The fractional-order discrete COVID-19 pandemic model: stability and chaos

Abderrahmane Abbes; Adel Ouannas; Nabil Shawagfeh; Hadi Jahanshahi

doi:10.1007/s11071-022-07766-z

The fractional-order discrete COVID-19 pandemic model: stability and chaos

Nonlinear Dyn. 2023;111(1):965-983. doi: 10.1007/s11071-022-07766-z. Epub 2022 Aug 15.

Authors

Abderrahmane Abbes¹, Adel Ouannas², Nabil Shawagfeh¹, Hadi Jahanshahi³

Affiliations

¹ Department of Mathematics, The University of Jordan, Amman, 11942 Jordan.
² Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, 04000 Oum El Bouaghi, Algeria.
³ Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6 Canada.

Abstract

This paper presents and investigates a new fractional discrete COVID-19 model which involves three variables: the new daily cases, additional severe cases and deaths. Here, we analyze the stability of the equilibrium point at different values of the fractional order. Using maximum Lyapunov exponents, phase attractors, bifurcation diagrams, the 0-1 test and approximation entropy (ApEn), it is shown that the dynamic behaviors of the model change from stable to chaotic behavior by varying the fractional orders. Besides showing that the fractional discrete model fits the real data of the pandemic, the simulation findings also show that the numbers of new daily cases, additional severe cases and deaths exhibit chaotic behavior without any effective attempts to curb the epidemic.

Keywords: COVID-19 model; Chaos; Commensurate and Incommensurate orders; Complexity; Stability.

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