American Institute of Mathematical Sciences

Advanced
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

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, 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.
Keywords: nonlinear incidence., endemic equilibrium state, global stability, Direct Lyapunov method.
Mathematics Subject Classification: 92D30, 34D2.
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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