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An unconditionally convergent discretization of the SEIR model

Author

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  • Jansen, H.
  • Twizell, E.H.

Abstract

The SEIR (susceptible, exposed, infectious, recovered) model has been discussed by many authors, in particular with reference to the spread of measles in an epidemic. In this paper, the SEIR model with constant rate of infection is solved using a first-order, finite-difference method in the form of a system of one-point iteration functions. This discrete system is seen to have two fixed points which are identical to the critical points of the (continuous) equations of the SEIR model and it is shown that they have the same stability properties. It is shown further that the solution sequence is attracted from any set of initial conditions to the correct (stable) fixed point for an arbitrarily large time step. Simulations confirm this and results are compared with well-known numerical methods.

Suggested Citation

  • Jansen, H. & Twizell, E.H., 2002. "An unconditionally convergent discretization of the SEIR model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(2), pages 147-158.
    • Handle: RePEc:eee:matcom:v:58:y:2002:i:2:p:147-158
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    Citations

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    Cited by:

    1. Dimitrov, Dobromir T. & Kojouharov, Hristo V., 2008. "Nonstandard finite-difference methods for predator–prey models with general functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(1), pages 1-11.
    2. Kimberly M. Thompson, 2016. "Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis," Risk Analysis, John Wiley & Sons, vol. 36(7), pages 1383-1403, July.
    3. Jódar, Lucas & Villanueva, Rafael J. & Arenas, Abraham J. & González, Gilberto C., 2008. "Nonstandard numerical methods for a mathematical model for influenza disease," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 622-633.
    4. Xu, Rui & Wang, Zhili & Zhang, Fengqin, 2015. "Global stability and Hopf bifurcations of an SEIR epidemiological model with logistic growth and time delay," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 332-342.
    5. Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    6. Xu, Rui, 2012. "Global dynamics of an SEIS epidemiological model with time delay describing a latent period," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 90-102.

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