## Journal of Applied Mathematics

### Global Stability of a SLIT TB Model with Staged Progression

#### 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 ${R}_{0}\le 1$, the disease-free equilibrium ${P}_{0}$ is globally asymptotically stable and the disease always dies out. If ${R}_{0}>1$, the unique endemic equilibrium ${P}^{\ast }$ 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