alexa The Role of Family in Initiating Methamphetamine Abuse Treatment: Insights through a Mathematical Model
ISSN: 2168-9679

Journal of Applied & Computational Mathematics
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Research Article

The Role of Family in Initiating Methamphetamine Abuse Treatment: Insights through a Mathematical Model

Mushanyuzy J1*, Nyabadza F2, Muchatibayaz G1 and Stewartz AGR1

1Department of Mathematics, University of Zimbabwe, Mount Pleasant, Harare, Box MP-167, Zimbabwe

2Department of Mathematical Sciences, Stellenbosch University, P. Bag X1, Matieland, 7602, South Africa

*Corresponding Author:
Mushanyu J
Department of Mathematics
University of Zimbabwe, Mount Pleasant
Harare, Box-MP-167, Zimbabwe
Tel: +2634307757
E-mail: [email protected]

Received Date: January 21, 2016; Accepted Date: February 09, 2016; Published Date: February 15, 2016

Citation: Mushanyuzy J, Nyabadza F, Muchatibayaz G, Stewartz AGR (2016) The Role of Family in Initiating Methamphetamine Abuse Treatment: Insights through a Mathematical Model. J Appl Computat Math 5:290. doi:10.4172/2168-9679.1000290

Copyright: © 2016 Mushanyuzy J, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

 

Methamphetamine addiction can be considered a family disease", and family involvement in helping a methamphetamine addict seek assistance is essential in combating the methamphetamine epidemic. We develop a mathematical model that takes into account the roles played by families in initiating methamphetamine treatment. An incidence term of newly admitted rehabilitants with probabilities β2 and β3 for joining inpatient and outpatient rehabilitation respectively, have been employed to this effect. Results indicate that family involvement is very crucial in lowering the threshold value a. Hence efforts targeted at encouraging family members to make appropriate referrals would be helpful in controlling the methamphetamine epidemic. The qualitative analysis of the model includes local and Lyapunov global stability of equilibrium. The approach of this paper is to suggest an extension of the drug abuse models which consider only one treatment option for drug users. It will be shown that the proposed model: (i) allows the drug users to choose between in-patient and out-patient rehabilitation, and (ii) is analyzed in the context of real data.

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