Application of Differential Transform Method for Solving Drug Abuse Model

Yekeen A. O., Etuk M. O., Ajiboye A. O., Adeyemo K. M.

Abstract


This study focused on establishing the positivity, stability analysis and numerical solution in modelling substance abuse. In this research work, a deterministic mathematical model of substance abuse using Prosecution approach is constructed from compartmentalized model. Building on the insights from epidemiology, our model entails for controlling the spread of abusers’ ideologies in the society. We introduce a simple compartmental model suitable to describe abusers’ group. The population N(t) is divided into six compartments: S(t), L(t), H(t), P(t), R(t) and C(t) denoting the Susceptible, Light substance users, Heavy substance users, Prosecuted compartment, Rehabilitated class and Capital punishment populations respectively. The motive is basically to examine whether the substance abusers population will persist or on the other hand cease to exist with the introduction of the compartment C control class. Next Generation Matrix method and algorithm for calculating the basic reproduction number R_0 was explicitly enumerated. The Differential Transform Method was employed as numerical solution of the system hence plot-visibility of each compartment behaviour; conclusively showing a significant decline in the P(t) and C(t) abusers’ control groups.


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References


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