- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Submit a Manuscript
- Table of Contents
Volume 2012 (2012), Article ID 621939, 13 pages
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.
- S. Bhattacharya, R. Black, L. Bourgeois et al., “The cholera crisis in Africa,” Science, vol. 324, no. 5929, p. 885, 2009.
- World Health Organization, “Cholera 2005,” Weekly Epidemiological Record, vol. 81, no. 31, pp. 297–308, 2006.
- A. Sulakvelidze, Z. Alavidze, and J. G. Morris, “Bacteriophage therapy,” Antimicrobial Agents and Chemotherapy, vol. 45, no. 3, pp. 649–659, 2001.
- R. Pollitzer, “Cholera studies,” Bulletin of the World Health Organization, vol. 13, no. 1, pp. 1–25, 1955.
- B. L. Sarkar, “Cholera bacteriophages revisited,” ICMR Bulletin, vol. 32, no. 10, 2002.
- R. M. Sayamov, “Treatment and prophylaxis of cholera with bacteriophage,” Bulletin of the World Health Organization, vol. 28, pp. 361–367, 1963.
- W. C. Summers, “Bacteriophage therapy,” Annual Review of Microbiology, vol. 55, pp. 437–451, 2001.
- S. M. Faruque, M. J. Islam, Q. S. Ahmad et al., “Self-limiting nature of seasonal cholera epidemics: role of host-mediated amplification of phage,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 17, pp. 6119–6124, 2005.
- M. A. Jensen, S. M. Faruque, J. J. Mekalanos, and B. R. Levin, “Modeling the role of bacteriophage in the control of cholera outbreaks,” Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 12, pp. 4652–4657, 2006.
- M. S. H. Zahid, S. M. N. Udden, A. S. G. Faruque, S. B. Calderwood, J. J. Mekalanos, and S. M. Faruque, “Effect of phage on the infectivity of vibrio cholerae and emergence of genetic variants,” Infection and Immunity, vol. 76, no. 11, pp. 5266–5273, 2008.
- K. Koelle, X. Rodó, M. Pascual, M. Yunus, and G. Mostafa, “Refractory periods and climate forcing in cholera dynamics,” Nature, vol. 436, no. 7051, pp. 696–700, 2005.
- A. I. Gil, V. R. Louis, I. N. G. Rivera et al., “Occurrence and distribution of Vibrio cholerae in the coastal environment of Peru,” Environmental Microbiology, vol. 6, no. 7, pp. 699–706, 2004.
- B. Lobitz, L. Beck, A. Huq et al., “Climate and infectious disease: use of remote sensing for detection of vibrio cholerae by indirect measurement,” Proceedings of the National Academy of Sciences of the United States of America, vol. 97, no. 4, pp. 1438–1443, 2000.
- M. Pascual, X. Rodo, S. P. Ellner, R. Colwell, and M. J. Bouma, “Cholera dynamics and El Nino-Southern oscillation,” Science, vol. 289, no. 5485, pp. 1766–1769, 2000.
- X. Rodó, M. Pascual, G. Fuchs, and A. S. G. Faruque, “ENSO and cholera: a nonstationary link related to climate change?” Proceedings of the National Academy of Sciences of the United States of America, vol. 99, no. 20, pp. 12901–12906, 2002.
- R. Politzer, Cholera, WHO, Geneva, Switzerland, 1959.
- O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, “On the definition and the computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations,” Journal of Mathematical Biology, vol. 28, no. 4, pp. 365–382, 1990.
- P. V. Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, 2002.
- V. Lakshmikantham, S. Leela, and A. A. Martynyuk, Stability Analysis of a Nonlinear Systems, Marcel Dekker, New York, NY, USA, 1989.
- R. J. Smith and S. M. Blower, “Could disease-modifying HIV vaccines cause population-level perversity?” Lancet Infectious Diseases, vol. 4, no. 10, pp. 636–639, 2004.
- W. M. Liu, “Criterion of Hopf bifurcations without using eigenvalues,” Journal of Mathematical Analysis and Applications, vol. 182, no. 1, pp. 250–256, 1994.
- P. Das, D. Mukherjee, and A. K. Sarkar, “Study of a carrier dependent infectious disease—cholera,” Journal of Biological Systems, vol. 13, no. 3, pp. 233–244, 2005.
- X. Mao, Stochastic Differential Equations and Application, Harwood, 1997.
- D. Mukherjee, “Stability analysis of a stochastic model for prey-predator system with disease in the prey,” Nonlinear Analysis: Modelling and Control, vol. 8, no. 2, pp. 83–92, 2003.
- Gikhman II and A. V. Skorokhod, The Theory of Stochastic Process, Springer, Berlin, Germany, 1974.
- V. N. Afanas’ev, V. B. Kolmanowskii, and V. R. Nosov, Mathematical Theory of Control Systems Design, Kluwer Academic, Dodrecht, The Netherlands, 1996.
- S. M. Faruque, I. B. Naser, M. J. Islam et al., “Seasonal epidemics of cholera inversely correlate with the prevalence of environmental cholera phages,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 5, pp. 1702–1707, 2005.