Spreading Speeds and Traveling Wave Solutions of Diffusive Vector-Borne Disease Models without Monotonicity
报告人：林国（兰州大学 ）
时间：2022.5.13上午10：00-11：00
地点：腾讯会议，415 246 745
摘要：We investigate the propagation dynamics of diffusive vector-borne disease models in the whole space, which models the spatial expansion of the infected hosts and infected vectors. Due to the lack of monotonicity, the comparison principle cannot be directly applied to this system. We establish the spreading speed and minimal wave speed when the basic reproduction number of the corresponding kinetic system is larger than one. The spreading speed is mainly estimated by the uniform persistence argument and generalized principal eigenvalue. We further show that solutions locally uniformly converge to the positive equilibrium by employing two auxiliary monotone systems. Moreover, it is proven that the spreading speed is the minimal wave speed of traveling wave solutions. In particular, the uniqueness and monotonicity of traveling waves are obtained. When the basic reproduction number of the corresponding kinetic system is not larger than one, it is shown that solutions approach to the disease-free equilibrium uniformly and there is no traveling wave solutions. This talk is based on the work joint with Dr. Xinjian Wang and Prof. Shigui Ruan.
专家简介：林国,毕业于兰州大学并获得理学学士、理学博士学位，现为兰州大学数学与统计学院教授，应用数学专业博士生导师。主要研究方向为微分方程与动力系统，主要研究兴趣为一些非合作扩散模型的空间传播理论。在刻画耦合系统的非合作性、非线性部分的非平凡效果中取得一些有特色的的研究成果。相关研究工作总结发表于50余篇学术论文中，并主持国家自然科学基金等项目。
