Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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TUBERCULOSIS TRANSMISSION MODEL WITH CASE DETECTION AND TREATMENT

  • Bhunu, C.P. (Department of Applied Mathematics, National University of Science and Techology) ;
  • Mushayabasa, S. (Department of Applied Mathematics, National University of Science and Techology) ;
  • Magombedze, G. (University of Cape Town,Computational Biology, IIDMM) ;
  • Roeger, L.I. (Department of Mathematics and Statistics Texas Tech University)
  • Received : 2010.05.30
  • Accepted : 2010.08.25
  • Published : 2011.05.30
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Abstract

A deterministic tuberculosis model for theoretically assessing the potential impact of the combined effects of case detection in the presence of treatment is formulated. The qualitative features of its equilibria are analyzed and it is found that the disease-free equilibrium may not be globally asymptotically stable when the reproduction number is less than unity. This disease threshold number is further used to assess the impact of active TB case finding alone and in conjunction with treatment. A critical threshold parameter ${\Theta}$ say for which case detection will have a positive impact is derived. Using the Centre Manifold theory, the model may exhibit the phenomenon of backward bifurcation (coexistence of a locally stable endemic equilibrium with a stable disease-free equilibrium) when the reproduction number is less than unity. It is shown that the possibility of backward bifurcation occurring decreases with increase case detection. Graphical representations suggest that increase in case finding accompanied by treatment of detected TB cases, result in a marked decrease of TB cases (both latent and active TB).

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References

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