Mathematical analysis of a cholera model with vaccination
type: Item
instance of: scholarly article
title: Mathematical analysis of a cholera model with vaccination
zbMATH Open document ID: 1406.92351
DOI: 10.1155/2014/324767
author: Zhanmin Wu
author: Jing-An Cui
author: Xueyong Zhou
published in: Journal of Applied Mathematics
publication date: 2019-02-01T00:00:00Z
review text: Summary: We consider a \(SVR-B\) cholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. We calculate the certain threshold known as the control reproduction number \(\mathscr{R}_v\). If \(\mathscr{R}_v<1\), we obtain sufficient conditions for the global asymptotic stability of the disease-free equilibrium; the diseases will be eliminated from the community. By comparison of arguments, it is proved that if \(\mathscr{R}_v>1\), the disease persists and the unique endemic equilibrium is globally asymptotically stable, which is obtained by the second compound matrix techniques and autonomous convergence theorems. We perform sensitivity analysis of \(\mathscr{R}_v\) on the parameters in order to determine their relative importance to disease transmission and show that an imperfect vaccine is always beneficial in reducing disease spread within the community.
Mathematics Subject Classification ID: 92C60
zbMATH DE Number: 7010599
Wikidata QID: Q59050920
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/324767
OpenAlex ID: W2167678976
description: scientific article; zbMATH DE number 7010599