The SEIR Covid-19 model described by fractional-order difference equations: analysis and application with real data in Brazil

References

• Available online: https://www.worldometers.info (accessed on 19 August 2022).
   Google Scholar
• Available online: https://www.data.albankaldawli.org (accessed on 16 April 2023).
   Google Scholar
• T. Abdeljawad, On Riemann and Caputo fractional differences, Comput. Math. Appl. 62 (2011), pp. 1602–1611.
   Web of Science ®Google Scholar
• A. Ajbar, R.T. Alqahtani, and M. Boumaza, Dynamics of an SIR-based COVID-19 model with linear incidence rate, nonlinear removal rate, and public awareness, Front. Phys. 9 (2021). DOI:10.3389/fphy.2021.634251.
   Web of Science ®Google Scholar
• R. Albadarneh, I. Batiha, A. Ouannas, and S. Momani, Modeling COVID-19 pandemic outbreak using fractional-order systems, Int. J. Math. Comput. Sci. 16 (2021), pp. 1405–1421.
   Web of Science ®Google Scholar
• L.J.S. Allen, Y. Lou, and A.L. Nevai, Spatial patterns in a discrete-time SIS patch model, J. Math. Biol. 58 (2009), pp. 339–375.
   PubMed Web of Science ®Google Scholar
• L.J.S. Allen and P. Driessche, The basic reproduction number in some discrete-time epidemic models, J. Differ. Equ. Appl. 14 (2008), pp. 1127–1147.
   Web of Science ®Google Scholar
• G.A. Anastassiou, Discrete fractional calculus and inequalities. 17 (2009), pp. 1–11. Available at arXiv:0911.3370v1.
   Google Scholar
• I.M. Batiha, A. Ouannas, and J. Emwas, A stabilization approach for a novel chaotic fractional-order discrete neural network, J. Math. Comput. Sci. 11 (2021), pp. 5514–5524.
   Google Scholar
• I.M. Batiha, S. Momani, A. Ouannas, Z. Momani, and S.B. Hadid, Fractional-order COVID-19 pandemic outbreak: modelling and stability analysis, Int. J. Biomath. 15 (2021), pp. 2150090. DOI:10.1142/S179352452150090X.
   Web of Science ®Google Scholar
• T.A. Biala and A.Q.M. Khaliq, A fractional-order compartmental model for the spread of the COVID-19 pandemic, Commun. Nonlinear Sci. Numer. Simul. 98 (2021), pp. 105764.
   PubMed Web of Science ®Google Scholar
• J. Čermák, I. Gy*ohuml;ri, and L. Nechvátal, On explicit stability conditions for a linear fractional difference system, Fract. Calc. Appl. Anal. 18 (2015), pp. 651–672.
   Web of Science ®Google Scholar
• A.N. Chatterjee and B. Ahmad, A fractional-order differential equation model of COVID-19 infection of epithelial cells, Chaos, Solitons & Fractals. 147 (2021), pp. 110952.
   PubMed Web of Science ®Google Scholar
• N. Debbouche, A. Ouannas, I.M. Batiha, and G. Grassi, Chaotic dynamics in a novel COVID-19 pandemic model described by commensurate and incommensurate fractional-order derivatives, Nonlinear. Dyn. 109 (2021), pp. 33–45. DOI:10.1007/s11071-021-06867-5.
   PubMed Web of Science ®Google Scholar
• A. DInnocenzo, F. Paladini, and L. Renna, A numerical investigation of discrete oscillating epidemic models, Physica. A. 364 (2006), pp. 497–512.
   Web of Science ®Google Scholar
• N. Djenina, A. Ouannas, I.M. Batiha, G. Grassi, and V.T. Pham, On the stability of linear incommensurate fractional-Order difference systems, Mathematics. 8 (2020), pp. 1754.
   Web of Science ®Google Scholar
• J. Fahd, A. Thabet, B. Dumitru, and B. Kübra, On the Stability of Some Discrete Fractional Nonautonomous Systems, Hindawi Publishing Corporation, 2012.
   Google Scholar
• G. Giordano, F. Blanchini, R. Bruno, P. Colaneri, A.D. Filippo, A.D. Matteo, and M. Colaneri, Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy, Nat. Med. 26 (2020), pp. 855–860.
   PubMed Web of Science ®Google Scholar
• S. Gounane, Y. Barkouch, A. Atlas, M. Bendahmane, F. Karami, and D. Meskine, An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting, Epidemiol. Methods. 10 (2021), pp. 20200044.
   Google Scholar
• Z.-Y. He, A. Abbes, H. Jahanshahi, N.D. Alotaibi, and Y. Wang, Fractional-order discrete-time SIR epidemic model with vaccination: chaos and complexity, Mathematics. 10(2) (2022), pp. 55–165.
   Web of Science ®Google Scholar
• M. Higazy, Novel fractional order SIDARTHE mathematical model of COVID-19 pandemic, Chaos, Solitons & Fractals. 138 (2020), pp. 110007.
   PubMed Web of Science ®Google Scholar
• H. Jahanshahi, A. Yousefpour, Z. Wei, R. Alcaraz, and S. Bekiros, A financial hyperchaotic system with coexisting attractors: dynamic investigation, entropy analysis. control and synchronization, Chaos, Solitons & Fractals. 126 (2019), pp. 66–77.
   Web of Science ®Google Scholar
• S. Jain and Y. El-Khatib, Stochastic covid-19 model with fractional global and classical piecewise derivative, Results Phys. 30 (2021), pp. 104788.
   PubMed Web of Science ®Google Scholar
• W. Kermack and A. McKendrick, Contributions to the mathematical theory of epidemics, Proc. R. Soc. A. 115 (1927), pp. 700–721.
   Google Scholar
• H. Khan, M. Ibrahim, A.-H. Abdel-Aty, M. Motawi Khashan, F.A. Khan, and A. Khan, A fractional order covid-19 epidemic model with Mittag-Leffler kernel, Chaos, Solitons & Fractals. 148 (2021), pp. 111030.
   PubMed Web of Science ®Google Scholar
• A.A. Khennaoui, A. Ouannas, S. Momani, I.M. Batiha, Z. Dibi, and G. Grassi, On dynamics of a fractional-Order discrete system with only one nonlinear term and without fixed points, Electronics. 9 (2020), pp. 2179.
   Web of Science ®Google Scholar
• A.A. Khennaoui, A.O. Almatroud, A. Ouannas, M.M. Al-sawalha, G. Grassi, V.T. Pham, and I.M. Batiha, An unprecedented 2-dimensional discrete-time fractional-order system and its hidden chaotic attractors, Math. Probl. Eng. 2021 (2021), pp. 1–10.
   Web of Science ®Google Scholar
• P. Kumara, V.S. Erturk, and M. Murillo-Arcila, A new fractional mathematical modelling of COVID-19 with the availability of vaccine, Results Phys 24 (2021), pp. 104213.
   PubMed Web of Science ®Google Scholar
• X.-P. Li, H.A. Bayatti, A. Din, and A. Zeb, A vigorous study of fractional order COVID-19 model via ABC derivatives, Results Phys. 29 (2021), pp. 104737.
   PubMed Web of Science ®Google Scholar
• J.P.S. Maurício de Carvalho and B. Moreira-Pinto, A fractional-order model for Covid-19 dynamics with reinfection and the importance of quarantine, Chaos, Solitons & Fractals. 151 (2021), pp. 111275.
   PubMed Web of Science ®Google Scholar
• H. Mohammadi, S. Rezapour, and A. Jajarmi, On the fractional SIRD mathematical model and control for the transmission of COVID-19: the first and the second waves of the disease in Iran and Japan, ISA. Trans. 124 (2021), pp. 103–114. DOI:10.1016/j.isatra.2021.04.012.
   PubMed Web of Science ®Google Scholar
• A. Omame, M. Abbas, and C.P. Onyenegecha, A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana–Baleanu derivative, Chaos, Solitons & Fractals. 153 (2021), pp. 111486.
   PubMed Web of Science ®Google Scholar
• A. Omame, D. Okuonghae, U.K. Nwajeri, and C.P. Onyenegecha, A fractional-order multi-vaccination model for COVID-19 with non-singular kernel, Alex. Eng. J. 61 (2022), pp. 6089–6104. DOI:10.1016/j.aej.2021.11.037.
   Web of Science ®Google Scholar
• V.S. Panwar, P.S. Sheik Uduman, and J.F. Gómez-Aguilar, Mathematical modeling of coronavirus disease COVID-19 dynamics using CF and ABC non-singular fractional derivatives, Chaos, Solitons & Fractals. 145 (2021), pp. 110757.
   PubMed Web of Science ®Google Scholar
• O. Postavaru, S.R. Anton, and A. Toma, COVID-19 pandemic and chaos theory, Math. Comput. Simul. 181 (2021), pp. 138–149.
   PubMed Web of Science ®Google Scholar
• K. Rajagopal, N. Hasanzadeh, F. Parastesh, I.I. Hamarash, S. Jafari, and I. Hussain, A fractional-order model for the novel coronavirus (COVID-19) outbreak, Nonlinear Dyn. 101 (2020), pp. 711–718.
   PubMed Web of Science ®Google Scholar
• M.T. Shatnawi, N. Djenina, A. Ouannas, I.M. Batiha, and G. Grassi, Novel convenient conditions for the stability of nonlinear incommensurate fractional-order difference systems, Alex. Eng. J. 61 (2022), pp. 1655–1663.
   Web of Science ®Google Scholar
• I. Talbi, A. Ouannas, A.A. Khennaoui, A. Berkane, I.M. Batiha, G. Grassi, and V.T. Pham, Different dimensional fractional-order discrete chaotic systems based on the caputo h-difference discrete operator: dynamics, control, and synchronization, Adv. Differ. Equ. 2020 (2020), pp. 1–15.
   PubMed Web of Science ®Google Scholar
• S. Thanin, Z. Anwar, C. Saowaluck, E. Zohreh, T. Mouhcine, and D. Salih, Analysis of a discrete mathematical COVID-19 model, Results Phys. 28 (2021), pp. 104668.
   PubMed Web of Science ®Google Scholar
• C. Xu, Y. Yu, Y. Chen, and Z. Lu, Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model, Nonlinear. Dyn. 101 (2020), pp. 1621–1634.
   PubMed Web of Science ®Google Scholar
• S. Yadav, D. Kumar, J. Singh, and D. Baleanu, Analysis and dynamics of fractional order covid-19 model with memory effect, Results Phys. 24 (2021), pp. 104017.
   Web of Science ®Google Scholar
• T.H. Zhao, O. Castillo, H. Jahanshahi, A. Yusuf, M.O. Alassafi, F.E. Alsaadi, and Y.M. Chu, A fuzzy-based strategy to suppress the novel coronavirus (2019-NCOV) massive outbreak, Appl. Comput. Math. 20(1) (2021), pp. 160.
   Web of Science ®Google Scholar