Non-Pharmaceutical Interventions as Controls to mitigate the spread of epidemics: An analysis using a spatiotemporal PDE model and COVID–19 data

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.