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Mathematical Biosciences and Engineering

2004, Volume 1, Issue 1: 57-60. doi: 10.3934/mbe.2004.1.57
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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
  • 2.
    Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB
  • Received: 01 February 2004 Accepted: 29 June 2018 Published: 01 March 2004

  • MSC : 92D30, 34D20.

  • Explicit Lyapunov functions for SIR and SEIR compartmental epidemic models with nonlinear incidence of the form βIpSq for the case p≤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[J]. Mathematical Biosciences and Engineering, 2004, 1(1): 57-60. doi: 10.3934/mbe.2004.1.57

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  • Explicit Lyapunov functions for SIR and SEIR compartmental epidemic models with nonlinear incidence of the form βIpSq for the case p≤1 are constructed. Global stability of the models is thereby established.


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