Modeling and Analysis of Cholera Dynamics with Vaccination

Nneamaka Judith Ezeagu^1, , Houénafa Alain Togbenon¹ and Edwin Moyo¹

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

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 R_h<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

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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