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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 703826, 11 pages
http://dx.doi.org/10.1155/2013/703826
Research Article

Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission

1Department of Mathematics, North University of China, Taiyuan, Shan'xi 030051, China
2Complex Systems Center, Shanxi University, Taiyuan, Shan'xi 030006, China
3Institute of Information Economy, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China
4School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received 4 October 2013; Accepted 7 November 2013

Academic Editor: Antonia Vecchio

Copyright © 2013 Ming-Tao Li et al. 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

For a multigroup cholera model with indirect transmission, the infection for a susceptible person is almost invariably transmitted by drinking contaminated water in which pathogens, V. cholerae, are present. The basic reproduction number is identified and global dynamics are completely determined by . It shows that is a globally threshold parameter in the sense that if it is less than one, the disease-free equilibrium is globally asymptotically stable; whereas if it is larger than one, there is a unique endemic equilibrium which is global asymptotically stable. For the proof of global stability with the disease-free equilibrium, we use the comparison principle; and for the endemic equilibrium we use the classical method of Lyapunov function and the graph-theoretic approach.