SIAM Journal on Applied Mathematics, Volume 80, Issue 3, Page 1247-1271, January 2020.
The effect of diffusion rates on the basic reproduction number of a general compartmental reaction-diffusion epidemic model in a heterogeneous environment is considered. It is shown that when the diffusion rates tend to zero, the limit of the basic reproduction number is the maximum value of the local reproduction number on the spatial domain. On the other hand, when the diffusion rates tend to infinity, the basic reproduction number tends to the spectral radius of the “average” next generation matrix. These asymptotic limits of basic reproduction number hold for a class of general spatially heterogeneous compartmental epidemic models, and they are applied to a wide variety of examples.

中文翻译：

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非均质环境中流行病基本繁殖数的渐近分布

SIAM应用数学杂志，第80卷，第3期，第1247-1271页，2020年1月
。考虑了异质环境中扩散速率对一般隔室反应扩散模型的基本繁殖数量的影响。可以看出，当扩散率趋于零时，基本再现次数的极限是空间域上局部再现次数的最大值。另一方面，当扩散率趋于无穷大时，基本再现数趋向于“平均”下一代矩阵的光谱半径。基本繁殖数量的这些渐近极限适用于一类一般的空间异质隔室流行病模型，并且它们被应用于各种各样的例子。