Optimal cost-effective control of drug abuse by students: insight from mathematical modeling

Illicit drug use (IDU) among students is now one of the increasingly major global public health issues. It can lead to students’ poor academic performance, physical and mental health issues, that in turn lead to poor development and productivity in their later life. The implementation of preventive and control measures for IDU carries a huge financial burden to the governments and the general public. Thus, the focus of this paper is to develop and analyse a non-linear optimal control problem based on an existing non-linear compartmental model of IDU dynamics in the student population with a view to providing insightful information to the government, decision and policy-makers about how to prioritise the implementations of public enlightenment policy, corrective measure and treatment control in terms of efficacy and cost benefits. The existing seven-dimensional deterministic model is modified to capture three time-dependent control variables denoting public enlightenment campaign, corrective measure and treatment. The non-linear optimal control model is rigorously analysed to explicitly prove the existence and characterize the optimal control triple using optimal control theory. Simulated results of the optimality system reveal that each of the single, double and triple interventions has positive impact in reducing the social crime of IDU. By carrying out the efficiency analysis on all the possible combinations of optimal controls, it is shown that implementing all the three optimal controls simultaneously are most efficient. Cost-effectiveness analysis indicates that the use of only public enlightenment policy is the single and overall most cost-effective strategy, while combination of only public enlightenment campaign and treatment is an alternative most cost-effective double intervention that may be adopted to prevent and control the menace of IDU with limited resources in the student population.