Statistics

Mathematical analysis

Epidemic model

Materials science

Artificial intelligence

Composite material

Range (aeronautics)

Physics

Nonlinear system

Population

Bifurcation

Mathematics

Fractional calculus

Quantum mechanics

Approximate entropy

Demography

Chaotic

Computer science

Hurst exponent

Statistical physics

Time series

Sociology

Attractor

Lyapunov exponent

Applied mathematics

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 γ2 = 0.77 and γ2 = 1. Furthermore, the complexity analysis is performed using approximate entropy (ApEn) and C0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.

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