The Hopf bifurcation analysis and optimal control of a delayed SIR epidemic model
type: Item
instance of: scholarly article
title: The Hopf bifurcation analysis and optimal control of a delayed SIR epidemic model
zbMATH Open document ID: 1390.92131
DOI: 10.1155/2014/940819
author: Abdelhadi Abta
author: Hassan Laarabi
author: Hamad Talibi Alaoui
published in: International Journal of Analysis
publication date: 2018-06-11T00:00:00Z
review text: Summary: We propose a delayed SIR model with saturated incidence rate. The delay is incorporated into the model in order to model the latent period. The basic reproductive number \(R_0\) is obtained. Furthermore, using time delay as a bifurcation parameter, it is proven that there exists a critical value of delay for the stability of diseases prevalence. When the delay exceeds the critical value, the system loses its stability and a Hopf bifurcation occurs. The model is extended to assess the impact of some control measures, by reformulating the model as an optimal control problem with vaccination and treatment. The existence of the optimal control is also proved. Finally, some numerical simulations are performed to verify the theoretical analysis.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 49N90
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 6883072
zbMATH Keywords: delayed SIR epidemic model
zbMATH Keywords: optimal control
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: vaccination
zbMATH Keywords: treatment
zbMATH Keywords: numerical simulation
Wikidata QID: Q59041491
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/940819
OpenAlex ID: W2023176379
description: scientific article; zbMATH DE number 6883072