Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility

Andrey V. Melnik; Andrei Korobeinikov

doi:10.3934/mbe.2013.10.369

Article Contents

2013, Volume 10, Issue 2: 369-378. Doi: 10.3934/mbe.2013.10.369

This issue Previous Article Uniqueness of limit cycles and multiple attractors in a Gause-type predator-prey model with nonmonotonic functional response and Allee effect on prey Next Article An extension of Gompertzian growth dynamics: Weibull and Fréchet models

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

Andrey V. Melnik^1, and
Andrei Korobeinikov^2,

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

Received: January 2012

Revised: September 2012

Published: December 2012

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Abstract

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.

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Mathematics Subject Classification: Primary: 92D30; Secondary: 35F31, 34D23.

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