Lyapunov functions for tuberculosis models with fast and slow progression

C. Connell Mccluskey

doi:10.3934/mbe.2006.3.603

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2006, Volume 3, Issue 4: 603-614. Doi: 10.3934/mbe.2006.3.603

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Lyapunov functions for tuberculosis models with fast and slow progression

C. Connell Mccluskey^1,

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

Received: September 2005

Revised: December 2005

Published: August 2006

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Abstract

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.

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Mathematics Subject Classification: 92D30, 34D23.

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