American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2019, 7(1), 1-8
DOI: 10.12691/ajams-7-1-1
Open AccessArticle

Modeling and Analysis of Cholera Dynamics with Vaccination

Nneamaka Judith Ezeagu1, , Houénafa Alain Togbenon1 and Edwin Moyo1

1Department of Mathematics, Pan African University Institute for Basic Sciences, Technology and Innovations (PAUISTI), Nairobi, Kenya

Pub. Date: December 24, 2018

Cite this paper:
Nneamaka Judith Ezeagu, Houénafa Alain Togbenon and Edwin Moyo. Modeling and Analysis of Cholera Dynamics with Vaccination. American Journal of Applied Mathematics and Statistics. 2019; 7(1):1-8. doi: 10.12691/ajams-7-1-1

Abstract

A mathematical model for the transmission of cholera dynamics with a class of quarantined and vaccination parameter as control strategies is proposed in this paper. It is shown through mathematical analysis that the solution of the model uniquely exist, is positive and bounded in a certain region. The disease-free and endemic equilibrium points of the model are obtained. By using the next generation matrix, the basic reproduction number was computed around the disease-free equilibrium points, and it was shown through the Jacobian matrix that the disease free equilibrium is locally asymptotic stable if Rh<1. Numerical simulation was carried to understand the impact of the incorporated controls as the system evolves over time. Results show that effective quarantine, vaccination and proper sanitation reduce the disease contact rates and thus eliminates the spread of cholera.

Keywords:
cholera vaccination basic reproduction number equilibrium points

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