Threshold dynamics for an age‐structured heroin epidemic model with distributed delays-Reference-Cited by-同舟云学术

Threshold dynamics for an age‐structured heroin epidemic model with distributed delays

Published:2023-04-15 Issue:13 Volume:46 Page:13595-13619
ISSN:0170-4214
Container-title:Mathematical Methods in the Applied Sciences
language:en
Short-container-title:Math Methods in App Sciences

Author:

Djilali Salih¹²^ORCID,Bentout Soufiane¹³,Touaoula Tarik Mohamed¹⁴,Atangana Abdon⁵^ORCID

Affiliation:

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

2. Department of Mathematics, Faculty of Exact Sciences and Informatics Hassiba Benbouali University Chlef 02000 Algeria

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

4. Department of Mathematics University of Tlemcen Tlemcen 13000 Algeria

5. Institute for Groundwater Studies, Faculty of Natural and Agricultural Science University of the Free State Bloemfontein 9300 South Africa

Abstract

We introduce, in this paper, a delayed hybrid epidemic model describing the evolution of heroin addiction in a given population. The main objective of our mathematical analysis will be to provide the global behavior of the solutions. To the best of our knowledge, there are no results about the global dynamics of such a model containing both age structure and distributed time delay. We will prove that our model has threshold dynamics in terms of the basic reproduction number . It will be established that for , the addiction‐free equilibrium is globally stable and for , the endemic equilibrium is globally stable. The theoretical results are checked numerically. Especially, we focus on the influence of the addiction rate on the population dynamic.

Publisher

Wiley

Subject

General Engineering,General Mathematics

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.9275

Reference34 articles.

1. INIDA InfoFacts Heroin.https://www.nida.nih.gov/infofacts/heroin.html

2. Illicit drug initiation among institutionalized drug users in China

3. CComiskey National prevalence of problematic opiate use in Ireland 1999. EMCDDA Tech. Report.

4. Overland heroin trafficking routes and HIV-1 spread in south and south-east Asia

5. Changes in HIV‐1 incidence in heroin users in Guangxi province, China;Lai S.;J. AIDS,2001