Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence
An SIR model with distributed delay and a general incidence function isstudied. Conditions are given under which the system exhibits thresholdbehaviour: the disease-free equilibrium is globally asymptotically stableif R00=1; if R0>1,then the unique endemic equilibrium is globally asymptotically...
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| Format: | Article |
| Language: | English |
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AIMS Press
2010-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.837 |
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| author | C. Connell McCluskey |
| author_facet | C. Connell McCluskey |
| author_sort | C. Connell McCluskey |
| collection | DOAJ |
| description | An SIR model with distributed delay and a general incidence function isstudied. Conditions are given under which the system exhibits thresholdbehaviour: the disease-free equilibrium is globally asymptotically stableif R00=1; if R0>1,then the unique endemic equilibrium is globally asymptotically stable.The global stability proofs use a Lyapunov functional and do not requireuniform persistence to be shown a priori. It is shown that thegiven conditions are satisfied by several common forms of the incidencefunction. |
| format | Article |
| id | doaj-art-79e354402c6c4a0ba3e435b1b7a3013f |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2010-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-79e354402c6c4a0ba3e435b1b7a3013f2025-01-24T02:00:58ZengAIMS PressMathematical Biosciences and Engineering1551-00182010-09-017483785010.3934/mbe.2010.7.837Global stability of an $SIR$ epidemic model with delay and general nonlinear incidenceC. Connell McCluskey0Department of Mathematics, Wilfrid Laurier University, Waterloo, OntarioAn SIR model with distributed delay and a general incidence function isstudied. Conditions are given under which the system exhibits thresholdbehaviour: the disease-free equilibrium is globally asymptotically stableif R00=1; if R0>1,then the unique endemic equilibrium is globally asymptotically stable.The global stability proofs use a Lyapunov functional and do not requireuniform persistence to be shown a priori. It is shown that thegiven conditions are satisfied by several common forms of the incidencefunction.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.837global stabilitylyapunov functionalnonlinear incidence.delay |
| spellingShingle | C. Connell McCluskey Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence Mathematical Biosciences and Engineering global stability lyapunov functional nonlinear incidence. delay |
| title | Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence |
| title_full | Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence |
| title_fullStr | Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence |
| title_full_unstemmed | Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence |
| title_short | Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence |
| title_sort | global stability of an sir epidemic model with delay and general nonlinear incidence |
| topic | global stability lyapunov functional nonlinear incidence. delay |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.837 |
| work_keys_str_mv | AT cconnellmccluskey globalstabilityofansirepidemicmodelwithdelayandgeneralnonlinearincidence |