Stability and Hopf bifurcation of a vector-borne disease model with saturated infection rate and reinfection
type: Item
instance of: scholarly article
title: Stability and Hopf bifurcation of a vector-borne disease model with saturated infection rate and reinfection
zbMATH Open document ID: 1423.92232
DOI: 10.1155/2019/1352698
author: Zhixing Hu
author: Shanshan Yin
author: Hui Wang
published in: Computational \& Mathematical Methods in Medicine
publication date: 2019-07-09T00:00:00Z
review text: Summary: This paper established a delayed vector-borne disease model with saturated infection rate and cure rate. First of all, according to the basic reproductive number \(R_0\), we determined the disease-free equilibrium \(E_0\) and the endemic equilibrium \(E_1\). Through the analysis of the characteristic equation, we consider the stability of two equilibriums. Furthermore, the effect on the stability of the endemic equilibrium \(E_1\) by delay was studied, the existence of Hopf bifurcations of this system in \(E_1\) was analyzed, and the length of delay to preserve stability was estimated. The direction and stability of the Hopf bifurcation were also been determined. Finally, we performed some numerical simulation to illustrate our main results.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K18
zbMATH DE Number: 7077753
zbMATH Keywords: vector-borne disease model
zbMATH Keywords: stability
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: reinfection
Wikidata QID: Q92155896
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2019/1352698
OpenAlex ID: W2948873219
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DBLP publication ID: journals/cmmm/HuYW19
description: scientific article; zbMATH DE number 7077753