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2014 Mathematical Analysis of a Cholera Model with Vaccination
Jing'an Cui, Zhanmin Wu, Xueyong Zhou
J. Appl. Math. 2014: 1-16 (2014). DOI: 10.1155/2014/324767

Abstract

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 v. If 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 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 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.

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Jing'an Cui. Zhanmin Wu. Xueyong Zhou. "Mathematical Analysis of a Cholera Model with Vaccination." J. Appl. Math. 2014 1 - 16, 2014. https://doi.org/10.1155/2014/324767

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010599
MathSciNet: MR3170443
Digital Object Identifier: 10.1155/2014/324767

Rights: Copyright © 2014 Hindawi

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