About this Journal Submit a Manuscript Table of Contents
ISRN Biomathematics
Volume 2012 (2012), Article ID 621939, 13 pages
http://dx.doi.org/10.5402/2012/621939
Research Article

Qualitative Analysis of a Cholera Bacteriophage Model

1Department of Public Health and Center for Infectious Disease Epidemiology Research, China Medical University, 91 Hsueh-Shih Road, Taichung 40402, Taiwan
2Department of Mathematics, Vivekananda College Thakurpukur, Kolkata 700 063, India

Received 22 January 2012; Accepted 19 February 2012

Academic Editors: A. MacKenzie and M. Santillán

Copyright © 2012 Prasenjit Das and Debasis Mukherjee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Cholera still remains as a severe global threat and is currently spreading in Africa and other parts of the world. The role of lytic bacteriophage as an intervention of cholera outbreaks is investigated using a mathematical model. Dynamics of cholera is discussed on basis of the basic reproduction number 𝑅 0 . Conditions of Hopf bifurcation are also derived for a positive net growth rate of Vibrio cholerae. Stability analysis and numerical simulations suggest that bacteriophage may contribute to lessening the severity of cholera epidemics by reducing the number of Vibrio cholerae in the environment. Hence with the presence of phage virus, cholera is self-limiting in nature. By using phage as a biological control agent in endemic areas, one may also influence the temporal dynamics of cholera epidemics while reducing the excessive use of chemicals. We also performed stochastic analysis which suggests that the model system is globally asymptotically stable in probability when the strengths of white noise are less than some specific quantities.