Preview tracking control of the SIR Model with saturation incidence rate

In this paper, considering the regional population changes, a SIR model with saturation incidence rate was constructed for cholera, hepatitis B and other infectious diseases with high infectivity but low radical cure rate. The asymptotic stability of the equilibrium point was analyzed by Jury criterion. On this basis, an augmented error system is constructed for the model by using the preview control method, and a corresponding state feedback preview controller is designed. By using the Lyapunov stability theory, sufficient conditions for the asymptotic stability of the closed-loop system are obtained so that the model can be stabilized in a finite time and the spread of infectious diseases can be controlled. Finally, the effectiveness of the proposed method is verified by numerical simulation.