title: On the Role of Imitation on Adolescence Methamphetamine Abuse Dynamics.
abstract: Adolescence methamphetamine use is an issue of considerable concern due to its correlation with later delinquency, divorce, unemployment and health problems. Understanding how adolescents initiate methamphetamine abuse is important in developing effective prevention programs. We formulate a mathematical model for the spread of methamphetamine abuse using nonlinear ordinary differential equations. It is assumed that susceptibles are recruited into methamphetamine use through imitation. An epidemic threshold value, [Formula: see text], termed the abuse reproduction number, is proposed and defined herein in the drug-using context. The model is shown to exhibit the phenomenon of backward bifurcation. This means that methamphetamine problems may persist in the population even if [Formula: see text] is less than one. Sensitivity analysis of [Formula: see text] was performed to determine the relative importance of different parameters in methamphetamine abuse initiation. The model is then fitted to data on methamphetamine users less than 20 years old reporting methamphetamine as their primary substance of abuse in the treatment centres of Cape Town and parameter values that give the best fit are chosen. Results show that the proportion of methamphetamine users less than 20 years old reporting methamphetamine as their primary substance of abuse will continue to decrease in Cape Town of South Africa. The results suggest that intervention programs targeted at reducing adolescence methamphetamine abuse, are positively impacting methamphetamine abuse.
authors.affiliation: Department of Mathematics, University of Zimbabwe, Box MP 167, Mount Pleasant, Harare, Zimbabwe. mushanyuj@gmail.com.
authors.forename: J
authors.initials: J
authors.lastname: Mushanyu
authors.affiliation: Department of Mathematical Sciences, Stellenbosch University, P. Bag X1, Matieland, 7602, South Africa.
authors.forename: F
authors.initials: F
authors.lastname: Nyabadza
authors.affiliation: Department of Mathematics, University of Zimbabwe, Box MP 167, Mount Pleasant, Harare, Zimbabwe.
authors.forename: G
authors.initials: G
authors.lastname: Muchatibaya
authors.affiliation: Department of Mathematics, University of Zimbabwe, Box MP 167, Mount Pleasant, Harare, Zimbabwe.
authors.forename: A G R
authors.initials: AG
authors.lastname: Stewart
mesh_terms: D000293:Adolescent; D019969:Amphetamine-Related Disorders / Q000453:epidemiology* / Q000534:rehabilitation*; D000697:Central Nervous System Stimulants / Q000494:pharmacology*; D006801:Humans; D008694:Methamphetamine / Q000494:pharmacology*; D008962:Models, Theoretical
chemical_list: D000697:Central Nervous System Stimulants; D008694:Methamphetamine
keywords: Adolescence; Imitation; Least squares curve fitting; Methamphetamine; Reproduction number