Mathematical Modelling of Drug Abuse Reduction Strategies taking into account the Treatment Type and Risks Level

Cicik Alfiniyah, Anisa Puspitasari, Fatmawati Fatmawati


Drug abuse is one of the global issues and has spread among teenagers. Drugs may lead to subordination, health problems and even death. There are several policies made in each country related to the problem of drug abuse, both punishment and treatment. In this paper, we discuss the treatment and strategy to reduce the number of drug users. Drug users can recover themselves by undergoing rehabilitation in the form of inpatient or outpatient care. We first conduct qualitative analyses including stability analysis of equilibrium points of the model, the basic reproduction number and parameter sensitivity analysis. Mathematical model of drug abuse reduction by concerning type of treatment along with risk level without control has two equilibrium points, namely non-endemic or drug-free equilibrium and endemic equilibrium. Sensitivity analysis is provided to investigate which parameter that most affects the dynamical behaviour of the drug abuse model in terms of stability of the non-endemic and endemic equilibrium point. Then we impose an anti-drug campaign on the model as strategy control to reduce the number of drug abusers. Simulation results show that the anti-drug campaign has a significant effect in reducing both the number of drug abusers who received any treatment and do not get any treatment.


Drug abuse; Rehabilitation; Campaign; Mathematical Model; Optimal Control

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