A Next Generation Matrix Method for the Basic Reproduction Number of Substance Abuse in Commercial Drivers’ Population with Prosecution

Yekeen A. O., Ibrahim M. O.

Abstract


This study focused on Next Generation Matrix Method for Reproductive numbers in modelling substance abuse. In this research work, a deterministic mathematical model of substance abuse using the Jailing approach is constructed from the compartmentalised 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 abusers' group. The population is divided into five compartments, denoting the Susceptible, substance Users, Abusers, Prosecuted and Rehabilitated commercial drivers’ populations respectively. The motive is basically to examine whether the substance abusers population will persist or on the other hand cease to exist. Following Generation Matrix method and algorithm for calculating the basic reproduction number were explicitly enumerated. Both the Next Generation Matrix and digraph reduction Method were evaluated and the results were found to be similar. These approaches could however also be practical for larger systems in the derivations for


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