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2012 (Vol. 4, Issue: 1)
Article Information:

Global Stability Results for a Tuberculosis Epidemic Model

S.A. Egbetade and M.O. Ibrahim
Corresponding Author:  S.A. Egbetade 

Key words:  Basic reproduction number, epidemic, equilibrium, global stability, infectious disease, tuberculosis model, uniform persistence
Vol. 4 , (1): 14-20
Submitted Accepted Published
December 09, 2011 February 15, 2012 February 25, 2012
Abstract:

In this study, we analyse models of TB dynamics in the literature and present a model of our own. We conduct global stability analysis of equilibrium states of the model. Our results show that the basic reproduction number R0 is a threshold parameter of the disease dynamics. In particular, either all positive solutions approach the disease-free equilibrium (R0≤1) or a unique endemic equilibrium (R0>1) . The Disease- Free Equilibrium (DFE) is shown to be Globally Asymptotically Stable (GAS) if R0≤1 and we investigate the endemic global stability using Lyapunov functions and Volterra-Lyapunov matrix properties.
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  Cite this Reference:
S.A. Egbetade and M.O. Ibrahim, 2012. Global Stability Results for a Tuberculosis Epidemic Model.  Research Journal of Mathematics and Statistics, 4(1): 14-20.
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ISSN (Online):  2040-7505
ISSN (Print):   2042-2024
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