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

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.

Hidden multistability of fractional discrete non-equilibrium point memristor based map

“…In this section, we will investigate the chaotic behavior of the proposed fractional DNEP memristor-based map (21) in both cases: the commensurate fractional orders (γ 1 = γ 2 = γ) and non-commensurate fractional orders (γ 1 ≠ γ 2 ). This investigation will be carried out using a variety of numerical methods, including Lyapunov exponents (LEs) calculations, bifurcation diagrams, and the display of phase portraits.…”

“…Discrete fractional calculus has drawn the interest of a great number of researchers during the last several years [8][9][10][11][12], and they have been increasingly interested in its potential applications in neural networks, secure communication, biology, and other domains [13][14][15]. Recently numerous different dynamics including chaos, hyperchaos and coexisting attractors in fractional-order systems have been explored [16][17][18][19][20][21][22]. For example, the coexisting chaos and hyperchaos in the fractional-order discrete SIE epidemic model have been analyzed in [23].…”

Global dynamics and bifurcations of Filippov SIR epidemic model with general nonlinear transmission and discontinuous control

“…p(S, I) is the incidence function. Notice that the R in the third equation of system (1) does not appear in the S and I equations of (1), so some scholar ignore the R equation and only consider the S and I equations of system (1).…”

“…[9,12,21,25,28,34,41,45,46], H.C. [14,23,24] and I.C. [22,25,26,44] and the other control [1,3,10,18,40,42]. Nevertheless, in this manuscript, we design a SIR epidemic system to address the D.T.C.…”

A new two-dimensional fractional discrete rational map: chaos and complexity

“…This recent topic has reached its peak of publications lately by proposing several fractional discrete-time operators, and stability analysis, transforms, and many theoretical results including [19][20][21]. This has contributed in proposing further fractional-order chaotic maps like [22][23][24][25][26][27][28] coupled with several control schemes and implementations like [29][30][31][32][33]. For instance in [22], Wu and Baleanu proposed a discrete fractional-order logistic map in the left Caputo discrete deltas sense.…”