EFFECT OF OCCASIONAL HEROIN CONSUMERS ON THE SPREAD OF HEROIN ADDICTION

Salih Djilali, Anwar Zeb and Tareq Saeed ()
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Salih Djilali: Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria2Department of Mathematics, Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University, Chlef, Algeria
Anwar Zeb: Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Pakistan
Tareq Saeed: Department of Mathematics, King Abdulaziz University, Jeddah 41206, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-13

Abstract: We aim in this research to show the global behavior of each equilibrium of a heroin epidemic model with distributed delays. We obtained that the global behavior of the considered system is completely governed by the value of the basic reproduction number ℜ0. For the case when ℜ0 is less than one, we established the global stability of the drug-free equilibrium using the Lyapunov direct method. However, for ℜ0 greater than one, the addiction persists and the drug equilibrium is globally asymptotically stable, which is shown also by the Lyapunov direct method. Moreover, we obtained that by controlling the density of occasional heroin users we can control the heroin epidemic spread, and this measure is more effective than the treatment measure.

Keywords: Heroin Model; Lyapunov Direct Method; Occasional Consumers; Basic Reproduction Number (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401648

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