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Hopf bifurcation analysis in an age-structured heroin model

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Abstract

Heroin is very dangerous for human health; hence, controlling it is crucial for public health. Through this paper, we investigate an age-structured heroin model for describing and predicting the outbreak of this opiate drug. In fact, the main idea for modeling red the outbreak of this opiate drug is to presume that it spreads as an infectious disease where the term infection can mean the influence of the drug consumer on the non-drug user to inter into the drug consumer class. Our goal is to investigate the impact of the remission of consuming drugs on the spread of this opiate drug in our society. This period can be considered as delay, so this delay can influence hugely the dynamical behavior of the solution, where we achieved the proof of the existence of Hopf bifurcation. For confirming the obtained mathematical findings, we used some numerical illustrations next to its epidemiological relevance.

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Acknowledgements

S. Bentout and S. Djilali are partially supported by DGESTR of Algeria No. C00L03UN130120200004.

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Authors and Affiliations

  1. Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria

    Soufiane Bentout & Salih Djilali

  2. Department of Mathematics and Informatics, Belhadj Bouchaib University of Ain Temouchent, BP 284 RP, 46000, Ain Temouchent, Algeria

    Soufiane Bentout

  3. Department of Mathematics, National Institute of Technology, Jamshedpur, 831014, Jharkhand, India

    Sunil Kumar

  4. Faculty of Exact Sciences and Informatics, Mathematics Department, Hassiba Benbouali University, Chlef, Algeria

    Salih Djilali

Authors
  1. Soufiane Bentout
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  2. Sunil Kumar
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  3. Salih Djilali
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Correspondence to Sunil Kumar.

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Bentout, S., Kumar, S. & Djilali, S. Hopf bifurcation analysis in an age-structured heroin model. Eur. Phys. J. Plus 136, 260 (2021). https://doi.org/10.1140/epjp/s13360-021-01167-8

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