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Threshold dynamics: Formulation, stability & sensitivity analysis of co-abuse model of heroin and smoking

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  • Li, Xuhui
  • Agarwal, Ravi P.
  • Gómez-Aguilar, J.F.
  • Badshah, Qaisar
  • Rahman, Ghaus ur

Abstract

In this study, a smoking and heroin co-abuse model is proposed for the first time in the literature. To research the dynamics and impacts of smoking-heroin co-morbidity in the workplace, a nonlinear dynamical system is built and qualitatively analyzed in this study. When R0<1, the threshold quantity of sub-models is obtained, and it is proven that they have latin hypercube sampling (LAS) at substance free equilibria. Conditions for existence of substance present equilibria of sub-models are also obtained. The impact of smokers on heroin users' dynamics is examined further. In terms of epidemiology, the results of uncertainty and sensitivity studies are crucial. As a result, the co-abuse model is treated with the (LHS) and partial rank correlation coefficient techniques.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005835
    DOI: 10.1016/j.chaos.2022.112373
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    References listed on IDEAS

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    1. ur Rahman, Ghaus & Agarwal, Ravi P. & Din, Qamar, 2019. "Mathematical analysis of giving up smoking model via harmonic mean type incidence rate," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 128-148.
    2. 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.
    3. Wei, Yongchang & Yang, Qigui & Li, Guangjie, 2019. "Dynamics of the stochastically perturbed Heroin epidemic model under non-degenerate noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    4. 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.
    5. Isaac Mwangi Wangari & Lewi Stone, 2017. "Analysis of a Heroin Epidemic Model with Saturated Treatment Function," Journal of Applied Mathematics, Hindawi, vol. 2017, pages 1-21, August.
    6. Ghanbari, Behzad & Atangana, Abdon, 2020. "A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
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    1. Sina Etemad & Albert Shikongo & Kolade M. Owolabi & Brahim Tellab & İbrahim Avcı & Shahram Rezapour & Ravi P. Agarwal, 2022. "A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability," Mathematics, MDPI, vol. 10(22), pages 1-31, November.

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