Mathematical analysis of a model for the transmission dynamics of bovine tuberculosis

✍ Scribed by Folashade B. Agusto; Suzanne Lenhart; Abba B. Gumel; Agricola Odoi

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 359 KB
• Volume: 34
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1486

✦ Synopsis

Communicated by W. Sprößig

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.