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2019 | OriginalPaper | Chapter

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

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

Published in: Dynamical Systems, Bifurcation Analysis and Applications

Publisher: Springer Singapore

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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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Metadata
Title
Analysis of a Discrete-Time Fractional Order SIR Epidemic Model for Childhood Diseases
Authors
Mahmoud A. M. Abdelaziz
Ahmad Izani Ismail
Farah A. Abdullah
Mohd Hafiz Mohd
Copyright Year
2019
Publisher
Springer Singapore
Book
Dynamical Systems, Bifurcation Analysis and Applications

Print ISBN: 978-981-329-831-6

Electronic ISBN: 978-981-329-832-3

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-981-32-9832-3_5

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