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Dynamically consistent discrete epidemic model with modified saturated incidence rate

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Abstract

A nonstandard finite difference scheme is constructed to solve a SIR epidemic model with modified saturated incidence rate. The dynamical properties of the resulting discrete system are then analyzed. It is shown that the discrete system is dynamically consistent with the continuous model because it preserves essential properties of the considered model, such as positivity and boundedness of solutions, equilibrium points and their stability properties. These properties are confirmed by numerical simulations.

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Acknowledgments

This research is financially supported by the Directorate General of Higher Education, Ministry of Education and Culture of Republic Indonesia via DIPA of Brawijaya University No.: 0636/023-04.2.16/15/2012, and based on letter of decision of Brawijaya University Rector No.: 058/SK/2012. The authors thank the referee(s) for their careful reading, valuable comments and suggestions to improve this paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Brawijaya University, Jl. Veteran, Malang, 65145, Indonesia

    A. Suryanto, W. M. Kusumawinahyu, I. Darti & I. Yanti

Authors
  1. A. Suryanto
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  2. W. M. Kusumawinahyu
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  3. I. Darti
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  4. I. Yanti
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Corresponding author

Correspondence to A. Suryanto.

Additional information

Communicated by Marcos Raydan.

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Suryanto, A., Kusumawinahyu, W.M., Darti, I. et al. Dynamically consistent discrete epidemic model with modified saturated incidence rate. Comp. Appl. Math. 32, 373–383 (2013). https://doi.org/10.1007/s40314-013-0026-6

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  • DOI: https://doi.org/10.1007/s40314-013-0026-6

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