Article

Global stability of a discrete tuberculosis model

  • CHEN Hui ,
  • LI Liang-Chen
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Received date: 2014-09-25

  Online published: 2015-12-23

Abstract

In this paper, a discrete tuberculosis model is investigated. By means of calculating the next generation matrix'sspectral radius, we derive the reproduction number $R_0 $ of themodel. The solutions of the model are bounded and positive, whichcan be verified through the relation theory of the differenceequation. It is proved that $R_0 =1$ is a threshold to determine thedisease extincation or persistence. The disease-free equilibrium isglobal asymptotically stable when the reproduction number $R_0 <1$.The endemic equilibrium is global asymptotically stable when the reproduction number $R_0 >1$

Cite this article

CHEN Hui , LI Liang-Chen . Global stability of a discrete tuberculosis model[J]. Journal of East China Normal University(Natural Science), 2015 , 2015(6) : 72 -80 . DOI: 10.3969/j.issn.1000-5641.2015.06.010

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