报 告 人：庾建设 教授
报告题目：Switching ODE models for mosquito population suppression
庾建设，教授，博士生导师，原广州大学校长。国家杰出青年基金获得者，国家有突出贡献的中青年专家，全国教育系统劳动模范。主要从事微分方程动力系统、差分方程及生物数学模型的理论与应用研究，在《Nature》、《SIAM J. Math. Anal.》、《SIAM J.Appl.Math.》、《J.Math. Biol.》、《J.Diff.Equa.》、《Math. Biosciences》、《Bull.Math.Biol.》等重要期刊上发表了一系列学术论文，是多个SCI期刊的编委。
The release of Wolbachia-infected mosquitoes in 2016 and 2017 enabled near-elimination of the sole dengue vector Aedes albopictus on Shazai and Dadaosha islands in Guangzhou. Mathematical analysis may offer guidance in designing effective mass release strategies for the area-wide application of this Wolbachia incompatible and sterile insect technique in the future. The two most crucial questions in designing release strategies are how often and in what amount should Wolbachiainfected mosquitoes be released in order to guarantee the success of population suppression. In this talk, I will introduce our recent works on answering the two questions, we may refer to J. Differ. Equations, 2020, 269(7): 6193-6215; 269(12): 10395-10415; SIAM J. Appl. Math., 2021, 81(2): 718-740. By treating the released mosquitoes as a given function, we proposed mosquito suppression models consisting of two sub-equations switching each other. An almost complete characterization of interactive dynamics of wild and released mosquitoes are offered, including the global asymptotic stability of zero solution and the exact number of periodic solutions of these models. It is well known that to obtain existence and also uniqueness conditions for periodic solutions are mathematically challenging for many dynamical systems and there are few such results existed. We hope the methods and techniques used in these three papers can be usefully applied to other model analysis as well.