Optimal Control and Cost-Effectiveness Analysis of an Illicit Drug Use Population Dynamics - Olaniyi, S.; Akanni, J. O.; Adepoju, O. A. (Journal of Applied Nonlinear Dynamics, 2026)
The problem of illicit drug use with its associated hazardous effects on social behavior and human population dynamics require an intervention. This paper presents the optimal intervention strategy for controlling the menace of illicit drug use at population levels. Two time-dependent intervention measures are incorporated into a nonlinear system of differential equations modelling illicit drug use population dynamics. The first measure aims to prevent the influence of drug users on non drug users while the second intervention measure is concerned with behavioral therapy. The control problem is analyzed using a popular Pontryagin's maximum principle to find the necessary condition for optimum solution. Assessment of single implementation of each the two measures and combination of both intervention measures are conducted to investigate the dynamic behaviour of illicit drug users in the population. Moreover, cost-effectiveness analysis based on incremental cost-effectiveness ratio is conducted to find the most cost effective intervention measure capable of averting good numbers of illicit drug users in the population at lowest cost. The results show that combination of both control variables reduce the spread of drug abuse mostly. However, single implementation of preventive control is the most cost-effective intervention.