Optimal Control of a Fractional-Order New Psychoactive Substance Model (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we develop a fractional-order model of new psychoactive substance (NPS) transmission. We first prove the non-negativity andboundedness of the model. Then, prevention function and treatment functionare introduced into the model to establish the fractional-order optimal controlmodel. The existence of the optimal control pair is proved, and the solution ofthe model is obtained. Finally, the numerical simulation of the optimal controlmodel is carried out. The results show that the fractional model is helpful forus to analyze the NPS dynamics model more deeply. Through the analysisof three control strategies, the optimal control strategy is the combination ofprevention and treatment measures. In addition, it is worth noting that thispaper obtains a new insight that prevention is more effective than treatmentin the early stage of NPS transmission, and the control strategy at this time isto invest in maximum prevention measures and moderate treatment measures.However, when the spread of NPS shows an epidemic trend, the influence ofpreventive measures is greatly reduced, and the control strategy at this time isto focus on increasing the investigation of addicts and improving the treatmentrate of psychological addicts.
Keywords: New psychoactive substances; fractional order model; optimal control; numerical simulation.