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Abstract
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Article Information:
Global Stability Results for a Tuberculosis Epidemic Model
S.A. Egbetade and M.O. Ibrahim
Corresponding Author: S.A. Egbetade
Submitted: December 09, 2011
Accepted: February 15, 2012
Published: February 25, 2012 |
Abstract:
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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.
Key words: Basic reproduction number, epidemic, equilibrium, global stability, infectious disease, tuberculosis model, uniform persistence
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Cite this Reference:
S.A. Egbetade and M.O. Ibrahim, . Global Stability Results for a Tuberculosis Epidemic Model. Research Journal of Mathematics and Statistics, (1): 14-20.
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ISSN (Online): 2040-7505
ISSN (Print): 2042-2024 |
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