SIR-PID: A Proportional-Integral-Derivative Controller for COVID-19 Outbreak Containment

Rossi, N.; Ianni, A.

Ongoing social restrictions, as distancing and lockdown, adopted by many countries for contrasting the COVID-19 epidemic spread, try to find a trade-off between induced economic crisis, healthcare system collapse and costs in terms of human lives. Applying and removing restrictions on a system with uncontrollable inertia, as represented by an epidemic outbreak, may create critical instabilities, overshoots and strong oscillations of infected people around the desirable set-point, defined as the maximum number of hospitalizations acceptable by a given healthcare system. A good understanding of the system reaction to a change of the input control variable can be reasonably achieved using a proportional-integral-derivative controller, widely used in technological applications. In this paper we make use of this basic control theory for understanding the reaction of COVID-19 propagation to social restrictions and for exploiting a very known technology to reduce the epidemic damages through the correct tuning of the containment policy.