Optimal Control Strategy for a Typical Drug Abuse Model

Yekeen Abiola Olatunde, Ibrahim Mohammed Olanrewaju

Abstract


This study focused on harnessing certain control strategies for checkmating the menace of substance abuse in a typical demographic society. This research uses a deterministic mathematical model of substance abuse using (the 3 strategies) from the compartmentalized model. Building on the insights from epidemiology, our model entails controlling the spread of abusers' ideologies in society. We introduce a simple compartmental model suitable to describe the abuser group. The population is divided into six compartments: denoting the Susceptible, Light substance users, Heavy substance users, Temporal Quitters’ class, Prosecuted compartment and Permanent Quitters populations respectively. The motive is basically to examine whether the substance abuser population will persist or on the other hand cease to exist with the introduction of the three control strategies. The generation Matrix method and algorithm for calculating the basic reproduction number  was explicitly enumerated and The Pontryagin Maximum Principle was employed for our optimization of the system hence the plot-visibility of each of the substance-embedded compartments; conclusively showing a significant decline in the  abusers’ groups


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