Optimal Control Approach for the COVID-19 Pandemic in Bahia and Santa Catarina, Brazil

Abstract

The COVID-19 pandemic is the most profound crisis of the twenty-first century. The SARS-CoV-2 virus was first registered in Brazil on March 2020, and its social and economic repercussions have been catastrophic. This paper investigates how to apply model predictive control (MPC) algorithms to plan appropriate social distancing policies that mitigate the pandemic effects. We consider MPC applications for the states of Bahia and Santa Catarina (Brazil), two regions of very different social and cultural demographics. We use Susceptible-Infected-Recovered-Deceased model to describe the pandemic dynamics in these two states, for which parameters are identified using a constrained optimization procedure. The control input to the process is a social isolation guideline passed to the population. Two MPC frameworks are developed and discussed: (a) a centralized approach, which coordinates a single predictive control policy for both states, and (b) a distributed strategy, for which a single MPC problem is solved for each state. We provide a series of simulation results in order to illustrate and compare the results obtained with both these MPC strategies. Discussions are drawn regarding the effectiveness of MPC to guide social distancing measures during pandemics and which approach (distributed, centralized) is more convenient, regarding different conditions.