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Research Article
Mathematical analysis of a model for the transmission dynamics of bovine tuberculosis
Article first published online: 8 SEP 2011
DOI: 10.1002/mma.1486
Copyright © 2011 John Wiley & Sons, Ltd.
Issue
Mathematical Methods in the Applied Sciences
Volume 34, Issue 15, pages 1873–1887, October 2011
Additional Information
How to Cite
Agusto, F. B., Lenhart, S., Gumel, A. B. and Odoi, A. (2011), Mathematical analysis of a model for the transmission dynamics of bovine tuberculosis. Math. Meth. Appl. Sci., 34: 1873–1887. doi: 10.1002/mma.1486
Publication History
- Issue published online: 26 SEP 2011
- Article first published online: 8 SEP 2011
- Manuscript Received: 30 JAN 2011
Funded by
- National Science Foundation
- US Department of Homeland Security
- US Department of Agriculture through NSF. Grant Number: EF-0832858
- University of Tennessee, Knoxville
- NIMBioS
- Abstract
- Article
- References
- Cited By
Keywords:
- bovine tuberculosis;
- equilibria;
- stability;
- reproduction number
A deterministic model for studying the transmission dynamics of bovine tuberculosis in a single cattle herd is presented and qualitatively analyzed. A notable feature of the model is that it allows for the importation of asymptomatically infected cattle (into the herd) because re-stocking from outside sources. Rigorous analysis of the model shows that the model has a globally-asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the reproduction number, is less than unity. In the absence of importation of asymptomatically infected cattle, the model has a unique endemic equilibrium whenever the reproduction number exceeds unity (this equilibrium is globally asymptotically stable for a special case). It is further shown that, for the case where asymptomatically infected cattle are imported into the herd, the model has a unique endemic equilibrium. This equilibrium is also shown to be globally asymptotically stable for a special case. Copyright © 2011 John Wiley & Sons, Ltd.