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

Zai-Yin He, Abderrahmane Abbes, Hadi Jahanshahi, Naif D. Alotaibi and Ye Wang
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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

Mathematics, 2022, vol. 10, issue 2, 1-18

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.

Keywords: discrete SIR epidemic model; commensurate order; incommensurate order; chaos; complexity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

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