Journal of Applied Mathematics

Global Stability of a SLIT TB Model with Staged Progression

Yakui Xue and Xiaohong Wang

Full-text: Open access

Abstract

Because the latent period and the infectious period of tuberculosis (TB) are very long, it is not reasonable to consider the time as constant. So this paper formulates a mathematical model that divides the latent period and the infectious period into n-stages. For a general n-stage stage progression (SP) model with bilinear incidence, we analyze its dynamic behavior. First, we give the basic reproduction number R 0 . Moreover, if R 0 1 , the disease-free equilibrium P 0 is globally asymptotically stable and the disease always dies out. If R 0 > 1 , the unique endemic equilibrium P is globally asymptotically stable and the disease persists at the endemic equilibrium.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 571469, 15 pages.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357153529

Digital Object Identifier
doi:10.1155/2012/571469

Mathematical Reviews number (MathSciNet)
MR2984194

Zentralblatt MATH identifier
1251.92032

Citation

Xue, Yakui; Wang, Xiaohong. Global Stability of a SLIT TB Model with Staged Progression. J. Appl. Math. 2012 (2012), Article ID 571469, 15 pages. doi:10.1155/2012/571469. https://projecteuclid.org/euclid.jam/1357153529


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