A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence

Andrei Korobeinikov; Philip K. Maini

doi:10.3934/mbe.2004.1.57

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2004, Volume 1, Issue 1: 57-60. Doi: 10.3934/mbe.2004.1.57

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A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence

Andrei Korobeinikov^1, and
Philip K. Maini^2,

1.
Centre for Mathematical Biology, Mathematical Institute University of Oxford, 24-29 St Giles', Oxford, OX1 3LB
2.
Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB

Received: January 31, 2004

Revised: January 31, 2004

Published: February 2004

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Abstract

Explicit Lyapunov functions for SIR and SEIR compartmental epidemic 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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Mathematics Subject Classification: 92D30, 34D20.

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