Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model

In this work, a fractional-order synthetic drugs transmission model with psychological addicts has been proposed along with psychological treatment. The effects of synthetic drugs are deadly and sometimes even violent. We have studied the local and global stability of the model with different criterion. The existence and uniqueness criterion along with positivity and boundedness of the solutions have also been established. The local and global stabilities are decided by the basic reproduction number R0 . We have also analyzed the sensitivity of parameters. An optimal control problem has been formulated by controlling psychological addiction and analyzed by the help of Pontryagin maximum principle. These results are verified by numerical simulations.