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http://dx.doi.org/10.14317/jami.2011.29.5_6.1097

GLOBAL STABILITY OF A TUBERCULOSIS MODEL WITH n LATENT CLASSES  

Moualeu, Dany Pascal (Department of Mathematics, University of Yaounde I)
Bowong, Samuel (Department of Mathematics and Computer Science, University of Douala)
Emvudu, Yves (Department of Mathematics, University of Yaounde I)
Publication Information
Journal of applied mathematics & informatics / v.29, no.5_6, 2011 , pp. 1097-1115 More about this Journal
Abstract
We consider the global stability of a general tuberculosis model with two differential infectivity, n classes of latent individuals and mass action incidence. This system exhibits the traditional threshold behavior. There is always a globally asymptotically stable equilibrium state. Depending on the value of the basic reproduction ratio $\mathcal{R}_0$, this state can be either endemic ($\mathcal{R}_0$ > 1), or infection-free ($\mathcal{R}_0{\leq}1$). The global stability of this model is derived through the use of Lyapunov stability theory and LaSalle's invariant set theorem. Both the analytical results and numerical simulations suggest that patients should be strongly encouraged to complete their treatment and sputum examination.
Keywords
Epidemiological models; Tuberculosis; Global stability;
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