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

[摘要] 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.

[关键词] Methamphetamine;Referrals;Reproduction number;Inpatient rehabilitation;Out-patient Rehabilitation;Least squares curve fitting