SEIR epidemiological model with varying infectivity and infinite delay
A new SEIR model with distributed infinite delay is derived whenthe infectivity depends on the age of infection. The basic reproduction numberR0, which is a threshold quantity for the stability of equilibria, is calculated.If $R_0$ 1, then an endemicequilibrium appears which is locally asymptotical...
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| Format: | Article |
| Language: | English |
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AIMS Press
2008-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.389 |
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| _version_ | 1832590175002165248 |
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| author | Gergely Röst Jianhong Wu |
| author_facet | Gergely Röst Jianhong Wu |
| author_sort | Gergely Röst |
| collection | DOAJ |
| description | A new SEIR model with distributed infinite delay is derived whenthe infectivity depends on the age of infection. The basic reproduction numberR0, which is a threshold quantity for the stability of equilibria, is calculated.If $R_0$ 1, then an endemicequilibrium appears which is locally asymptotically stable. Applying a perma-nence theorem for infinite dimensional systems, we obtain that the disease isalways present when $R_0$ > 1. |
| format | Article |
| id | doaj-art-2b4e15071f1c447386e9cbe46d83220f |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2008-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-2b4e15071f1c447386e9cbe46d83220f2025-01-24T01:58:10ZengAIMS PressMathematical Biosciences and Engineering1551-00182008-02-015238940210.3934/mbe.2008.5.389SEIR epidemiological model with varying infectivity and infinite delayGergely Röst0Jianhong Wu1Analysis and Stochastics Research Group, Hungarian Academy of Sciences, Bolyai Institute, University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1.Analysis and Stochastics Research Group, Hungarian Academy of Sciences, Bolyai Institute, University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1.A new SEIR model with distributed infinite delay is derived whenthe infectivity depends on the age of infection. The basic reproduction numberR0, which is a threshold quantity for the stability of equilibria, is calculated.If $R_0$ 1, then an endemicequilibrium appears which is locally asymptotically stable. Applying a perma-nence theorem for infinite dimensional systems, we obtain that the disease isalways present when $R_0$ > 1.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.389mathematical epidemiologypermanence.stabilityseir modelinfinite delay |
| spellingShingle | Gergely Röst Jianhong Wu SEIR epidemiological model with varying infectivity and infinite delay Mathematical Biosciences and Engineering mathematical epidemiology permanence. stability seir model infinite delay |
| title | SEIR epidemiological model with varying infectivity and infinite delay |
| title_full | SEIR epidemiological model with varying infectivity and infinite delay |
| title_fullStr | SEIR epidemiological model with varying infectivity and infinite delay |
| title_full_unstemmed | SEIR epidemiological model with varying infectivity and infinite delay |
| title_short | SEIR epidemiological model with varying infectivity and infinite delay |
| title_sort | seir epidemiological model with varying infectivity and infinite delay |
| topic | mathematical epidemiology permanence. stability seir model infinite delay |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.389 |
| work_keys_str_mv | AT gergelyrost seirepidemiologicalmodelwithvaryinginfectivityandinfinitedelay AT jianhongwu seirepidemiologicalmodelwithvaryinginfectivityandinfinitedelay |