Mathematical Modeling and Control of COVID-19 Using Super Twisting Sliding Mode and Nonlinear Techniques

Abstract

Since the outbreak of the COVID-19 epidemic, several control strategies have been proposed. The rapid spread of COVID-19 globally, allied with the fact that COVID-19 is a serious threat to people's health and life, motivated many researchers around the world to investigate new methods and techniques to control its spread and offer treatment. Currently, the most effective approach to containing SARS-CoV-2 (COVID-19) and minimizing its impact on education and the economy remains a vaccination control strategy, however. In this paper, a modified version of the susceptible, exposed, infectious, and recovered (SEIR) model using vaccination control with a novel construct of active disturbance rejection control (ADRC) is thus used to generate a proper vaccination control scheme by rejecting those disturbances that might possibly affect the system. For the COVID-19 system, which has a unit relative degree, a new structure for the ADRC has been introduced by embedding the tracking differentiator (TD) in the control unit to obtain an error signal and its derivative. Two further novel nonlinear controllers, the nonlinear PID and a super twisting sliding mode (STC-SM) were also used with the TD to develop a new version of the nonlinear state error feedback (NLSEF), while a new nonlinear extended state observer (NLESO) was introduced to estimate the system state and total disturbance. The final simulation results show that the proposed methods achieve excellent performance compared to conventional active disturbance rejection controls.