IJPAM: Volume 111, No. 2 (2016)

Title

MATHEMATICAL ANALYSIS OF A CHOLERA
TRANSMISSION MODEL INCORPORATING
MEDIA COVERAGE

Authors

Musundi O. Beryl$^1$, Lawi O. George$^2$, Nyamwala O. Fredrick$^3$
$^{1,2}$Department of Mathematics and Physics
Moi University
P.O. Box 3900, Eldoret, KENYA
$^2$Department of Mathematics
Masinde Muliro University of Science and Technology
P.O. Box 190, Kakamega, KENYA

Abstract

Diarrhoeal diseases are the major cause of child mortality in developing countries, where access to clean drinking water and sanitation is a problem. In this paper, we develop and analyse a mathematical model for cholera transmission incorporating media coverage. The existence and stability of the equilibrium points is established. Analysis of the model shows that the disease free equilibrium is both locally and globally asymptotically stable when the basic reproduction number is less than unity while the endemic equilibrium is locally asymptotically stable when the reproduction number is greater than unity. Numerical simulations done using the MATLAB software indicate that when media coverage is very efficient, the number of cholera infectives decreases faster, impliying that media alert and awareness campaigns are vital in controlling the spread of cholera.

History

Received: August 22, 2016
Revised: October 5, 2016
Published: December 11, 2016

AMS Classification, Key Words

AMS Subject Classification: 92B05
Key Words and Phrases: mathematical model, cholera, media coverage, stability, basic reproduction number

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How to Cite?

DOI: 10.12732/ijpam.v111i2.8 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 111
Issue: 2
Pages: 219 - 231


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