Fractional order sliding mode control for vaccination in epidemic systems

SEIR model has been utilized to represent the behavior of various epidemic systems. Several kinds of diseases have been proposed and studied based on this model. The design of the vaccine law or policies to regulate the infection system is one of the important areas of studies. The vaccine policies can be determined based on the knowledge of the nonlinear control theory as seen in literature. The sliding mode control (SMC) method is one of the successful methods, which has been employed in various engineering and biological systems. Furthermore, the method has been developed as the fractional order sliding mode control (FOSMC) method, which has drawn interests of many researchers as proposed in literature. Thus, the study of the FOSMC method employing on the SEIR model was conducted to investigate the performance of the FOSMC method by simulation. Then, the controlled system by the FOSMC method was simulated and compared with that of the conventional SMC method. The simulation results showed that using the FOSMC method could manipulate all state variables to the desired reference signals with the faster convergence rate compared to the conventional SMC method. Therefore, the control of the epidemic system described by SEIR model with vaccination can be suitably obtained by using the fractional order sliding mode control method.