Global Stability of a SLIT TB Model with Staged Progression
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/571469 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |