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Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay

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  • Xamxinur Abdurahman
  • Ling Zhang
  • Zhidong Teng

Abstract

We derive a discretized heroin epidemic model with delay by applying a nonstandard finite difference scheme. We obtain positivity of the solution and existence of the unique endemic equilibrium. We show that heroin-using free equilibrium is globally asymptotically stable when the basic reproduction number , and the heroin-using is permanent when the basic reproduction number .

Suggested Citation

  • Xamxinur Abdurahman & Ling Zhang & Zhidong Teng, 2014. "Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, October.
    • Handle: RePEc:hin:jnlaaa:742385
    DOI: 10.1155/2014/742385
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    Cited by:

    1. Li, Xuhui & Agarwal, Ravi P. & Gómez-Aguilar, J.F. & Badshah, Qaisar & Rahman, Ghaus ur, 2022. "Threshold dynamics: Formulation, stability & sensitivity analysis of co-abuse model of heroin and smoking," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Zizhen Zhang & Fangfang Yang & Wanjun Xia, 2019. "Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays," Complexity, Hindawi, vol. 2019, pages 1-17, November.

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