The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.

2020 年 COVID-19 的爆发导致人们对传染病数学建模的兴趣激增。这种模型通常被定义为隔间模型，其中研究的人群根据定性特征分为隔间，对隔间转移的性质和速率有不同的假设。尽管最常被表述为常微分方程模型，其中隔间仅取决于时间，但最近的工作也集中在偏微分方程 (PDE) 模型上，将流行病在空间中的变化纳入其中。在易感、感染、暴露、恢复和死亡框架内对 PDE 模型进行的此类研究已在重现 COVID-19 传染动态方面取得了可喜的结果。在本文中，我们通过在比其他类似研究更长时间内考虑不同几何形状来评估该建模框架的稳健性。我们首先通过重现之前在意大利伦巴第大区显示的结果来验证我们的代码。然后，我们将重点放在美国乔治亚州和巴西里约热内卢州，这是世界上受影响最严重的地区之一。我们的结果表明，跨主要地区和三个不同大陆的所有地区在时间和空间上与现实世界的流行病学数据有很好的一致性，这表明建模方法既有效又稳健。乔治亚州和巴西里约热内卢州，这是世界上受影响最严重的地区之一。我们的结果表明，跨主要地区和三个不同大陆的所有地区在时间和空间上与现实世界的流行病学数据有很好的一致性，这表明建模方法既有效又稳健。乔治亚州和巴西里约热内卢州，这是世界上受影响最严重的地区之一。我们的结果表明，跨主要地区和三个不同大陆的所有地区在时间和空间上与现实世界的流行病学数据有很好的一致性，这表明建模方法既有效又稳健。