Model reference adaptive control of the nonlinear fractional order – stochastic model of the corona virus

In this paper, the Model Reference Adaptive Control (MRAC) method along with a state feedback controller is employed for synchronizing NFSCV, a complex nonlinear fractional-order stochastic model of the coronavirus. MRAC is a methodology that combines both linear feedback controllers and adaptive law techniques for designing a simple but robust adaptive feedback system. We have added a stochastic noise term to the coronavirus model representing sudden mutations and external disturbances. Also, we will implement the realization of fractional-order differential equations, and it gives us a real representation of the virus. In this paper, we address the question of when the controlled model 'infective or slave system' states can be observed and tuned to the master or reference model 'healthy and vaccination' states for our objective functions attempting a minimization between tracking errors of the states of master and slave systems, variance, and squared error integrals. In this paper, we further show that the system is asymptotically stable using the stochastic analysis along with Lyapunov theory. Through these simulations, we are able to see that by using our control algorithm, the infected individuals can be driven to follow a trajectory close to the one followed by the vaccinated individuals.