Global Dynamics of Drug Use Model and Its Optimal Control Analysis
Keywords:drug use, awareness and educational program, family and friends care, basic reproduction number, optimal control
In this paper, we propose and analyze a mathematical model of drug use involving rehabilitation. With our model, we assume that the use of drugs can be initiated by three groups of people; light drug users, heavy drug users and drug users under rehabilitation. In this model, the nonnegativity and boundedness of solutions are verified, and two equilibrium points (drug-free and drug-endemic) are obtained. The basic reproduction number is calculated. We show that each equilibrium point is stable locally and globally under some conditions. Further, an optimal control problem is applied to the model by adding three control variables; awareness and educational program control, family and friends care control, and rehabilitation campaign control. The numerical simulation of this optimal control model is performed, and the results show that each control alone could already reduce the number of drug users for some certain amount, however, a combination of all three controls gives the best result in reducing overall drug use.
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