ABSTRACT

In this paper, we investigate the traveling wave solutions of diffusive disease models with a general incidence rate, nonlocal interaction and transmission delay. We prove that a positive traveling wave solution exists if the wave speed is bigger than a threshold value and does not exist if the wave speed is smaller than this value. We also investigate the dependence of this critical wave speed on the diffusion coefficient of the infected population and average transmission delay. In the critical case when the wave speed equals the threshold value, we obtain the existence of nontrivial traveling waves without nonlocal interaction or transmission delay. We further develop numerical methods to simulate traveling wave solutions and estimate disease propagation speed. It is observed from numerical simulations that disease propagation speed is strictly less than the critical wave speed.

摘要

在本文中，我们研究了具有一般发病率、非局部相互作用和传输延迟的扩散性疾病模型的行波解。我们证明如果波速大于阈值则存在正行波解，如果波速小于该值则不存在正行波解。我们还研究了该临界波速对受感染人群扩散系数和平均传输延迟的依赖性。在波速等于阈值的临界情况下，我们获得了不存在非局部相互作用或传输延迟的非平凡行波。我们进一步开发数值方法来模拟行波解和估计疾病传播速度。