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 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.
Highlights
Epidemiology is a topic of research in the biological sciences, which explores all the elements that influence whether there are diseases and disorders
We examine the case of incommensurate orders because it is more representative of reality than the case of commensurate orders, as each variable changes and moves independently of the others, implying that the rank of the influencer varies from one equation to another
We dealt with the dynamics of a new fractional-order discrete-time
Summary
Epidemiology is a topic of research in the biological sciences, which explores all the elements that influence whether there are diseases and disorders. To the best of our knowledge, the dynamic analysis of a fractional-order discrete-time epidemic model with vaccination based on a Caputo-like difference operator has not yet been investigated. This piqued our interest and inspired us to study the phenomenon and investigate the behavior of a fractional SIR epidemic model with vaccination when the fractional orders are commensurate and incommensurate. The goal of this article is to contribute to the field of epidemiology by introducing a novel discrete-time SIR epidemic model with vaccination with both commensurate and incommensurate fractional orders. Throughout the paper, numerical simulations are used to demonstrate and verify the results
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