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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Main Authors: Andrei Korobeinikov, Philip K. Maini
Format: Article
Language:English
Published: AIMS Press 2004-02-01
Series:Mathematical Biosciences and Engineering
Subjects:
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.
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institution Kabale University
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publishDate 2004-02-01
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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
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