Epidemiological Control of COVID-19 Through the Theory of Variable Structure and Sliding Mode Systems

Santos, Débora Marques Lopes; Rodrigues, Victor Hugo Pereira; Oliveira, Tiago Roux

This paper proposes a new mathematical model called SIRDQ considering control laws for the government actions in order to reduce the quarantine periods. The proposed control laws guarantee the regulation of the effective number of reproduction to a desired value, which is directly related to the propagation of the epidemic model. We consider two control strategies based on first-order sliding mode and super-twisting algorithm due to its robustness with respect to parametric uncertainties and disturbances, as found in epidemiological models. The stability analysis of the closed-loop system is rigorously presented. Simulations show that the employed control strategies assure better levels of isolation to be adopted.