TY - JOUR
T1 - Optimal Control of a Fractional-Order New Psychoactive Substance Model
AU - Wang , Xinxin
AU - Wang , Xiaoyun
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 573
EP - 588
PY - 2024
DA - 2024/08
SN - 6
DO - http://doi.org/10.12150/jnma.2024.573
UR - https://global-sci.org/intro/article_detail/jnma/23349.html
KW - New psychoactive substances, fractional order model, optimal
control, numerical simulation.
AB - <p style="text-align: justify;">In this paper, we develop a fractional-order model of new psychoactive substance (NPS) transmission. We first prove the non-negativity and
boundedness of the model. Then, prevention function and treatment function
are introduced into the model to establish the fractional-order optimal control
model. The existence of the optimal control pair is proved, and the solution of
the model is obtained. Finally, the numerical simulation of the optimal control
model is carried out. The results show that the fractional model is helpful for
us to analyze the NPS dynamics model more deeply. Through the analysis
of three control strategies, the optimal control strategy is the combination of
prevention and treatment measures. In addition, it is worth noting that this
paper obtains a new insight that prevention is more effective than treatment
in the early stage of NPS transmission, and the control strategy at this time is
to invest in maximum prevention measures and moderate treatment measures.
However, when the spread of NPS shows an epidemic trend, the influence of
preventive measures is greatly reduced, and the control strategy at this time is
to focus on increasing the investigation of addicts and improving the treatment
rate of psychological addicts.</p>