Lyapunov functions and global properties of some tuberculosis models
This work examines the global stability of the disease equilibria of three tuberculosis mathematical models that considered the effect of case detection vis a vis the implementation of the direct observation therapy strategy, factors that enhances the case detection rate and effect of heterogeneity in susceptibility and disease progression. Both linear and non-linear Lyapunov functions are constructed and used to show that the disease-free equilibrium is globally asymptotically stable when the corresponding effective reproduction number is less than or equal to one. However, under some special cases where the disease-induced death is insignificant, the endemic equilibrium is globally asymptotically stable when the effective reproduction number is greater than one.
lyapunov tuberculosis global stability mathematical model case detection heterogeneity