Optimal synthesize control for an SIR epidemic model

This paper considers the synthesize control for an SIR epidemic model with standard incidence rate, which not only isolate infective and susceptible, but also immunize susceptible. The threshold of the models system is analyzed. In order to calculate the optimal values of the isolate rate and immunize rate, it constructs a performance index that is calculated explicitly as an algebraic function of the controller parameters by solving Zubov´s partial differential equation, and standard optimization techniques are employed. The ultimate aim is to eliminate the disease. The simulation result shows the method is viable and effectively.