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CHEN Hui, LI Liang-Chen. Global stability of a discrete tuberculosis model[J]. Journal of East China Normal University (Natural Sciences), 2015, (6): 72-80. doi: 10.3969/j.issn.1000-5641.2015.06.010
Citation:
CHEN Hui, LI Liang-Chen. Global stability of a discrete tuberculosis model[J]. Journal of East China Normal University (Natural Sciences), 2015, (6): 72-80. doi: 10.3969/j.issn.1000-5641.2015.06.010
CHEN Hui, LI Liang-Chen. Global stability of a discrete tuberculosis model[J]. Journal of East China Normal University (Natural Sciences), 2015, (6): 72-80. doi: 10.3969/j.issn.1000-5641.2015.06.010
Citation:
CHEN Hui, LI Liang-Chen. Global stability of a discrete tuberculosis model[J]. Journal of East China Normal University (Natural Sciences), 2015, (6): 72-80. doi: 10.3969/j.issn.1000-5641.2015.06.010
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 $R_0 1$