Mathematical Biosciences and Engineering, 2013, 10(3): 843-860. doi: 10.3934/mbe.2013.10.843.

Primary: 92D25, 92D30; Secondary: 92B05, 91D10.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

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

1. Department of Mathematical Science, University of Stellenbosch, Private Bag X1, Matieland, Stellenbosch 7602

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.
  Figure/Table
  Supplementary
  Article Metrics

Keywords reproduction number; Drug barons; contagion; law enforcement.

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

References

  • 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.

 

This article has been cited by

  • 1. J.B.H. Njagarah, F. Nyabadza, A metapopulation model for cholera transmission dynamics between communities linked by migration, Applied Mathematics and Computation, 2014, 241, 317, 10.1016/j.amc.2014.05.036
  • 2. Farai Nyabadza, Lezanie Coetzee, A Systems Dynamic Model for Drug Abuse and Drug-Related Crime in the Western Cape Province of South Africa, Computational and Mathematical Methods in Medicine, 2017, 2017, 1, 10.1155/2017/4074197
  • 3. Liang’an Huo, Li Wang, Guoxiang Song, Global stability of a two-mediums rumor spreading model with media coverage, Physica A: Statistical Mechanics and its Applications, 2017, 482, 757, 10.1016/j.physa.2017.04.027

Reader Comments

your name: *   your email: *  

Copyright Info: 2013, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved