# American Institute of Mathematical Sciences

2006, 3(4): 603-614. doi: 10.3934/mbe.2006.3.603

## Lyapunov functions for tuberculosis models with fast and slow progression

 1 Department of Mathematics, Wilfrid Laurier University, 75 University Ave West, Waterloo, ON, N2L 3C5, Canada

Received  September 2005 Revised  December 2005 Published  August 2006

The spread of tuberculosis is studied through two models which include fast and slow progression to the infected class. For each model, Lyapunov functions are used to show that when the basic reproduction number is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is globally asymptotically stable.
Citation: C. Connell Mccluskey. Lyapunov functions for tuberculosis models with fast and slow progression. Mathematical Biosciences & Engineering, 2006, 3 (4) : 603-614. doi: 10.3934/mbe.2006.3.603
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