We investigate the spatiotemporal dynamics and control of an epidemic using a partial differential equation (PDE) based Susceptible–Latent–Infected–Recovered (SLIR) model. We first validate the model using empirical $COVID$–19 data corresponding to a period of 45 days from the state of Ohio, United States. Upon optimizing the model parameters in the learning phase of the analysis using actual infection data from a period of the first 30 days, we then find that the model output closely tracks the actual data for the next 15 days. Next, we introduce a control input into the model to represent the Non-Pharmaceutical Intervention of social distancing. Implementing the control using two distinct schemes, we find that in both cases the control input is able to significantly mitigate the infection spread. In addition to opening a novel pathway towards the characterization, analysis and implementation of Non-Pharmaceutical Interventions across multiple geographical scales using Control frameworks, our results highlight the importance of first-principles based PDE models in understanding the spatiotemporal dynamics of epidemics triggered by novel pathogens.

我们使用基于偏微分方程 (PDE) 的易感-潜在-感染-恢复 (SLIR) 模型来研究流行病的时空动态和控制。我们首先使用经验验证模型$C○五我D$–19 数据对应于来自美国俄亥俄州的 45 天期间。在使用前 30 天的实际感染数据优化分析学习阶段的模型参数后，我们发现模型输出密切跟踪接下来 15 天的实际数据。接下来，我们在模型中引入一个控制输入来表示社交距离的非药物干预。使用两种不同的方案实施控制，我们发现在这两种情况下，控制输入都能够显着减轻感染传播。除了使用控制框架为跨多个地理尺度的非药物干预的表征、分析和实施开辟一条新途径外，