数学与统计学院学术预告两则

报告题目1：Bifurcation Analysis of a Mosquito Population Model with a Saturated Release Rate of Sterile Mosquitoes

报告人：黄继才教授

报告时间：2020年10月24日（周六）8:30—10:00

报告地点：腾讯会议ID: 601 661 207

报告摘要：Release sterile mosquitoes is a method of mosquito control using area-wide inundative releases of sterile male mosquitoes to reduce reproduction in a field population of wild mosquitoes. In this talk, we consider a mosquito population model with a nonlinear saturated release rate of sterile mosquitoes and study the complex dynamics and bifurcations of the model by performing bifurcation analysis. It is shown that there are a weak focus of multiplicity 3 and a nilpotent cusp of codimension 4 for various parameter values and the model exhibits Hopf bifurcation of codimension 3 and Bogdanov-Takens bifurcation of codimension 2 as the parameter values vary. Our analysis also shows that there exists a critical release rate of sterile mosquitoes, above which the mosquitoes population can be eliminated and below which the interacting sterile and wild mosquitoes will coexist in the form of multiple periodic oscillations or steady states for some initial populations.

个人简介：黄继才，华中师范大学教授、博士生导师。1999年、2002年分别本科、硕士毕业于华中师范大学数学系，2005年获得中国科学院数学与系统科学研究院数学所博士学位。主要从事常微分方程定性理论、分支理论及其应用研究。在J. Differential Equations、SIAM J. Appl. Math.、SIAM J. Appl. Dyn. Syst.、Bull. Math. Biol. 等期刊发表学术论文三十多篇。主持国家自然科学基金4项。

报告题目2：Effects of Human Movement on Infection Size

报告人：高道舟教授

报告时间：2020年10月24日（周六）10:00—11:30

报告地点：腾讯会议ID: 601 661 207

报告摘要：In this talk, based on an SIS patch model with standard incidence, we first show that the basic reproduction number of is either strictly decreasing and strictly convex with respect to the diffusion coefficient of infected subpopulation if the patch reproduction numbers of at least two patches in isolation are distinct or constant otherwise. Biologically, it means that fast diffusion of the infected people reduces the risk of infection. This completely solves and generalizes a conjecture by Allen et al. (SIAM J Appl Math, 67: 1283-1309, 2007). Then we give some general results on the number of infections over all patches and disease prevalence in each patch at the endemic equilibrium. For the two-patch submodel, a complete classification of the model parameter space as to whether dispersal is beneficial or detrimental to disease control is obtained. Particularly, fast diffusion decreases the basic reproduction number but may increase the total infection size, highlighting the necessity of evaluating control measures with other quantities besides the basic reproduction number.

个人简介：高道舟，上海师范大学数学系教授、博士生导师。2012年5月获得迈阿密大学博士学位。2012/06-2015/11，在加州大学旧金山分校（UCSF）从事博士后研究，2015年入选上海市特聘教授（东方学者）。主要研究领域为数学传染病学和种群生态学，在SIAM J Appl Math, J Math Biol, Proc Amer Math Soc, Am J Trop Med Hyg, Bull Math Biol, Math Biosci, Sci Rep等期刊发表学术论文40余篇，主持国家自然科学基金项目2项，国家自然科学基金通讯评审专家，研究成果被CTV（加拿大电视网）、O Globo（巴西《环球报》）、El Comercio（秘鲁《商报》）、ScienceDaily、SIAM news、果壳网等媒体所报道。担任SCI期刊Math Biosci Eng编委和30多份国际期刊审稿人，曾受邀并获全额资助参加世界卫生组织专家评审会议。

欢迎广大师生参加！