Abstract
In this paper, psychoactive drug abuse and prevention in a host community is illustrated by a mathematical model, studying the human population into four groups: those who are at risk of being initiated into psychoactive drug abuse, those who are currently abusing psychoactive drugs, those who are undergoing treatment for psychoactive drug abuse, and those who give up drug abuse through willingness or therapy. The positivity and invariant region of the model are investigated. The basic reproduction number $R_drg$ was also obtained. The numerical simulations were performed using the computer software MATLAB. The dynamics of variables and the sensitivity of parameters are displayed graphically to demonstrate that treatment and willingness to stop drug abuse are effective ways to reduce the threat of psychoactive drug abuse in a host community.
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