Adaptive Backstepping Control of two-group SEIAR Epidemic Model in the Presence of Input Saturation and External Disturbances

This paper proposes a robust adaptive control strategy based on integral backstepping for nonlinear epidemic systems under input saturation, model uncertainties, and external disturbances. The proposed method combines backstepping for systematic control design, sliding mode control for robustness, and adaptive control to handle unknown parameters dynamically. To address input saturation, a novel auxiliary design system combined with Nussbaum gain functions is introduced, mitigating saturation effects and ensuring stability. The epidemic dynamics are modeled using the SEIAR framework, which includes Susceptible, Exposed, Infected, Asymptomatic, and Recovered populations. The controller employs three control inputs—vaccination, social distancing measures, and treatment of infected individuals—to drive the populations of susceptible, exposed, and infected individuals to zero. Simulation results demonstrate that the proposed control scheme effectively eliminates infections, ensuring that the recovered population converges to the total population size. The method provides precise trajectory tracking despite input constraints and external disturbances. These findings highlight its strong potential for real-world epidemic management, particularly in resource-limited and uncertain environments.