# American Institute of Mathematical Sciences

2004, 1(1): 57-60. doi: 10.3934/mbe.2004.1.57

## 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, United Kingdom 2 Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, United Kingdom

Received  February 2004 Revised  February 2004 Published  March 2004

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.
Citation: Andrei Korobeinikov, Philip K. Maini. A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence. Mathematical Biosciences & Engineering, 2004, 1 (1) : 57-60. doi: 10.3934/mbe.2004.1.57
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