title: Modeling Illicit Drug Use Dynamics and Its Optimal Control Analysis.
abstract: The global burden of death and disability attributable to illicit drug use, remains a significant threat to public health for both developed and developing nations. This paper presents a new mathematical modeling framework to investigate the effects of illicit drug use in the community. In our model the transmission process is captured as a social "contact" process between the susceptible individuals and illicit drug users. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction number. Using our model, we present illustrative numerical results with a case study in Cape Town, Gauteng, Mpumalanga and Durban communities of South Africa. In addition, the basic model is extended to incorporate time dependent intervention strategies.
authors.affiliation: University of Zimbabwe, Department of Mathematics, P.O. Box MP 167, Harare, Zimbabwe.
authors.forename: Steady
authors.identifier: 0000-0002-7423-2934
authors.initials: S
authors.lastname: Mushayabasa
authors.affiliation: University of Zimbabwe, Department of Mathematics, P.O. Box MP 167, Harare, Zimbabwe.
authors.forename: Gift
authors.identifier: 0000-0001-5133-2505
authors.initials: G
authors.lastname: Tapedzesa
mesh_terms: D050936:Basic Reproduction Number; D019295:Computational Biology; D006801:Humans; D013287:Illicit Drugs; D055641:Mathematical Concepts; D015233:Models, Statistical; D013019:South Africa / Q000453:epidemiology; D019966:Substance-Related Disorders / Q000453:epidemiology* / Q000517:prevention & control
chemical_list: D013287:Illicit Drugs
references.citation: Lancet. 2013 Nov 9;382(9904):1575-86
references.pmid: 23993280
references.citation: J Acquir Immune Defic Syndr. 1992;5(11):1116-8
references.pmid: 1403641
references.citation: Lancet. 1991 Aug 17;338(8764):438-9
references.pmid: 1678097
references.citation: Bull Math Biol. 2013 Jan;75(1):24-48
references.pmid: 23196353
references.citation: Math Biosci. 2002 Nov-Dec;180:29-48
references.pmid: 12387915
references.citation: Nat Rev Neurosci. 2007 Nov;8(11):885-95
references.pmid: 17925811
references.citation: AIDS. 1997;11 Suppl A:S57-60
references.pmid: 9451967
references.citation: Math Biosci. 2007 Jul;208(1):312-24
references.pmid: 17174346