Mathematical analysis of a model for the transmission dynamics of bovine tuberculosis |
| |
| Authors: | Folashade B Agusto Suzanne Lenhart Abba B Gumel Agricola Odoi |
| |
| Institution: | 1. National Institute for Mathematical and Biological Synthesis, University of Tennessee, , Knoxville, 37996 TN, USA;2. Department of Mathematics, University of Tennessee, , Knoxville, 37996 TN, USA;3. Department of Mathematics, University of Manitoba, , Winnipeg, Manitoba, R3T 2N2 Canada;4. Department of Comparative Medicine, University of Tennessee, , Knoxville, 37996 TN, USA |
| |
| Abstract: | 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. |
| |
| Keywords: | bovine tuberculosis equilibria stability reproduction number |
|
|
