Mathematical Biosciences and Engineering (MBE)

Lyapunov functions for tuberculosis models with fast and slow progression

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

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C. Connell Mccluskey - Department of Mathematics, Wilfrid Laurier University, 75 University Ave West, Waterloo, ON, N2L 3C5, Canada (email)

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.

Keywords:  Lyapunov function, global stability, tuberculosis, fast and slow progression.
Mathematics Subject Classification:  92D30, 34D23.

Received: September 2005;      Accepted: December 2005;      Available Online: August 2006.