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Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

Author

Listed:
  • Zai-Yin He

    (School of Mathematics, Hunan University, Changsha 410082, China)

  • Abderrahmane Abbes

    (Department of Mathematics, University of Jordan, Amman 11942, Jordan)

  • Hadi Jahanshahi

    (Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada)

  • Naif D. Alotaibi

    (Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Ye Wang

    (Department of Mathematics, Huzhou University, Huzhou 313000, China
    Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311131, China)

Abstract

This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between γ = 0.8712 and γ = 1, while the reasonable range of incommensurate fractional orders is between γ 2 = 0.77 and γ 2 = 1. Furthermore, the complexity analysis is performed using approximate entropy ( A p E n ) and C 0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.

Suggested Citation

  • Zai-Yin He & Abderrahmane Abbes & Hadi Jahanshahi & Naif D. Alotaibi & Ye Wang, 2022. "Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:165-:d:718669
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    References listed on IDEAS

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    1. Din, Anwarud & Khan, Amir & Baleanu, Dumitru, 2020. "Stationary distribution and extinction of stochastic coronavirus (COVID-19) epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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