Impact of Optimal Intervention Strategies on Psychoactive Substance Abuse Dynamics With Addicted Immigrants: A Mathematical Study

In this work, the population dynamics of psychoactive substance abuse model governed by a system of nonlinear ordinary differential equations is studied through the efficacy and economic analyses. The study considers three time-variant intervention strategies, such as screening of addicted immigrants, advocacy against substance abuse and rehabilitation therapy for the control of substance abuse spread in the population. Most sensitive parameters to be targeted by the control interventions are examined through sensitivity analysis using the normalized forward sensitivity index. By employing optimal control theory, the existence of optimal control is qualitatively analysed and the control triple is characterized using Pontryagin’s maximum principle. To further assess the impact of the intervention strategies, three different policies combining any two of the intervention strategies, namely, Policy A (combination of screening of addicted immigrants and advocacy against substance abuse), Policy B (combination of screening of addicted immigrants and rehabilitation therapy) and Policy C (combination of advocacy against substance abuse and rehabilitation therapy), are considered. Efficacy and economic analyses are extensively conducted on each of the policies, and it is revealed that Policy B is the most efficient intervention, while Policy C is the most cost-effective intervention. As a result, the policy that averts the highest number of psychoactive substance abuse cases when limited resources are available is recommended.