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
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.