论文标题
非本地扩散的流行病模型中的空间传播：初始数据和分散的影响
Spatial Propagation in an Epidemic Model with Nonlocal Diffusion: the Influences of Initial Data and Dispersals
论文作者
论文摘要
本文研究了一个非局部分散的流行病模型。我们专注于初始数据和非局部分散对其空间传播的影响。在这里，当流行病爆发和非局部分散时，初始数据代表了传染剂和传染性人口的空间浓度，这意味着其扩散策略。考虑了两种类型的初始数据衰减，将指数型或更快地考虑到零。对于第一种类型，我们表明传播速度是两个常数，其符号随着某些元素的数量而变化。此外，我们发现了一个有趣的现象：非局部分散的不对称性会影响溶液的传播方向和稳态的稳定性。对于第二种类型，我们表明，相对于初始数据的指数衰减率，传播速度正在降低，此外，其最小值与第一种类型的扩散速度相吻合。此外，我们给出一些有关行驶波解决方案不存在的结果和溶液的单调特性。最后，提出了一些应用程序来说明理论结果。
This paper studies an epidemic model with nonlocal dispersals. We focus on the influences of initial data and nonlocal dispersals on its spatial propagation. Here the initial data stand for the spatial concentrations of infectious agent and infectious human population when the epidemic breaks out and the nonlocal dispersals mean their diffusion strategies. Two types of initial data decaying to zero exponentially or faster are considered. For the first type, we show that the spreading speeds are two constants whose signs change with the number of elements in some set. Moreover, we find an interesting phenomenon: the asymmetry of nonlocal dispersals can influence the propagating directions of solutions and the stability of steady states. For the second type, we show that the spreading speed is decreasing with respect to the exponentially decaying rate of initial data, and further, its minimum value coincides with the spreading speed for the first type. In addition, we give some results about the nonexistence of traveling wave solutions and the monotone property of solutions. Finally, some applications are presented to illustrate the theoretical results.
