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2013, 10(2): 369-378. doi: 10.3934/mbe.2013.10.369

## Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility

 1 OCCAM, Mathematical Institute, 24 - 29 St Giles', Oxford, OX1 3LB, United Kingdom 2 Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona, Spain

Received  January 2012 Revised  September 2012 Published  January 2013

We consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.
Citation: Andrey V. Melnik, Andrei Korobeinikov. Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility. Mathematical Biosciences & Engineering, 2013, 10 (2) : 369-378. doi: 10.3934/mbe.2013.10.369
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