[COLLOQUIUM] Uniqueness and stability of periodic solutions in a delay mosquito population suppression model

Based on the idea that only those sexually active sterile mosquitoes are included in the modeling process, we study the dynamics of the interactive wild and sterile mosquito model with time delay, which consists of three sub-equations. Due to the fact that the maturation period of sterile mosquitoes bred in the lab or mosquito factories is the same time period of wild adults mature from larvae, we particularly assume that the waiting period for two consecutive releases of sterile mosquitoes equals the maturation period of wild mosquitoes, as a new practical sterile mosquito release strategy. We first ingeniously solve the delay model with the initial functions that are solutions of the corresponding equation without delay, referred to as ``good" solutions. Using  ``good'' solution control method, we obtain sufficient and necessary conditions for the trivial solution and a unique periodic solution of the delay model to be globally asymptotically stable, respectively. We provide a numerical example to demonstrate the model dynamics and brief discussions of our findings as well. We are confident that the results obtained and the methods used in this paper can be applied to other similar situations where no existing results and methods are available. This is a joint work with Professor Jia Li.

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       庾建设教授简介：博士生导师，国家杰出基金获得者，国家有突出贡献的中青年专家，国家“百千万人才工程”第一层次、第二层次人选，教育部跨世纪优秀人才，享受政府特殊津贴专家，广州大学应用数学研究中心主任。长期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，先后主持国家自然科学基金项目10余项，其中重点项目3项，数学交叉研究平台项目2项；曾获国家级教学成果一等奖1项，省部级科技成果、教学成果一等奖3项；2020年获得广东省科学技术奖自然科学奖一等奖。近十年来，致力于应用数学的理论研究及其在基因表达、蚊媒传染疾病防控等方面的应用，已在《Nature》、《PLoS Comput. Biol.》、《J. Differential Equations》、《SIAM J. Appl. Math.》、《J. Math. Biol.》、《J. Theor. Biol.》等重要数学、应用数学国际刊物发表论文多篇。