{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:33:33Z","timestamp":1760150013381,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T00:00:00Z","timestamp":1696377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>In recent times, the global community has been faced with the unprecedented challenge of the coronavirus disease (COVID-19) pandemic, which has had a profound and enduring impact on both global health and the global economy. The utilization of mathematical modeling has become an essential instrument in the characterization and understanding of the dynamics associated with infectious illnesses. In this study, the utilization of the differential quadrature method (DQM) was employed in order to anticipate the characterization of the dynamics of COVID-19 through a fractional mathematical model. Uniform and non-uniform polynomial differential quadrature methods (PDQMs) and a discrete singular convolution method (DSCDQM) were employed in the examination of the dynamics of COVID-19 in vulnerable, exposed, deceased, asymptomatic, and recovered persons. An analysis was conducted to compare the methodologies used in this study, as well as the modified Euler method, in order to highlight the superior efficiency of the DQM approach in terms of code-execution times. The results demonstrated that the fractional order significantly influenced the outcomes. As the fractional order tended towards unity, the anticipated numbers of vulnerable, exposed, deceased, asymptomatic, and recovered individuals increased. During the initial week of the inquiry, there was a substantial rise in the number of individuals who contracted COVID-19, which was primarily attributed to the disease\u2019s high transmission rate. As a result, there was an increase in the number of individuals who recovered, in tandem with the rise in the number of infected individuals. These results highlight the importance of the fractional order in influencing the dynamics of COVID-19. The utilization of the DQM approach, characterized by its proficient code-execution durations, provided significant insights into the dynamics of COVID-19 among diverse population cohorts and enhanced our comprehension of the evolution of the pandemic. The proposed method was efficient in dealing with ordinary differential equations (ODEs), partial differential equations (PDEs), and fractional differential equations (FDEs), in either linear or nonlinear forms. In addition, the stability of the DQM and its validity were verified during the present study. Moreover, the error analysis showed that DQM has better error percentages in many applications than other relevant techniques.<\/jats:p>","DOI":"10.3390\/computation11100198","type":"journal-article","created":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T11:58:57Z","timestamp":1696420737000},"page":"198","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Mathematical Investigation of the Infection Dynamics of COVID-19 Using the Fractional Differential Quadrature Method"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1354-6857","authenticated-orcid":false,"given":"M.","family":"Mohamed","sequence":"first","affiliation":[{"name":"Department of Basic Science, Faculty of Engineering, Delta University for Science and Technology, Gamasa 11152, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1877-3944","authenticated-orcid":false,"given":"S. M.","family":"Mabrouk","sequence":"additional","affiliation":[{"name":"Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig 44519, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7800-2768","authenticated-orcid":false,"given":"A. S.","family":"Rashed","sequence":"additional","affiliation":[{"name":"Department of Basic Science, Faculty of Engineering, Delta University for Science and Technology, Gamasa 11152, Egypt"},{"name":"Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig 44519, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Rezaei, N. (2021). Coronavirus Disease\u2014COVID-19, Springer.","DOI":"10.1007\/978-3-030-63761-3"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Murphy, P. (2020). COVID-19: Proportionality, Public Policy and Social Distancing, Palgrave Macmillan.","DOI":"10.1007\/978-981-15-7514-3"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"24","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_4","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier. [1st ed.]."},{"key":"ref_5","unstructured":"Lakshmikantham, V., Leela, S., and Vasundhara Devi, J. (2009). Theory of Fractional Dynamic Systems, CSP."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Mathai, A.M., and Haubold, H.J. (2017). An Introduction to Fractional Calculus, Nova Science Publishers.","DOI":"10.1142\/10639"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Singh, J., Hristov, J.Y., and Hammouch, Z. (2020). New Trends in Fractional Differential Equations with Real-World Applications in Physics, Frontiers Media SA.","DOI":"10.3389\/978-2-88966-304-0"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"512","DOI":"10.3390\/fractalfract7070512","article-title":"Probing Families of Optical Soliton Solutions in Fractional Perturbed Radhakrishnan\u2013Kundu\u2013Lakshmanan Model with Improved Versions of Extended Direct Algebraic Method","volume":"7","author":"Yasmin","year":"2023","journal-title":"Fractal Fract."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yasmin, H., Aljahdaly, N.H., Saeed, A.M., and Shah, R. (2023). Investigating Families of Soliton Solutions for the Complex Structured Coupled Fractional Biswas\u2014Arshed Model in Birefringent Fibers Using a Novel Analytical Technique. Fractal Fract., 7.","DOI":"10.3390\/fractalfract7070491"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Naeem, M., Yasmin, H., Shah, R., Shah, N.A., and Nonlaopon, K. (2023). Investigation of Fractional Nonlinear Regularized Long-Wave Models via Novel Techniques. Symmetry, 15.","DOI":"10.3390\/sym15010220"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5287","DOI":"10.1016\/j.aej.2021.04.032","article-title":"Study of COVID-19 mathematical model of fractional order via modified Euler method","volume":"60","author":"Nazir","year":"2021","journal-title":"Alex. Eng. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"101195","DOI":"10.1016\/j.imu.2023.101195","article-title":"Analysis of COVID-19 mathematical model for predicting the impact of control measures in Rwanda","volume":"37","author":"Mpinganzima","year":"2023","journal-title":"Inform. Med. Unlocked"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.ijregi.2023.01.003","article-title":"Compartmental mathematical modelling of dynamic transmission of COVID-19 in Rwanda","volume":"6","author":"Mpinganzima","year":"2023","journal-title":"IJID Reg."},{"key":"ref_14","first-page":"100210","article-title":"A fractional-order mathematical model for malaria and COVID-19 co-infection dynamics","volume":"4","author":"Abioye","year":"2023","journal-title":"Heal. Anal."},{"key":"ref_15","first-page":"100230","article-title":"A fractional-order mathematical model for examining the spatiotemporal spread of COVID-19 in the presence of vaccine distribution","volume":"4","author":"Alaje","year":"2023","journal-title":"Heal. Anal."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Avusuglo, W., Mosleh, R., Ramaj, T., Li, A., Sharbayta, S.S., Fall, A.A., Ghimire, S., Shi, F., Lee, J.K., and Thommes, E. (2023). Workplace absenteeism due to COVID-19 and influenza across Canada: A mathematical model. J. Theor. Biol., 572.","DOI":"10.1016\/j.jtbi.2023.111559"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"101235","DOI":"10.1016\/j.imu.2023.101235","article-title":"Mathematical modelling and analysis of COVID-19 and tuberculosis transmission dynamics","volume":"38","author":"Singh","year":"2023","journal-title":"Inform. Med. Unlocked"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"562494","DOI":"10.1155\/2011\/562494","article-title":"On Riemann-Liouville and Caputo Derivatives","volume":"2011","author":"Li","year":"2011","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1111\/j.1365-246X.1967.tb02303.x","article-title":"Linear Models of Dissipation whose Q is almost Frequency Independent\u2014II","volume":"13","author":"Caputo","year":"1967","journal-title":"Geophys. J. Int."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Zong, Z., and Zhang, Y. (2009). Advanced Differential Quadrature Methods, CRC Press.","DOI":"10.1201\/9781420082494"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Shu, C. (2000). Differential Quadrature and Its Application in Engineering, Springer.","DOI":"10.1007\/978-1-4471-0407-0"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"49","DOI":"10.5539\/mas.v13n7p49","article-title":"Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method","volume":"13","author":"Ragb","year":"2019","journal-title":"Mod. Appl. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"8930","DOI":"10.1063\/1.478812","article-title":"Discrete singular convolution for the solution of the Fokker\u2013Planck equation","volume":"110","author":"Wei","year":"1999","journal-title":"J. Chem. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1002\/fld.253","article-title":"Numerical solution of incompressible flows by discrete singular convolution","volume":"38","author":"Wan","year":"2002","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1016\/j.ijmecsci.2006.05.005","article-title":"Local adaptive differential quadrature for free vibration analysis of cylindrical shells with various boundary conditions","volume":"48","author":"Zhang","year":"2006","journal-title":"Int. J. Mech. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1890","DOI":"10.1002\/cnm.1279","article-title":"Free vibration analysis of Timoshenko beams by DSC method","volume":"26","author":"Civalek","year":"2010","journal-title":"Int. J. Numer. Methods Biomed. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.compositesb.2016.11.030","article-title":"Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method","volume":"111","author":"Civalek","year":"2017","journal-title":"Compos. Part B Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7847","DOI":"10.1002\/mma.7241","article-title":"Fractional order mathematical modeling of novel corona virus (COVID-19)","volume":"46","author":"Ahmad","year":"2021","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Anley, E.F., and Zheng, Z. (2020). Finite Difference Method for Two-Sided Two Dimensional Space Fractional Convection-Diffusion Problem with Source Term. Mathematics, 8.","DOI":"10.3390\/math8111878"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1515\/math-2021-0036","article-title":"Numerical methods for time-fractional convection-diffusion problems with high-order accuracy","volume":"19","author":"Dong","year":"2021","journal-title":"Open Math."},{"key":"ref_31","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_32","doi-asserted-by":"crossref","unstructured":"Yousif, R., Jeribi, A., and Al-Azzawi, S. (2023). Fractional-Order SEIRD Model for Global COVID-19 Outbreak. Mathematics, 11.","DOI":"10.3390\/math11041036"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/10\/198\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:05:25Z","timestamp":1760130325000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/10\/198"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,4]]},"references-count":32,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["computation11100198"],"URL":"https:\/\/doi.org\/10.3390\/computation11100198","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2023,10,4]]}}}