Abstract
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.
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Okuonghae, D. Lyapunov functions and global properties of some tuberculosis models. J. Appl. Math. Comput. 48, 421–439 (2015). https://doi.org/10.1007/s12190-014-0811-4
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DOI: https://doi.org/10.1007/s12190-014-0811-4