Lyapunov functions for tuberculosis models with fast and slow progression

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

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

Received: 01 September 2005 Accepted: 29 June 2018 Published: 01 August 2006
MSC : 92D30, 34D23.

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.
- fast and slow progression.,
- Lyapunov function,
- global stability,
- tuberculosis
Citation: C. Connell Mccluskey. Lyapunov functions for tuberculosis models with fast and slow progression[J]. Mathematical Biosciences and Engineering, 2006, 3(4): 603-614. doi: 10.3934/mbe.2006.3.603

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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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© 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)