Global stability for an SEIR epidemiological model with varying infectivity and infinite delay
A recent paper (Math. Biosci. and Eng. (2008) 5:389-402)presented an SEIR model using an infinite delay to account for varyinginfectivity. The analysis in that paper did not resolve the globaldynamics for R0 >1. Here, we show that the endemic equilibriumis globally stable for R0 >1. The pro...
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| Format: | Article |
| Language: | English |
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AIMS Press
2009-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.603 |
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| author | C. Connell McCluskey |
| author_facet | C. Connell McCluskey |
| author_sort | C. Connell McCluskey |
| collection | DOAJ |
| description | A recent paper (Math. Biosci. and Eng. (2008) 5:389-402)presented an SEIR model using an infinite delay to account for varyinginfectivity. The analysis in that paper did not resolve the globaldynamics for R0 >1. Here, we show that the endemic equilibriumis globally stable for R0 >1. The proof uses a Lyapunovfunctional that includes an integral over all previous states. |
| format | Article |
| id | doaj-art-c56d2ecdd7a44f77a08cc4521f4a8f94 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c56d2ecdd7a44f77a08cc4521f4a8f942025-01-24T01:59:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-05-016360361010.3934/mbe.2009.6.603Global stability for an SEIR epidemiological model with varying infectivity and infinite delayC. Connell McCluskey0Department of Mathematics, Wilfrid Laurier University, Waterloo, OntarioA recent paper (Math. Biosci. and Eng. (2008) 5:389-402)presented an SEIR model using an infinite delay to account for varyinginfectivity. The analysis in that paper did not resolve the globaldynamics for R0 >1. Here, we show that the endemic equilibriumis globally stable for R0 >1. The proof uses a Lyapunovfunctional that includes an integral over all previous states.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.603lyapunov functional.infinite delayglobal stability |
| spellingShingle | C. Connell McCluskey Global stability for an SEIR epidemiological model with varying infectivity and infinite delay Mathematical Biosciences and Engineering lyapunov functional. infinite delay global stability |
| title | Global stability for an SEIR epidemiological model with varying infectivity and infinite delay |
| title_full | Global stability for an SEIR epidemiological model with varying infectivity and infinite delay |
| title_fullStr | Global stability for an SEIR epidemiological model with varying infectivity and infinite delay |
| title_full_unstemmed | Global stability for an SEIR epidemiological model with varying infectivity and infinite delay |
| title_short | Global stability for an SEIR epidemiological model with varying infectivity and infinite delay |
| title_sort | global stability for an seir epidemiological model with varying infectivity and infinite delay |
| topic | lyapunov functional. infinite delay global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.603 |
| work_keys_str_mv | AT cconnellmccluskey globalstabilityforanseirepidemiologicalmodelwithvaryinginfectivityandinfinitedelay |