题目：Traveling Waves in Epidemic Models: Diffusion and Mon-monotonicity
报告人：汪翔升 教授（University of Louisiana at Lafayette）
时间：5月15日（星期一），上午 10:00-11:00
地点：致远楼102室
汪翔升，美国University of Louisiana at Lafayette大学助理教授，主要研究渐近分析、微分方程、动力系统和生物数学。迄今为止已在Journal of Differential Equations、Journal of Dynamics and Differential Equations、Journal of Theoretical Biology、Physics Review E、Proceedings of American Mathematical Society、Statistica Sinica等国际期刊上发表学术论文近三十篇。
报告摘要
We study the existence and nonexistence of traveling waves of diffusive epidemic models. The model systems are non-monotone because the disease models exhibit a predator-prey mechanism. We will construct a suitable convex set in a weighted function space, and then apply Schauder fixed point theorem. It turns out that the basic reproduction number of the corresponding ordinary differential equations plays an important role in the existence theory of traveling waves. Moreover, the critical wave speed can be explicitly obtained in terms of the model parameters. We will also prove that the positive traveling wave solution does not exist if the basic reproduction number is no more than one, or the wave speed is less than the critical value.
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