Vaziry Arvin, Kolokolnikov T, Kevrekidis P G
Department of Mathematics and Statistics, Dalhousie University Halifax, Nova Scotia, Canada B3H3J5.
Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA.
R Soc Open Sci. 2022 Oct 5;9(10):220064. doi: 10.1098/rsos.220064. eCollection 2022 Oct.
We present a simple model for the spread of an infection that incorporates spatial variability in population density. Starting from first-principle considerations, we explore how a novel partial differential equation with state-dependent diffusion can be obtained. This model exhibits higher infection rates in the areas of higher population density-a feature that we argue to be consistent with epidemiological observations. The model also exhibits an infection wave, the speed of which varies with population density. In addition, we demonstrate the possibility that an infection can 'jump' (i.e. tunnel) across areas of low population density towards areas of high population density. We briefly touch upon the data reported for coronavirus spread in the Canadian province of Nova Scotia as a case example with a number of qualitatively similar features as our model. Lastly, we propose a number of generalizations of the model towards future studies.
我们提出了一个用于传染病传播的简单模型，该模型纳入了人口密度的空间变异性。从第一性原理出发，我们探索了如何得到一个具有状态依赖扩散的新型偏微分方程。该模型在人口密度较高的区域表现出更高的感染率——我们认为这一特征与流行病学观察结果一致。该模型还表现出感染波，其速度随人口密度而变化。此外，我们证明了感染有可能“跨越”（即穿越）低人口密度区域向高人口密度区域传播。我们简要提及了加拿大新斯科舍省报告的冠状病毒传播数据，作为一个与我们模型具有一些定性相似特征的案例。最后，我们针对未来研究提出了该模型的一些推广方向。
