Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples
Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples
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DOI：
10.1103/physreve.104.024412
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发表时间：
2021-08-12
影响因子：
2.4
通讯作者：
Kevrekidis, G. A.
中科院分区：
文献类型：
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作者：
Kevrekidis, P. G.;Cuevas-Maraver, J.;Kevrekidis, G. A.
我们研究了新冠肺炎在两个地区爆发的空间模型：西班牙安达卢西亚自治社区和希腊大陆。我们从零维(0D；常-微分方程式水平)区隔流行病学模型(SEAIHR模型)开始，该模型由易感人群、暴露人群、无症状人群、(有症状)感染人群、住院人群、康复人群和死亡人群组成。我们强调病毒潜伏期的重要性(反映在暴露人群中)和无症状人群的关键作用。我们通过将预测与累计感染人数和总死亡人数进行比较来优化两个地区的模型参数，通过最小化预测和观测数据之间的差异的L(2)范数，我们发现报告的数据是最可靠的。我们考虑了模型预测对模型参数和初始条件合理变化的敏感性，并讨论了参数可辨识性问题。我们通过病毒传播率随时间的变化来模拟检疫前和检疫后疫情的演变，病毒传播率是对遏制措施的反应。随后，以反应扩散方程的形式发展了0D模型的空间分布版本。我们认为，在最初的局部播种感染后，其传播是由无症状和症状感染人群的扩散(和0D模型“反应”)控制的，这些扩散和反应随着实施的限制措施而减少。我们插入了这两个区域的地图，并将人口密度数据导入到有限元软件包COMSOL MultiPhysitics(R)中，随后使用该软件包对模型偏微分方程组进行数值求解。在讨论如何使0D模型适应这种空间环境时，我们表明这些模型在捕捉两个地区大流行的良好混合的零维描述和空间扩展方面具有巨大的潜力。还探讨了模型假设对未来工作的潜在改进脉络。
We examine the spatial modeling of the outbreak of COVID-19 in two regions: the autonomous community of Andalusia in Spain and the mainland of Greece. We start with a zero-dimensional (0D; ordinary-differential-equation-level) compartmental epidemiological model consisting of Susceptible, Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, and deceased populations (SEAIHR model). We emphasize the importance of the viral latent period (reflected in the exposed population) and the key role of an asymptomatic population. We optimize model parameters for both regions by comparing predictions to the cumulative number of infected and total number of deaths, the reported data we found to be most reliable, via minimizing the l(2) norm of the difference between predictions and observed data. We consider the sensitivity of model predictions on reasonable variations of model parameters and initial conditions, and we address issues of parameter identifiability. We model both the prequarantine and postquarantine evolution of the epidemic by a time-dependent change of the viral transmission rates that arises in response to containment measures. Subsequently, a spatially distributed version of the 0D model in the form of reaction-diffusion equations is developed. We consider that, after an initial localized seeding of the infection, its spread is governed by the diffusion (and 0D model "reactions") of the asymptomatic and symptomatically infected populations, which decrease with the imposed restrictive measures. We inserted the maps of the two regions, and we imported population-density data into the finite-element software package COMSOL Multiphysics (R), which was subsequently used to numerically solve the model partial differential equations. Upon discussing how to adapt the 0D model to this spatial setting, we show that these models bear significant potential towards capturing both the well-mixed, zero-dimensional description and the spatial expansion of the pandemic in the two regions. Veins of potential refinement of the model assumptions towards future work are also explored.