Eur. Phys. J. Plus (2021) 136: 260
https://doi.org/10.1140/epjp/s13360-021-01167-8

Regular Article

Hopf bifurcation analysis in an age-structured heroin model

¹ Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria
² Department of Mathematics and Informatics, Belhadj Bouchaib University of Ain Temouchent, BP 284 RP, 46000, Ain Temouchent, Algeria
³ Department of Mathematics, National Institute of Technology, 831014, Jamshedpur, Jharkhand, India
⁴ Faculty of Exact Sciences and Informatics, Mathematics Department, Hassiba Benbouali University, Chlef, Algeria

^b skiitbhu28@gmail.com, skumar.math@nitjsr.ac.in

Received: 19 December 2020
Accepted: 29 January 2021
Published online: 25 February 2021

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.