{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T18:33:08Z","timestamp":1771007588158,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,6,16]],"date-time":"2021-06-16T00:00:00Z","timestamp":1623801600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Coronaviruses are a group of RNA (ribonucleic acid) viruses with the capacity for rapid mutation and recombination. Coronaviruses are known to cause respiratory or intestinal infections in humans and animals. In this paper, a biologically compatible set of nonlinear fractional differential equations governing the outbreak of the novel coronavirus is suggested based on a model previously proposed in the literature. Then, this set is numerically solved utilizing two new methods employing sine\u2013cosine and Bernoulli wavelets and their operational matrices. Moreover, the convergence of the solution is experimentally studied. Furthermore, the accuracy of the solution is proved via comparing the results with those obtained in previous research for the primary model. Furthermore, the computational costs are compared by measuring the CPU running time. Finally, the effects of the fractional orders on the outbreak of the COVID-19 are investigated.<\/jats:p>","DOI":"10.3390\/axioms10020122","type":"journal-article","created":{"date-parts":[[2021,6,16]],"date-time":"2021-06-16T10:27:07Z","timestamp":1623839227000},"page":"122","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["New Procedures of a Fractional Order Model of Novel Coronavirus (COVID-19) Outbreak via Wavelets Method"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5258-3880","authenticated-orcid":false,"given":"Maryamsadat","family":"Hedayati","sequence":"first","affiliation":[{"name":"Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj 3149968111, Iran"}]},{"given":"Reza","family":"Ezzati","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj 3149968111, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2307-0891","authenticated-orcid":false,"given":"Samad","family":"Noeiaghdam","sequence":"additional","affiliation":[{"name":"Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia"},{"name":"Department of Applied Mathematics and Programming, South Ural State University, Lenin Prospect 76, 454080 Chelyabinsk, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"655","DOI":"10.3389\/fvets.2020.582287","article-title":"The Coronaviruses of Animals and Birds: Their Zoonosis, Vaccines, and Models for SARS-CoV and SARS-CoV2","volume":"7","author":"Alluwaimi","year":"2020","journal-title":"Front. Vet. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1001\/jamacardio.2020.1286","article-title":"Potential effects of coronaviruses on the cardiovascular system: A review","volume":"5","author":"Madjid","year":"2020","journal-title":"JAMA Cardiol."},{"key":"ref_3","unstructured":"WHO (2020). Novel Coronavirus (2019-nCoV): Situation Report 3, WHO."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40249-020-00640-3","article-title":"A mathematical model for simulating the phase-based transmissibility of a novel coronavirus","volume":"9","author":"Chen","year":"2020","journal-title":"Infect. Dis. Poverty"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2379","DOI":"10.1016\/j.aej.2020.02.033","article-title":"Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative","volume":"59","author":"Khan","year":"2020","journal-title":"Alex. Eng. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1007\/s11071-020-05757-6","article-title":"A fractional-order model for the novel coronavirus (COVID-19) outbreak","volume":"101","author":"Rajagopal","year":"2020","journal-title":"Nonlinear Dyn."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s10700-020-09342-9","article-title":"Numerical solution and parameter estimation for uncertain SIR model with application to COVID-19","volume":"20","author":"Chen","year":"2021","journal-title":"Fuzzy Optim. Decis. Mak."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1186\/s13662-020-02984-4","article-title":"A numerical solution by alternative Legendre polynomials on a model for novel coronavirus (COVID-19)","volume":"2020","author":"Hashemizadeh","year":"2020","journal-title":"Adv. Differ. Equ."},{"key":"ref_9","unstructured":"Kisela, T. (2008). Fractional Differential Equations and Their Applications, Faculty of Mechanical Engineering Institute of Mathematics."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.chaos.2019.06.027","article-title":"A fractional mathematical model of breast cancer competition model","volume":"127","author":"Atangana","year":"2019","journal-title":"Chaos Solitons Fractals"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13662-020-02845-0","article-title":"Existence of solution and stability for the fractional order novel coronavirus (nCoV-2019) model","volume":"2020","author":"Hussain","year":"2020","journal-title":"Adv. Differ. Equ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"109860","DOI":"10.1016\/j.chaos.2020.109860","article-title":"Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?","volume":"136","author":"Atangana","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4699","DOI":"10.1016\/j.aej.2020.08.027","article-title":"Dynamical characteristic of analytical fractional solitons for the space-time fractional Fokas-Lenells equation","volume":"59","author":"Wang","year":"2020","journal-title":"Alex. Eng. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"103156","DOI":"10.1016\/j.rinp.2020.103156","article-title":"Traveling wave solutions constructed by Mittag\u2013Leffler function of a (2 + 1)-dimensional space-time fractional NLS equation","volume":"17","author":"Yu","year":"2020","journal-title":"Results Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"103710","DOI":"10.1016\/j.rinp.2020.103710","article-title":"Soliton dynamics based on exact solutions of conformable fractional discrete complex cubic Ginzburg\u2013Landau equation","volume":"20","author":"Fang","year":"2021","journal-title":"Results Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"106583","DOI":"10.1016\/j.aml.2020.106583","article-title":"Fractional white noise functional soliton solutions of a wick-type stochastic fractional NLSE","volume":"110","author":"Wang","year":"2020","journal-title":"Appl. Math. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wang, B.-H., Wang, Y.-Y., and Dai, C.-Q. (2021). Fractional optical solitons with stochastic properties of a wick-type stochastic fractional NLSE driven by the Brownian motion. Waves Random Complex Media, 1\u201314.","DOI":"10.1080\/17455030.2021.1905910"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s40324-018-0163-3","article-title":"A novel technique to solve the modified epidemiological model of computer viruses","volume":"76","author":"Noeiaghdam","year":"2019","journal-title":"SEMA J."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Noeiaghdam, S., and Micula, S. (2021). Dynamical Strategy to Control the Accuracy of the Nonlinear Bio-Mathematical Model of Malaria Infection. Mathematics, 9.","DOI":"10.3390\/math9091031"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s40096-018-0261-5","article-title":"Solving a modified nonlinear epidemiological model of computer viruses by homotopy analysis method","volume":"12","author":"Noeiaghdam","year":"2018","journal-title":"Math. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"110107","DOI":"10.1016\/j.chaos.2020.110107","article-title":"A mathematical model for COVID-19 transmission by using the Caputo fractional derivative","volume":"140","author":"Tuan","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_22","first-page":"383","article-title":"Wavelet operational matrix method for solving fractional differential equations with variable coefficients","volume":"230","author":"Yi","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3422","DOI":"10.1016\/j.apm.2015.10.009","article-title":"Legendre wavelets method for the numerical solution of fractional integro-differential equations with weakly singular kernel","volume":"40","author":"Yi","year":"2016","journal-title":"Appl. Math. Model."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1080\/00207720210161768","article-title":"Sine-cosine wavelets operational matrix of integration and its applications in the calculus of variations","volume":"33","author":"Razzaghi","year":"2002","journal-title":"Int. J. Syst. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6960","DOI":"10.1002\/mma.5802","article-title":"Sine-cosine wavelet method for fractional oscillator equations","volume":"42","author":"Saeed","year":"2019","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1186\/s13662-017-1270-7","article-title":"Sine-cosine wavelet operational matrix of fractional order integration and its applications in solving the fractional order Riccati differential equations","volume":"2017","author":"Wang","year":"2017","journal-title":"Adv. Differ. Equ."},{"key":"ref_27","first-page":"569","article-title":"Numerical solution of linear integro-differential equation by using sine\u2013cosine wavelets","volume":"180","author":"Kajani","year":"2006","journal-title":"Appl. Math. Comput."},{"key":"ref_28","first-page":"250","article-title":"Kronecker operational matrices for fractional calculus and some applications","volume":"187","author":"Kilicman","year":"2007","journal-title":"Appl. Math. Comput."},{"key":"ref_29","first-page":"17","article-title":"Bernoulli wavelets method for solution of fractional differential equations in a large interval","volume":"2","author":"Keshavarz","year":"2016","journal-title":"Math. Res."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/j.cam.2016.06.005","article-title":"Numerical solution of fractional pantograph differential equations by using generalized fractional-order Bernoulli wavelet","volume":"309","author":"Rahimkhani","year":"2017","journal-title":"J. Comput. Appl. Math."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4283","DOI":"10.1016\/j.apm.2012.09.032","article-title":"A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation","volume":"37","author":"Tohidi","year":"2013","journal-title":"Appl. Math. Model."},{"key":"ref_32","first-page":"3936","article-title":"Numerical solution of variable fractional order advection-dispersion equation using Bernoulli wavelet method and new operational matrix of fractional order derivative","volume":"43","author":"Arabameri","year":"2020","journal-title":"Math. Methods Appl. Sci."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/122\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:17:10Z","timestamp":1760163430000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,16]]},"references-count":32,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["axioms10020122"],"URL":"https:\/\/doi.org\/10.3390\/axioms10020122","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,16]]}}}