Dynamics of mycobacterium and bovine tuberculosis in a human-buffalo population

A. S. Hassan, S. M. Garba, Abba Gumel, J. M S Lubuma

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A new model for the transmission dynamics of Mycobacterium tuberculosis and bovine tuberculosis in a community, consisting of humans and African buffalos, is presented. The buffalo-only component of the model exhibits the phenomenon of backward bifurcation, which arises due to the reinfection of exposed and recovered buffalos, when the associated reproduction number is less than unity. This model has a unique endemic equilibrium, which is globally asymptotically stable for a special case, when the reproduction number exceeds unity. Uncertainty and sensitivity analyses, using data relevant to the dynamics of the two diseases in the Kruger National Park, show that the distribution of the associated reproduction number is less than unity (hence, the diseases would not persist in the community). Crucial parameters that influence the dynamics of the two diseases are also identified. Both the buffalo-only and the buffalo-human model exhibit the same qualitative dynamics with respect to the local and global asymptotic stability of their respective disease-free equilibrium, as well as with respect to the backward bifurcation phenomenon. Numerical simulations of the buffalo-human model show that the cumulative number of Mycobacterium tuberculosis cases in humans (buffalos) decreases with increasing number of bovine tuberculosis infections in humans (buffalo).

Original languageEnglish (US)
Article number912306
JournalComputational and Mathematical Methods in Medicine
Volume2014
DOIs
StatePublished - 2014
Externally publishedYes

Fingerprint

Bovine Tuberculosis
Tuberculosis
Buffaloes
Mycobacterium tuberculosis
Reproduction number
Backward Bifurcation
Reproduction
Population
Local Asymptotic Stability
Model
Endemic Equilibrium
Globally Asymptotically Stable
Global Asymptotic Stability
Asymptotic stability
Uncertainty
Infection
Exceed
Human
Numerical Simulation
Decrease

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Medicine(all)
  • Immunology and Microbiology(all)

Cite this

Dynamics of mycobacterium and bovine tuberculosis in a human-buffalo population. / Hassan, A. S.; Garba, S. M.; Gumel, Abba; Lubuma, J. M S.

In: Computational and Mathematical Methods in Medicine, Vol. 2014, 912306, 2014.

Research output: Contribution to journalArticle

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