness arguments, which shows that both competitive exclusion and coexistence are possible. For general values of parameters, we take both analytic and numerical approaches to understand further the potential behaviors of $\Gamma_1$ and $\Gamma_2$, and numerically observe that beside the competitive exclusion and coexistence, the bistable phenomenon is also possible, which is different from the known results of competitive ODE and reaction-diffusion systems (where bistability is impossible). The implication of our numerical results on the future work is also discussed.

报告人简介：聂华，教授、博士生导师，研究方向：反应扩散方程与空间生态种群模型。现任中国生物数学学会理事、中国计算数学学会理事。2006年获得博士学位，2012年入选教育部“新世纪优秀人才支持计划”；2015年入选陕西省“青年科技新星”；多次赴美国明尼苏达大学、澳大利亚新英格兰大学、台湾清华大学合作研究与访问。已主持国家自然科学基金项目4项，主持完成省部级项目3项；已在“SIAM J. Appl. Math.”、“SIAM J. Math. Anal.”、“J. Differential Equations”、“J. Math. Biol.”、“Math. Biosci.”、“European J. Appl. Math.”、“Proc. London Math. Soc.”、“Sci. China Math.”等国内外知名刊物上发表学术论文60多篇。

学术报告二

题目：Threshold dynamics of a nonlocal and delayed cholera model in a spatially heterogeneous environment

报告摘要：A nonlocal and delayed cholera model with two transmission mechanisms in a spatially heterogeneous environment is derived. We introduce two basic reproduction numbers of environment and infection, respectively. If the basic reproduction number of environment is strictly less than one and the basic reproduction number of infection is no more than one, we prove globally asymptotically stability of the infection-free steady state. Otherwise, the infection will persist and there exists at least one endemic steady state. For the special homogeneous case, the endemic steady state is actually unique and globally asymptotically stable. Under some conditions, the basic reproduction number of infection is strictly decreasing with respect to the diffusion coefficients of susceptible and infectious hosts. When these conditions are violated, numerical simulation suggests that spatial diffusion may not only spread the infection from high-risk region to low-risk region, but also increase the infection level in high-risk region.

报告人简介：舒洪英，2010年获哈尔滨工业大学博士学位。2008年在加拿大阿尔伯塔大学留学两年，2011年至2014年先后在加拿大新不伦瑞克大学、加拿大瑞尔森大学和约克大学任AARMS博士后研究员。2014年至2018年任职同济大学特聘研究员，博士生导师。2018年至今任陕西师范大学特聘教授，博士生导师。2016年获上海市浦江人才计划。主持2项国家自然科学基金项目，1项上海市自然科学基金项目和1项加拿大科研基金项目。主要研究微分动力系统及生物数学方面的应用。已发表SCI收录论文30余篇，分别发表在J. Math. Pures Appl., Journal of Differential Equations, SIAM Journal of Applied Mathematics, Nonlinearity, Journal of Dynamics and Differential Equations, Journal of Mathematical Biology，Bulletin of Mathematical Biology等SCI期刊上。