Impacts of Quantifying Social Distancing Measures on Mpc Performance for Sir-Type Systems

Currently, there has been a sharp increase in epidemic control research as a result of recent epidemic outbreaks. Several strategies aiming to minimize the Epidemic Final Size and/or to keep the Infected Peak Prevalence under a specific value were proposed. However, not many strategies focused on analyzing the impact of applying quantified measures instead of continuous control action. This analysis is a crucial aspect since policymakers design their non-pharmaceutical intervention based on a discrete scale of intensity, from mask-wearing to hard lockdown. In this work, we present a quantized-input non-linear Model Predictive Control strategy to manage non-pharmaceutical interventions during an epidemic outbreak. The impact of quantifying the social distancing measure is computed through several simulations based on a COVID-19 epidemic model and considering different quantization levels of the non-pharmaceutical intervention. Finally, the control performance in each quantization level is evaluated with the computation of four epidemic indices.