Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes
We study a model of disease transmission with continuous age-structure for latentlyinfected individuals and for infectious individuals. The model is very appropriate fortuberculosis. Key theorems, including asymptotic smoothness and uniform persistence,are proven by reformulating the system as a s...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-09-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.819 |
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| Summary: | We study a model of disease transmission with continuous age-structure for latentlyinfected individuals and for infectious individuals. The model is very appropriate fortuberculosis. Key theorems, including asymptotic smoothness and uniform persistence,are proven by reformulating the system as a system of Volterra integral equations. Thebasic reproduction number $\mathcal{R}_{0}$ is calculated. For $\mathcal{R}_{0}1$, a Lyapunov functionalis used to show that the endemic equilibrium is globally stable amongst solutions forwhich the disease is present. Finally, some special cases are considered. |
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| ISSN: | 1551-0018 |