Global dynamics of a staged progression model for infectious diseases
We analyze a mathematical model for infectious diseases thatprogress through distinct stages within infected hosts. An exampleof such a disease is AIDS, which results from HIV infection. For ageneral $n$-stage stage-progression (SP) model with bilinearincidences, we prove that the global dynamics ar...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2006-04-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.513 |
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| Summary: | We analyze a mathematical model for infectious diseases thatprogress through distinct stages within infected hosts. An exampleof such a disease is AIDS, which results from HIV infection. For ageneral $n$-stage stage-progression (SP) model with bilinearincidences, we prove that the global dynamics are completelydetermined by the basic reproduction number $R_0.$ If $R_0\le 1,$then the disease-free equilibrium $P_0$ is globally asymptoticallystable and the disease always dies out. If $R_0>1,$ $P_0$ isunstable, and a unique endemic equilibrium $P^*$ is globallyasymptotically stable, and the disease persists at the endemicequilibrium. The basic reproduction numbers for the SP model withdensity dependent incidence forms are also discussed. |
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| ISSN: | 1551-0018 |