Optimal control and dynamical aspects of a fractional giving up smoking model

This paper investigates a fractional model of giving up smoking. Using some dynamic system tools, the model is analyzed.The epidemiological and mathematical well-posedness of the governing model is demonstrated through the positivity and boundedness properties of solutions. The equilibrium points and basic reproduction number of the model are determined. Also, sensitivity analyses are done to show how the basic reproduction number of the model is affected by changes in the model's parameters. Then, the global stability behavior of the model at the smoking-free equilibrium points is studied.