题目：Mosquito suppression models consisting of two sub-equations switching each other
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 Wolbachia-infected 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 which have been published in the following three papers.
? J. Differ. Equations, 2020, 269(7): 6193-6215.
? J. Differ. Equations, 2020, 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 is 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.
郑波，广州大学数学与信息科学学院教授，博士生导师。近五年来从事生物数学与泛函微分方程的研究，在《Nature》、《SIAM Journal of Applied Mathematics》、《Journal of Mathematical Biology》、《中国科学》、《Journal of Theoretical Biology》、《Theoretical Population Biology》等国际国内重要刊物上发表论文20余篇。先后主持国家自然科学基金4项、广州市教育局3项，2014年入选广东省高校优秀青年教师培育对象，是教育部创新团队“泛函微分方程及相关问题”的骨干成员。2019年获得首届秦元勋青年数学奖。