报告一题目：Switching discrete models based on environmental change

报告人：庾建设

报告时间：2023年06月30日（周五）8:00-10:00

报告地点：数学楼315会议室

报告摘要：There is currently great interest in releasing Wolbachia-infected Aedes mosquitoes worldwide to replace wild ones and mitigate arbovirus transmission. For Wolbachia establishment in natural field populations, we should consider the impact of environmental heterogeneity. To the end, we develop a discrete periodic switching model to characterize the Wolbachia spread dynamics in mosquito populations with non-overlapping generations, where the environmental change is periodic. The introduction threshold of Wolbachia-infected mosquitoes that must be surpassed for Wolbachia establishment is located, together with the location of that infection will ultimately reach. When the environments switch periodically, we find that the introduction threshold becomes an unstable periodic solution, and the infection will ultimately reach a stable periodic solution when maternal transmission is imperfect. Our model not only includes all the existing work since 1959, but also raises some theoretical questions that need further investigations.

报告人简介：庾建设，广州大学教授，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。庾建设教授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，发表多篇SCI学术论文。

报告二题目：Mathematical modeling of interactive wild and transgenic sterile mosquitoes

报告人：李佳

报告时间：2023年06月30日（周五）10:00-12:00

报告地点：数学楼315会议室

报告摘要：

To more effectively control mosquitoes, a modified genetic sterile insect technique (SIT) is used and strategies of releasing mosquitoes carrying a dominant lethal (RIDL) are proposed and developed. There are four strategies implemented, including early acting bisex (EBS) lethality, late acting bisex (LBS) lethality, early acting female-killing (EFK) lethality, and late acting female-killing (EFK) lethality.Inthistalk, we introduce homogeneous mosquito population models based on different differential equations and incorporate the four transgenic SIT implementations in the models, respectively. Wediscussthe model dynamics and compare these different release strategies.

报告人简介：

李佳，美国阿拉巴马大学(汉斯维尔校区)教授，Mathematical Biology and Engineering、Journal of Biological Dynamics、Annuals of Differential Equations、Journal of Mathematics and Computer Science等杂志副主编。主要从事于动力系统、数学建模、人口动力学、数学生态学、数学传染病学及数学生态毒理学等方面的研究，在SCI源期刊上发表论文80余篇，获得多项美国国家科学基金项目，组织和参与多次有关生物数学方面的国际学术会议，具有较高的国际影响力。

报告三题目：Existence and stability of periodic solutions for a mosquito population suppression model with time delay

报告人：郑波

报告时间：2023年06月30日（周五）12:00-14:00

报告地点：数学楼315会议室

报告摘要：

By including the maturation period τ wild mosquitoes, we develop a delay differential equation model to study the suppression of wild mosquito population by releasing Wolbachia-infected male mosquitoes with a release period τ=mT where m is a positive integer. We obtain sufficient conditions for non-existence of periodic solutions and existence of a unique or exactly two periodic solutions by taking the initial function as a solution to the delay-free model. We prove the global asymptotic stability of the unique periodic solution, and that one periodic solution is stable and the other is unstable when there are two periodic solutions.

报告人简介：

郑波，博士，广州大学教授，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 ofDifferential Equations》、《Journalof Dynamics and Differential Equations》、《Journal of Theoretical Biology》、《Theoretical Population Biology》等国际国内重要刊物上发表论文30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。