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Mathematical Biosciences and Engineering

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

  • 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.

    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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  • 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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