A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence
Explicit Lyapunov functions for SIR and SEIR compartmentalepidemic models with nonlinear incidence of the form $\beta I^p S^q$for the case $p \leq 1$are constructed. Global stability of the models is thereby established.
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AIMS Press
2004-02-01
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Series: | Mathematical Biosciences and Engineering |
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Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.57 |
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author | Andrei Korobeinikov Philip K. Maini |
author_facet | Andrei Korobeinikov Philip K. Maini |
author_sort | Andrei Korobeinikov |
collection | DOAJ |
description | Explicit Lyapunov functions for SIR and SEIR compartmentalepidemic models with nonlinear incidence of the form $\beta I^p S^q$for the case $p \leq 1$are constructed. Global stability of the models is thereby established. |
format | Article |
id | doaj-art-f8320eb2fb364dd9ab072fc1946a1b83 |
institution | Kabale University |
issn | 1551-0018 |
language | English |
publishDate | 2004-02-01 |
publisher | AIMS Press |
record_format | Article |
series | Mathematical Biosciences and Engineering |
spelling | doaj-art-f8320eb2fb364dd9ab072fc1946a1b832025-01-24T01:46:28ZengAIMS PressMathematical Biosciences and Engineering1551-00182004-02-0111576010.3934/mbe.2004.1.57A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidenceAndrei Korobeinikov0Philip K. Maini1Centre for Mathematical Biology, Mathematical Institute University of Oxford, 24-29 St Giles', Oxford, OX1 3LBCentre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LBExplicit Lyapunov functions for SIR and SEIR compartmentalepidemic models with nonlinear incidence of the form $\beta I^p S^q$for the case $p \leq 1$are constructed. Global stability of the models is thereby established.https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.57nonlinear incidence.endemic equilibrium stateglobal stabilitydirect lyapunov method |
spellingShingle | Andrei Korobeinikov Philip K. Maini A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence Mathematical Biosciences and Engineering nonlinear incidence. endemic equilibrium state global stability direct lyapunov method |
title | A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence |
title_full | A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence |
title_fullStr | A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence |
title_full_unstemmed | A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence |
title_short | A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence |
title_sort | lyapunov function and global properties for sir and seir epidemiological models with nonlinear incidence |
topic | nonlinear incidence. endemic equilibrium state global stability direct lyapunov method |
url | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.57 |
work_keys_str_mv | AT andreikorobeinikov alyapunovfunctionandglobalpropertiesforsirandseirepidemiologicalmodelswithnonlinearincidence AT philipkmaini alyapunovfunctionandglobalpropertiesforsirandseirepidemiologicalmodelswithnonlinearincidence AT andreikorobeinikov lyapunovfunctionandglobalpropertiesforsirandseirepidemiologicalmodelswithnonlinearincidence AT philipkmaini lyapunovfunctionandglobalpropertiesforsirandseirepidemiologicalmodelswithnonlinearincidence |