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 |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.819 |
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| author | C. Connell McCluskey |
| author_facet | C. Connell McCluskey |
| author_sort | C. Connell McCluskey |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5608df143dde4a23874c7398fd085ee9 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5608df143dde4a23874c7398fd085ee92025-01-24T02:07:06ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-09-019481984110.3934/mbe.2012.9.819Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classesC. Connell McCluskey0Department of Mathematics, Wilfrid Laurier University, Waterloo, OntarioWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.819global stabilitytuberculosisage-structurelatencyepidemiology.lyapunov functional |
| spellingShingle | C. Connell McCluskey Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes Mathematical Biosciences and Engineering global stability tuberculosis age-structure latency epidemiology. lyapunov functional |
| title | Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes |
| title_full | Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes |
| title_fullStr | Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes |
| title_full_unstemmed | Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes |
| title_short | Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes |
| title_sort | global stability for an sei epidemiological model with continuous age structure in the exposed and infectious classes |
| topic | global stability tuberculosis age-structure latency epidemiology. lyapunov functional |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.819 |
| work_keys_str_mv | AT cconnellmccluskey globalstabilityforanseiepidemiologicalmodelwithcontinuousagestructureintheexposedandinfectiousclasses |