We investigate spreading properties of solutions for a spatially distributed system of equations modelling the evolutionary epidemiology of plant-pathogen interactions. In this work the mutation process is described using a non-local convolution operator in the phenotype space. Initially equipped with a localized amount of infection, we prove that spreading occurs with a definite spreading speed that coincides with the minimal speed of the travelling wave solutions discussed in [1]. Moreover, the solution of the Cauchy problem asymptotically converges to some specific function for which the moving frame variable and the phenotype one are separated.

中文翻译：

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非局部进化流行系统的渐近传播速度

我们研究了空间分布方程组的解的传播特性，该方程组模拟了植物-病原体相互作用的进化流行病学。在这项工作中，突变过程是使用表型空间中的非局部卷积算子来描述的。最初配备了局部感染量，我们证明了传播以一个确定的传播速度发生，该速度与[中讨论的行波解决方案的最小速度一致]1]。此外，柯西问题的解渐近收敛到某个特定的函数，对于该函数，移动坐标系变量和表型变量是分开的。