A Lyapunov function and global properties for <em>SIR</em> and <em>SEIR</em> epidemiological models with nonlinear incidence

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

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: 01 February 2004 Accepted: 29 June 2018 Published: 01 March 2004
MSC : 92D30, 34D20.

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.
- nonlinear incidence.,
- endemic equilibrium state,
- global stability,
- Direct Lyapunov method
Citation: Andrei Korobeinikov, Philip K. Maini. A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence[J]. Mathematical Biosciences and Engineering, 2004, 1(1): 57-60. doi: 10.3934/mbe.2004.1.57

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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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