Isolation control for sir epidemic model with bilinear Incidence Rates

An isolation control of SIR epidemic model are proposed and analyzed, which not only isolate infective, but also isolate susceptible. In order to calculate the optimal values of the isolate rates, 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 optimally. The simulation result shows the method is viable and effectively.