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

Area of Science:

• Epidemiology
• Control Theory
• Mathematical Modeling

Background:

• The COVID-19 pandemic necessitates effective control strategies, with vaccination being paramount.
• Existing models require advanced control techniques to manage disease spread and system uncertainties.
• The susceptible, exposed, infectious, and recovered (SEIR) model is a key tool for understanding epidemic dynamics.

Purpose of the Study:

• To develop a robust vaccination control scheme for COVID-19 using a modified SEIR model.
• To introduce a novel active disturbance rejection control (ADRC) strategy for enhanced epidemic management.
• To improve the estimation of system states and disturbances in epidemic models.

Main Methods:

• A modified SEIR model incorporating vaccination control.
• A novel Active Disturbance Rejection Control (ADRC) structure with an embedded Tracking Differentiator (TD).
• Development of Nonlinear PID and Super Twisting Sliding Mode (STC-SM) controllers within a Nonlinear State Error Feedback (NLSEF) framework.
• Introduction of a Nonlinear Extended State Observer (NLESO) for state and disturbance estimation.

Main Results:

• The proposed ADRC-based vaccination control scheme demonstrated excellent performance in simulations.
• The novel ADRC structure effectively rejected disturbances affecting the COVID-19 SEIR model.
• The NLESO accurately estimated system states and total disturbances, enhancing control precision.
• The advanced nonlinear controllers outperformed conventional ADRC methods.

Conclusions:

• The developed ADRC strategy offers a promising approach for effective COVID-19 vaccination control.
• The integration of novel nonlinear control techniques and observers significantly improves epidemic modeling and management.
• This research contributes to the advancement of mathematical and control-theoretic methods for infectious disease outbreaks.