# 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)
• Accepted : 2011.04.02
• Published : 2011.09.30

#### 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.

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