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Analysis of a Discrete-Time Fractional Order SIR Epidemic Model for Childhood Diseases

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Dynamical Systems, Bifurcation Analysis and Applications (DySBA 2018)

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Abstract

In this paper, a discrete-time fractional order SIR epidemic model for a childhood disease with constant vaccination program is investigated. The local asymptotic stability and bifurcation of the equilibrium points are analyzed using basic reproduction number. Flip and Neimark-Sacker (N-S) bifurcations are investigated for endemic equilibrium point and numerical simulations are carried out to illustrate the dynamical behaviors of the model. Chaos phenomenon is observed through numerical simulation inside the flip and N-S bifurcation regions. Results of the numerical simulations support the theoretical analysis.

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Acknowledgements

The authors would like to thank the editor and the referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

    Mahmoud A. M. Abdelaziz, Ahmad Izani Ismail, Farah A. Abdullah & Mohd Hafiz Mohd

Authors
  1. Mahmoud A. M. Abdelaziz
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  2. Ahmad Izani Ismail
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  3. Farah A. Abdullah
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  4. Mohd Hafiz Mohd
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Corresponding author

Correspondence to Mahmoud A. M. Abdelaziz .

Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, USM, Penang, Malaysia

    Mohd Hafiz Mohd

  2. School of Mathematical Sciences, Universiti Sains Malaysia, USM, Penang, Malaysia

    Norazrizal Aswad Abdul Rahman

  3. School of Mathematical Sciences, Universiti Sains Malaysia, USM, Penang, Malaysia

    Nur Nadiah Abd Hamid

  4. School of Mathematical Sciences, Universiti Sains Malaysia, USM, Penang, Malaysia

    Yazariah Mohd Yatim

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Abdelaziz, M.A.M., Ismail, A.I., Abdullah, F.A., Mohd, M.H. (2019). Analysis of a Discrete-Time Fractional Order SIR Epidemic Model for Childhood Diseases. In: Mohd, M., Abdul Rahman, N., Abd Hamid, N., Mohd Yatim, Y. (eds) Dynamical Systems, Bifurcation Analysis and Applications. DySBA 2018. Springer Proceedings in Mathematics & Statistics, vol 295. Springer, Singapore. https://doi.org/10.1007/978-981-32-9832-3_5

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