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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 2: 369-378. doi: 10.3934/mbe.2013.10.369
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Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility

  • 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: 01 January 2012 Accepted: 29 June 2018 Published: 01 January 2013

  • MSC : Primary: 92D30; Secondary: 35F31, 34D23.

  • We consider global asymptotic properties for the SIR and SEIRage structured models for infectious diseases where the susceptibilitydepends on the age. Using the direct Lyapunov method with Volterratype Lyapunov functions, we establish conditions for the global stabilityof 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 withage-dependent susceptibility[J]. Mathematical Biosciences and Engineering, 2013, 10(2): 369-378. doi: 10.3934/mbe.2013.10.369

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  • We consider global asymptotic properties for the SIR and SEIRage structured models for infectious diseases where the susceptibilitydepends on the age. Using the direct Lyapunov method with Volterratype Lyapunov functions, we establish conditions for the global stabilityof a unique endemic steady state and the infection-free steady state.


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