Global Stability of a SLIT TB Model with Staged Progression

Yakui Xue and Xiaohong Wang

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

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 R0. Moreover, if R0 ≤ 1, the disease‐free equilibrium P0 is globally asymptotically stable and the disease always dies out. If R0 > 1, the unique endemic equilibrium P∗ is globally asymptotically stable and the disease persists at the endemic equilibrium.

Date: 2012
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https://doi.org/10.1155/2012/571469

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:571469

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