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.

Analysis of epidemic spread dynamics using a PDE model and COVID-19 data from Hamilton County OH USA.

We study the spatiotemporal dynamics of an epidemic spread using a compartmentalized PDE model. The model is validated using COVID-19 data from Hamilton County, Ohio, USA. The model parameters are estimated using a month of recorded data and then used to forecast the infection spread over the next ten days. The model is able to accurately estimate the key dynamic characteristics of COVID-19 spread in the county. Additionally, a stability analysis indicates that the model is robust to disturbances and perturbations which, for instance, could be used to represent the effects of super spreader events. We also use the modeling framework to analyse and discuss the impact of Non-pharmaceutical interventions (NPIs) for mitigation of infection. Our results suggest that such models can yield useful short and medium term predictive characterization of an epidemic spread in a restricted geographical region and also help formulate effective NPIs for mitigation. The results also signify the importance of further research into the accurate analytical representation of specific NPIs and hence their dampening effects on an infection spread.