Control of COVID-19 Outbreak for Preventing Collapse of Healthcare Capacity

Mathematical models are a powerful tool to study and predict he dynamic behaviour of processes and systems, physical and biological, as well as to assist in decision making, and to design control systems. In the case of the coronavirus pandemic, COVID-19, its dynamic behaviour is generally in line with traditional models proposed, such as the Susceptible-Infected-Recovered (SIR) or the (SEIR), that includes the Exposed, which are useful tools to estimate the spread of the virus, the number of infected, the recovered individuals, and amount of deaths, as well as finding the outbreak start, the rise time, the peak time and overshoot, and fading stage. In COVID-19, the knowledge of the maximum peak and its delay time are important to prepare the healthcare system capacity, and therefore have enough intensive care units (ICUs) with automatic ventilators. In this work, a simple but robust control strategy for sequencing social distancing and confinement is proposed. The main control objective is to control the COVID-19 outbreak to avoid the collapse of the healthcare system and saturation of ICUs capacity, generating a control action sequence of social distancing and confinement such as the number of new cases requiring ICU is below a threshold set-point. An On-Off control action is analysed, and a Proportional-Integral-Derivative (PID) controller is proposed to generate a public policy (a sequence of decisions) applied once a week or every fortnight. Simulation results showing the practical feasibility and performance of the approach are given, and somehow supporting and validating strategies carried out by many healthcare teams from many countries.