SIAM Journal on Applied Mathematics, Volume 80, Issue 5, Page 2144-2169, January 2020.
Human movement facilitates the spatial spread of infectious diseases and poses a serious threat to disease prevention and control. A large number of spatial epidemic models have been proposed and analyzed in the past few decades. The vast majority of these studies focus on establishing a threshold result between disease persistence and extinction in terms of the basic reproduction number. In reality, disease eradication is difficult and even impossible for many infectious diseases. Thus, it is crucial to understand how population dispersal affects the total infection size and its distribution across the environment. Based on a susceptible-infected-susceptible patch model with standard incidence, some general results on the number of infections over all patches and disease prevalence in each patch are obtained. For the two-patch submodel, we give a complete classification of the model parameter space as to whether dispersal is beneficial or detrimental to disease control. Particularly, fast diffusion decreases the basic reproduction number but may increase the total infection size, highlighting the necessity of evaluating control measures with other quantities besides the basic reproduction number. Higher infection risk means higher disease prevalence in the two-patch case. However, numerical simulations find that the patch with the highest risk of infection may not have the highest disease prevalence when three or more patches are concerned. Besides spatial heterogeneity and diffusion coefficient, the total infection size is also significantly affected by patch connectivity.

中文翻译：

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分散如何影响感染大小？

SIAM应用数学杂志，第80卷，第5期，第2144-2169页，2020年1月。
人类的运动促进了传染病的空间传播，对疾病的预防和控制构成了严重威胁。在过去的几十年中，已经提出并分析了大量的空间流行病模型。这些研究中的绝大部分集中在根据基本繁殖数量确定疾病持久性与灭绝之间的阈值结果。实际上，对于许多传染病而言，根除疾病是困难的，甚至是不可能的。因此，了解种群扩散如何影响总感染规模及其在环境中的分布至关重要。基于具有标准发病率的易感性感染易感斑块模型，可以获得有关所有斑块的感染数和每个斑块中疾病发生率的一些常规结果。对于两补丁子模型，我们给出了模型参数空间的完整分类，以确定扩散对疾病控制是有益还是有害。特别地，快速扩散减少了基本繁殖数量，但是可能增加了总感染量，突出了需要用基本繁殖数量以外的其他数量来评估控制措施。两次感染病例中较高的感染风险意味着较高的疾病患病率。但是，数值模拟发现，当涉及三个或更多补丁时，具有最高感染风险的补丁可能不会具有最高的患病率。除空间异质性和扩散系数外，总感染大小还受到斑片连接性的显着影响。