报告题目：Time-Switched Differential Equations Models for Mosquito Population Suppression

报告人：郑波 (广州大学)

报告时间：2023年5月12号15:00-16:30

报告地点：复杂系统研究所 (腾讯会议)

报告人简介：郑波，博士，教授，博士生导师。主要从事常微分方程、泛函微分方程及生物数学模型的理论与应用研究，在《Nature》、《SIAM Journal of Applied Mathematics》 、《Journal of Mathematical Biology》、《中国科学》、《Journal of Differential Equations》《Journal of Dynamics and Differential Equations》《Ecological Modelling》等国际国内重要刊物上发表论文40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。获得首届秦元勋青年数学奖。

摘要：Releasing Wolbachia-infected male mosquitoes to suppress wild female mosquitoes through cytoplasmic incompatibility has shown great promise in controlling and preventing mosquito-borne diseases. Based on the practical release strategies implemented in Guangzhou. We proposed a new modeling idea that only takes sexually active male mosquitoes into consideration. Under impulsive and periodic release strategies, the models read as time-switched differential equation models. The switch brings rich dynamics, including the existence of a unique periodic solution or exactly two periodic solutions, which are proved by using the qualitative property of the Poincare map. Sufficient conditions are also obtained for determining the stability of the periodic solutions.