Abstract
The production and use of addictive stimulants has been a major problem in South Africa. Although research has shown increased demand for drug abuse treatment, the actual size of the drug-abusing population remains unknown. Thus the prevalence of drug abuse requires estimation through available tools. Many questions remain unanswered with regard to interventions, new cases of substance abuse and relapse in recovering persons. A six-state compartmental model including a core and non-core group, with fast and slow progression to addiction, was formulated with the aim of qualitatively investigating the dynamics of substance abuse and predicting drug abuse trends. The analysis of the model was presented in terms of the substance abuse epidemic threshold R0. Numerical simulations were performed to fit the model to available data for methamphetamine use in the Western Cape and to determine the role played by some key parameters. The model was also fitted to data on methamphetamine users who enter rehabilitation using the least squares curve fitting method. It was shown that the model exhibits a backward bifurcation where a stable drug-free equilibrium coexists with a stable drug-persistent equilibrium for a certain defined range of values of R0. The stabilities of the model equilibria were ascertained and persistence conditions established. It was found that it is not sufficient to reduce R0 below unit to control the substance abuse epidemic. The reproduction number should be brought below a determined threshold, R0c. The results also suggested that the substance abuse epidemic can be reduced by intervention programmes targeted at light drug users and by increasing the uptake rate into treatment for those addicted. Projected trends showed a steady decline in the prevalence of methamphetamine abuse until 2015.
Highlights
Substance abuse remains a major global health and social problem.[1]
We extended the compartmental model presented by Nyabadza and Hove-Musekwa[15], which provided a structure in which numbers of individuals in each compartment can be tracked in time as relationships between compartments, described in mathematical terms, evolve
Our aim was to qualitatively study the dynamics of a substance abuse epidemic in a scenario where the population is subdivided into a core group NC and a non-core group NP in the presence of treatment
Summary
Substance abuse remains a major global health and social problem.[1] The production and abuse of addictive stimulants has increased dramatically in South Africa in the last decade and, in particular, there has been an increase in demand for treatment services for first-time admissions in recent years.[2] has this increase impacted on costs to the public health system, but other epidemics, such as HIV, have increased significantly. In South Africa, data is collected on admission for treatment for drug abuse every 6 months as a regular monitoring system for drug use trends. Treatment or rehabilitation services for substance abuse problems have not kept pace with the increase in demand for treatment and the treatment programmes do not operate on evidence-based treatment models.[4] It is important to monitor drug use patterns and predict trends over time
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