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

Folashade B. Agusto, Suzanne Lenhart, Abba Gumel, Agricola Odoi

Research output: Contribution to journalArticle

11 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1873-1887
Number of pages15
JournalMathematical Methods in the Applied Sciences
Volume34
Issue number15
DOIs
StatePublished - Oct 2011
Externally publishedYes

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Tuberculosis
Mathematical Analysis
Globally Asymptotically Stable
Reproduction number
Endemic Equilibrium
Model
Deterministic Model
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Keywords

  • bovine tuberculosis
  • equilibria
  • reproduction number
  • stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Mathematical analysis of a model for the transmission dynamics of bovine tuberculosis. / Agusto, Folashade B.; Lenhart, Suzanne; Gumel, Abba; Odoi, Agricola.

In: Mathematical Methods in the Applied Sciences, Vol. 34, No. 15, 10.2011, p. 1873-1887.

Research output: Contribution to journalArticle

Agusto, Folashade B. ; Lenhart, Suzanne ; Gumel, Abba ; Odoi, Agricola. / Mathematical analysis of a model for the transmission dynamics of bovine tuberculosis. In: Mathematical Methods in the Applied Sciences. 2011 ; Vol. 34, No. 15. pp. 1873-1887.
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