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Global asymptotic properties of a heroin epidemic model with treat-age

Author

Listed:
  • Fang, Bin
  • Li, Xue-Zhi
  • Martcheva, Maia
  • Cai, Li-Ming

Abstract

In this paper, a model for the use of heroin with treat-age is formulated based on the principles of mathematical epidemiology. The model accounts for relapse rate that depends on how long the host has been in treatment for heroin addiction. An explicit formula for the reproductive number of the heroin spread is obtained. By using the method of Lyapunov functional, we established the dynamical properties of the heroin epidemic model, and the results show that the global dynamics of the model is completely determined by the basic reproduction number. It is shown that the drug-free equilibrium is locally and globally asymptotically stable if the basic reproduction number is less than one. In addition, the heroin spread system is uniform persistence and the unique drug spread equilibrium is locally and globally asymptotically stable if the basic reproduction number is greater than one.

Suggested Citation

  • Fang, Bin & Li, Xue-Zhi & Martcheva, Maia & Cai, Li-Ming, 2015. "Global asymptotic properties of a heroin epidemic model with treat-age," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 315-331.
    • Handle: RePEc:eee:apmaco:v:263:y:2015:i:c:p:315-331
    DOI: 10.1016/j.amc.2015.04.055
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    Cited by:

    1. Zara, M.C. & Monteiro, L.H.A., 2021. "The negative impact of technological advancements on mental health: An epidemiological approach," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    2. 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).
    3. 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.
    4. Haoxiang Tang & Mingtao Li & Xiangyu Yan & Zuhong Lu & Zhongwei Jia, 2021. "Modeling the Dynamics of Drug Spreading in China," IJERPH, MDPI, vol. 18(1), pages 1-25, January.
    5. Wang, Jinliang & Wang, Jing & Kuniya, Toshikazu, 2019. "Analysis of an age-structured multi-group heroin epidemic model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 78-100.
    6. Wei Wang & Sifen Lu & Haoxiang Tang & Biao Wang & Caiping Sun & Pai Zheng & Yi Bai & Zuhong Lu & Yulin Kang, 2022. "A Scoping Review of Drug Epidemic Models," IJERPH, MDPI, vol. 19(4), pages 1-18, February.

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