报告题目：Modeling the impact of awareness programs on the transmission dynamics of dengue and optimal control

报告人：万辉教授（南京师范大学）

报告时间：2023年12月29日下午15:30 - 16:30

报告地点：复杂系统研究所（商学楼五层）

报告人简介：万辉，南京师范大学数学科学学院教授、博士生导师，中国生物数学会理事，美国《数学评论》(Mathematical Reviews)评论员；主要研究方向包括生物与生态数学模型研究、传染病动力学、微分方程与动力系统及其应用等；2009年博士毕业于南京师范大学，导师崔景安教授；2009年至2010年，在加拿大约克大学从事博士后研究工作，导师朱怀平教授；2017年访问美国普渡大学，合作导师冯芝兰教授；在《Journal of Theoretical Biology》、《Bulletin of Mathematical Biology》、《Mathematical Biosciences》、《Discrete and Continuous Dynamical Systems》等国际国内重要刊物上发表论文多篇；主持在研或完成科研项目5项，其中国家自然科学基金天元基金项目1项，国家自然科学基金青年基金项目1项，国家自然科学基金面上项目1项。

报告摘要：In this work, we first propose a mathematical model to study the impact of awareness programs on dengue transmission. The basic reproduction number R0is derived. The existence and stability of equilibria are investigated. The uniform persistence is established when R0 is larger than one. Our results suggest that awareness programs have significant impacts on dengue transmission dynamics although they cannot affect R0 . When R0  is less than one, awareness programs can shorten the prevailing time effectively. When R0 is larger than one, awareness programs may destabilize the unique interior equilibrium and a stable periodic solution appears due to Hopf bifurcation. In particular, we find that the occurrence of Hopf bifurcation depends not only on the intensity of awareness programs but also on the level of R0. Besides, large fluctuations in the number of infected individuals caused by the stable periodic solution may bring pressure on limited medical resources. Therefore, different from intuitive ideas, blindly increasing the intensity of awareness programs is not necessarily conducive to control the transmission of dengue. The decision-making department should decide to adopt different publicity strategies according to the current level of R0. Finally, we consider the optimal control problem of the model and find the optimal control strategy corresponding to awareness programs by Pontryagin’s Maximum Principle. The results manifest that the optimal control strategy can effectively mitigate the transmission of dengue.

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