We present an early version of a Susceptible–Exposed–Infected–Recovered–Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The model describes the spatio-temporal spread of the COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features. To test the model, we compare the outputs generated by a finite-element solver with measured data over the Italian region of Lombardy, which has been heavily impacted by this crisis between February and April 2020. Our results show a strong qualitative agreement between the simulated forecast of the spatio-temporal COVID-19 spread in Lombardy and epidemiological data collected at the municipality level. Additional simulations exploring alternative scenarios for the relaxation of lockdown restrictions suggest that reopening strategies should account for local population densities and the specific dynamics of the contagion. Thus, we argue that data-driven simulations of our model could ultimately inform health authorities to design effective pandemic-arresting measures and anticipate the geographical allocation of crucial medical resources.

我们提出了基于偏微分方程和异质扩散模型的易感-暴露-感染-康复-死亡 (SEIRD) 数学模型的早期版本。该模型描述了 COVID-19 大流行的时空传播，旨在捕捉基于人类习惯和地理特征的动态。为了测试该模型，我们将有限元求解器生成的输出与意大利伦巴第地区的测量数据进行了比较，该地区在 2020 年 2 月至 4 月期间受到了这场危机的严重影响。我们的结果表明，模拟结果之间存在很强的定性一致性对伦巴第大区 COVID-19 时空传播的预测以及在市一级收集的流行病学数据。探索放松封锁限制的替代方案的其他模拟表明，重新开放策略应考虑当地人口密度和传染病的具体动态。因此，我们认为，我们的模型的数据驱动模拟最终可以告知卫生当局设计有效的大流行遏制措施，并预测关键医疗资源的地理分配。