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A graph theoretical perspective of a drug abuse epidemic model

Author

Listed:
  • Nyabadza, F.
  • Mukwembi, S.
  • Rodrigues, B.G.

Abstract

A drug use epidemic can be represented by a finite number of states and transition rules that govern the dynamics of drug use in each discrete time step. This paper investigates the spread of drug use in a community where some users are in treatment and others are not in treatment, citing South Africa as an example. In our analysis, we consider the neighbourhood prevalence of each individual, i.e., the proportion of the individual’s drug user contacts who are not in treatment amongst all of his or her contacts. We introduce parameters α∗,β∗ and γ∗, depending on the neighbourhood prevalence, which govern the spread of drug use. We examine how changes in α∗, β∗ and γ∗ affect the system dynamics. Simulations presented support the theoretical results.

Suggested Citation

  • Nyabadza, F. & Mukwembi, S. & Rodrigues, B.G., 2011. "A graph theoretical perspective of a drug abuse epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1723-1732.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:10:p:1723-1732
    DOI: 10.1016/j.physa.2011.01.014
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    References listed on IDEAS

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    1. Mukwembi, Simon, 2008. "A note on the effects of replenishment of depleted cells on HIV infection dynamics: A graph-theoretic approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1200-1204.
    2. Rossi, Carla, 2004. "Operational models for epidemics of problematic drug use: the Mover-Stayer approach to heterogeneity," Socio-Economic Planning Sciences, Elsevier, vol. 38(1), pages 73-90, March.
    3. Nyabadza, Farai & Mukwembi, Simon & Rodrigues, Bernardo Gabriel, 2009. "A tuberculosis model: The case of ‘reasonable’ and ‘unreasonable’ infectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(10), pages 1995-2000.
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