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Codimension one and two bifurcations of a discrete-time fractional-order SEIR measles epidemic model with constant vaccination

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

Abstract

In this paper, a discrete-time SEIR measles epidemic model with fractional-order and constant vaccination is investigated. The basic reproduction number with an algebraic criterion are used to study the local asymptotic stability of the equilibrium points. Two types of codimension one bifurcation namely, flip and Neimark-Sacker (N-S) bifurcations and their intersection codimension two flip-N-S bifurcation, are discussed. The necessary and sufficient conditions for detecting these types of bifurcation are derived using algebraic criterion methods. The criterions employed are based on the coefficients of characteristic equations rather than the properties of eigenvalues of Jacobian matrix. The output is a semi-algebraic system composed of a set of equations, inequalities and inequations. These criterions represent appropriate conditions for codim-1 and codim-2 bifurcations of high dimensional maps.

Suggested Citation

  • Abdelaziz, Mahmoud A.M. & Ismail, Ahmad Izani & Abdullah, Farah A. & Mohd, Mohd Hafiz, 2020. "Codimension one and two bifurcations of a discrete-time fractional-order SEIR measles epidemic model with constant vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305014
    DOI: 10.1016/j.chaos.2020.110104
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    References listed on IDEAS

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    1. Pang, Liuyong & Ruan, Shigui & Liu, Sanhong & Zhao, Zhong & Zhang, Xinan, 2015. "Transmission dynamics and optimal control of measles epidemics," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 131-147.
    2. Niu, Wei & Shi, Jian & Mou, Chenqi, 2016. "Analysis of codimension 2 bifurcations for high-dimensional discrete systems using symbolic computation methods," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 934-947.
    3. R. Khoshsiar Ghaziani & W. Govaerts & C. Sonck, 2011. "Codimension-Two Bifurcations of Fixed Points in a Class of Discrete Prey-Predator Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-27, June.
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    Cited by:

    1. Dalal Yahya Alzahrani & Fuaada Mohd Siam & Farah A. Abdullah, 2023. "Elucidating the Effects of Ionizing Radiation on Immune Cell Populations: A Mathematical Modeling Approach with Special Emphasis on Fractional Derivatives," Mathematics, MDPI, vol. 11(7), pages 1-21, April.
    2. Zhang, Zizhen & Rahman, Ghaus ur & Gómez-Aguilar, J.F. & Torres-Jiménez, J., 2022. "Dynamical aspects of a delayed epidemic model with subdivision of susceptible population and control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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