Model predictive control for optimal social distancing in a type SIR-switched model

TL;DR

This paper develops a model predictive control approach for social distancing in a switched SIR model, aiming to minimize epidemic size, social restriction duration, and healthcare overload, with simulations demonstrating its effectiveness.

Contribution

It introduces a switching nonlinear model predictive control strategy for optimizing social distancing measures in SIR models, balancing epidemic control and social-economic impacts.

Findings

The control strategy effectively reduces epidemic final size.

It minimizes social restriction duration.

It prevents healthcare system overload during outbreaks.

Abstract

Social distancing strategies have been adopted by governments to manage the COVID-19 pandemic, since the first outbreak began. However, further epidemic waves keep out the return of economic and social activities to their standard levels of intensity. Social distancing interventions based on control theory are needed to consider a formal dynamic characterization of the implemented SIR-type model to avoid unrealistic objectives and prevent further outbreaks. The objective of this work is twofold: to fully understand some dynamical aspects of SIR-type models under control actions (associated with second waves) and, based on it, to propose a switching non-linear model predictive control that optimize the non-pharmaceutical measures strategy. Opposite to other strategies, the objective here is not just to minimize the number of infected individuals at any time, but to minimize the final size of the epidemic while minimizing the time of social restrictions and avoiding the infected prevalence peak to overpass a maximum established by the healthcare system capacity. Simulations illustrate the benefits of the aforementioned proposal.