An application of finite time synergetic control for vaccination in epidemic systems

Vaccination is one of the approaches to control the epidemic system. The concept of the feedback control can be applied to define the epidemic vaccination policy as seen in the literature. Generally, the application can be achieved by using the sliding mode control (SMC). However, the control system can be interfered by chattering phenomena. Hence, it is beneficial to overcome the chattering in the control signal. Another desirable characteristic of the control system is the finite time convergence. To achieve these, this study examined the application of the finite time synergetic control in defining the vaccination policy for the SEIR epidemic system. Here, the vaccination policy was defined based on the FTSC method so that the recovered subpopulation could track the total population. The capability of the FTSC method was presented and evaluated through the simulation of the control epidemic system. Then, the simulation results of both FTSC and SC methods were compared. According to the simulation results, under the FTSC method, the state variable corresponding to recovered subpopulation could track the reference signal accurately as that of the SC method did. Additionally, the convergence rate of the tracking error could be improved by using the FTSC method with appropriate selection of controller parameters. Furthermore, vaccination policy was defined without chattering as a favorable characteristic of the SC method. Thus, it is evident that the finite time synergetic control method can be successfully implemented for the vaccination control in the SEIR epidemic system.