A novel Covid-19 model with fractional differential operators with singular and non-singular kernels: Analysis and numerical scheme based on Newton polynomial

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dc.authoridIGRET ARAZ, SEDA/0000-0002-7698-0709
dc.contributor.authorAtangana, Abdon
dc.contributor.authorAraz, Seda IGret
dc.date.accessioned2024-12-24T19:25:10Z
dc.date.available2024-12-24T19:25:10Z
dc.date.issued2021
dc.departmentSiirt Üniversitesi
dc.description.abstractTo capture more complexities associated to the spread of Covid-19 within a given population, we considered a system of nine differential equations that include a class of susceptible, 5 sub-classes of infected population, recovered, death and vaccine. The mathematical model was suggested with a lockdown function such that after the lockdown, the function follows a fading memory rate, a concept that is justified by the effect of social distancing that suggests, susceptible class should stay away from infected objects and humans. We presented a detailed analysis that includes reproductive number and stability analysis. Also, we introduced the concept of fractional Lyapunov function for Caputo, Caputo-Fabrizio and the Atangana-Baleanu fractional derivatives. We established the sign of the fractional Lyapunov function in all cases. Additionally we proved that, if the fractional order is one, we recover the results Lyapunov for the model with classical differential operators. With the nonlinearity of the differential equations depicting the complexities of the Covid-19 spread especially the cases with nonlocal operators, and due to the failure of existing analytical methods to provide exact solutions to the system, we employed a numerical method based on the Newton polynomial to derive numerical solutions for all cases and numerical simulations are provided for different values of fractional orders and fractal dimensions. Collected data from Turkey case for a period of 90 days were compared with the suggested mathematical model with Atangana-Baleanu fractional derivative and an agreement was reached for alpha 1:009. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
dc.identifier.doi10.1016/j.aej.2021.02.016
dc.identifier.endpage3806
dc.identifier.issn1110-0168
dc.identifier.issn2090-2670
dc.identifier.issue4
dc.identifier.scopus2-s2.0-85102070642
dc.identifier.scopusqualityQ1
dc.identifier.startpage3781
dc.identifier.urihttps://doi.org/10.1016/j.aej.2021.02.016
dc.identifier.urihttps://hdl.handle.net/20.500.12604/6300
dc.identifier.volume60
dc.identifier.wosWOS:000637530300009
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier
dc.relation.ispartofAlexandria Engineering Journal
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectNovel mathematical Covid-19 model
dc.subjectFractional derivatives
dc.subjectFractional Lyapunov function
dc.subjectNon-singular and singular kernels
dc.titleA novel Covid-19 model with fractional differential operators with singular and non-singular kernels: Analysis and numerical scheme based on Newton polynomial
dc.typeArticle

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