Modelling the role of drug barons on the prevalence of drug epidemics

  • Received: 01 May 2012 Accepted: 29 June 2018 Published: 01 April 2013
  • MSC : Primary: 92D25, 92D30; Secondary: 92B05, 91D10.

  • Substance abuse is a global menace with immeasurable consequences to the health of users, the quality of life and the economy of countries affected. Although the prominently known routes of initiation into drug use are; by contact between potential users and individuals already using the drugs and self initiation, the role played by a special class of individuals referred to as drug lords can not be ignored. We consider a simple but useful compartmental model of drug use that accounts for the contribution of contagion and drug lords to initiation into drug use and drug epidemics. We show that the model has a drug free equilibrium when the threshold parameter $R_{0}$ is less that unity and a drug persistent equilibrium when $R_{0}$ is greater than one. In our effort to ascertain the effect of policing in the control of drug epidemics, we include a term accounting for law enforcement. Our results indicate that increased law enforcement greatly reduces the prevalence of substance abuse. In addition, initiation resulting from presence of drugs in circulation can be as high as seven times higher that initiation due to contagion alone.

    Citation: John Boscoh H. Njagarah, Farai Nyabadza. Modelling the role of drug barons on the prevalence of drug epidemics[J]. Mathematical Biosciences and Engineering, 2013, 10(3): 843-860. doi: 10.3934/mbe.2013.10.843

    Related Papers:

  • Substance abuse is a global menace with immeasurable consequences to the health of users, the quality of life and the economy of countries affected. Although the prominently known routes of initiation into drug use are; by contact between potential users and individuals already using the drugs and self initiation, the role played by a special class of individuals referred to as drug lords can not be ignored. We consider a simple but useful compartmental model of drug use that accounts for the contribution of contagion and drug lords to initiation into drug use and drug epidemics. We show that the model has a drug free equilibrium when the threshold parameter $R_{0}$ is less that unity and a drug persistent equilibrium when $R_{0}$ is greater than one. In our effort to ascertain the effect of policing in the control of drug epidemics, we include a term accounting for law enforcement. Our results indicate that increased law enforcement greatly reduces the prevalence of substance abuse. In addition, initiation resulting from presence of drugs in circulation can be as high as seven times higher that initiation due to contagion alone.


    加载中
    [1] Management Science, 46 (2000), 333-347.
    [2] Math. Biosci. Eng., 159 (1999), 1-20.
    [3] Int. Stat. Rev., 64 (1994), 229-243.
    [4] Math Comput. Modelling, 28 (1998), 21-29.
    [5] 97, Springer-Verlag, 1993.
    [6] Math. Biosci. Eng., 1 (2004), 361-404.
    [7] Int. J. Bifurcat Chaos, 16 (2006), 3275-3289.
    [8] Bull. Math. Biol., 70 (2008), 1272-1296.
    [9] J. Dyn. Differ. Equ., 20 (2008), 31-53.
    [10] 2008. UNISCI Discussion Papers, No 16, ISSN 1696-2206.
    [11] Drug Policy Research Centre, 1994.
    [12] 2000, U.S. Department of Justice: Office of Justice Programs.
    [13] Socio-Econ. Plann. Sci., 29 (1995), 305-314.
    [14] AJHP Supplement, 64 (1974), 1-10.
    [15] J. Biol. Dyn., 2 (2008), 154-168.
    [16] Math. Biosci., 146 (1997), 15-35.
    [17] Int. J. Drug Policy, 20 (2009), 317-323.
    [18] Theor. Biol. Med. Model., 54 (2008).
    [19] Math. Biosci., 155 (1999), 77-108.
    [20] second edition, 2006. World Bank, Washington D.C.
    [21] Taylor & Francis Group, LLC, 2007.
    [22] Society for Industrial and Applied Mathematics, 1976.
    [23] NIDA, 1989.
    [24] Lippincott Williams & Wilkins, 2005.
    [25] Springer, 2008.
    [26] Math. Biosci., 208 (2009), 131-141.
    [27] 2012. Available from http://www.drugabuse.gov/publications/drugfacts/cigarettes-other-tobacco-products.
    [28] Math. Biosci., 225 (2010), 134-140.
    [29] Am. J. Drug and Alcohol Abuse, 30 (2004), 167-185.
    [30] SAJP, 13 (2008), 126-131.
    [31] Socio-Econ. Plan. Sci., 38 (2004), 73-90.
    [32] Bulletin on Narcotics, LIV (2002), 33-44.
    [33] SACENDU Research Briefs, 2006, 12.
    [34] Appl. Math. Comp., 195 (2008), 475-499.
    [35] B. Math Biol., 72 (2010), 1506-1533.
    [36] Nat. Photonics, 1 (2007), 97-105.
    [37] 1995. Copenhagen, 6-12 March.
    [38] 2009. United Nations, New York.
    [39] 2009. Vienna, 16-24 April.
    [40] Math. Biosci., 180 (2002), 29-48.
    [41] J. Math. Anal. Appl., 291 (2004), 775-793.
    [42] Math. Biosci., 208 (2007), 312-324.
  • Reader Comments
  • © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1894) PDF downloads(485) Cited by(6)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog