Lyapunov functions for tuberculosis models with fast and slow progression

Abstract

The spread of tuberculosis is studied through two models whichinclude fast and slow progression to the infected class. For each model, Lyapunovfunctions are used to show that when the basic reproduction numberis less than or equal to one, the disease-free equilibrium is globally asymptoticallystable, and when it is greater than one there is an endemic equilibriumwhich is globally asymptotically stable.

Keywords

• fast and slowprogression.
• lyapunov function
• global stability
• tuberculosis