{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T15:13:57Z","timestamp":1771946037550,"version":"3.50.1"},"reference-count":17,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T00:00:00Z","timestamp":1676419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Appl. Math. Stat."],"abstract":"<jats:p>In this study, we formulated a mathematical model of COVID-19 with the effects of partially and fully vaccinated individuals. Here, the purpose of this study is to solve the model using some numerical methods. It is complex to solve four equations of the <jats:italic>SEIR<\/jats:italic> model, so we introduce the Euler and the fourth-order Runge\u2013Kutta method to solve the model. These two methods are efficient and practically well suited for solving initial value problems. Therefore, we formulated a simple nonlinear <jats:italic>SEIR<\/jats:italic> model with the incorporation of partially and fully vaccinated parameters. Then, we try to solve our model by transforming our equations into the Euler and Runge\u2013Kutta methods. Here, we not only study the comparison of these two methods, also found out the differences in solutions between the two methods. Furthermore, to make our model more realistic, we considered the capital of Kerala, Trivandrum city for the simulation. We used MATLAB software for simulation purpose. At last, we discuss the numerical comparison between these two methods with real world data.<\/jats:p>","DOI":"10.3389\/fams.2023.1124897","type":"journal-article","created":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T09:26:07Z","timestamp":1676453167000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":20,"title":["Mathematical modeling and simulation of SEIR model for COVID-19 outbreak: A case study of Trivandrum"],"prefix":"10.3389","volume":"9","author":[{"given":"Aakash","family":"M","sequence":"first","affiliation":[]},{"given":"Gunasundari","family":"C","sequence":"additional","affiliation":[]},{"given":"Qasem M.","family":"Al-Mdallal","sequence":"additional","affiliation":[]}],"member":"1965","published-online":{"date-parts":[[2023,2,15]]},"reference":[{"key":"B1","unstructured":"2021"},{"key":"B2","doi-asserted-by":"publisher","first-page":"816","DOI":"10.1016\/S2213-2600(20)30304-0","article-title":"COVID-19 associated acute respiratory distress syndrome: is a different approach to management warranted?","volume":"8","author":"Eddy","year":"2020","journal-title":"Lancet Respir Med"},{"key":"B3","doi-asserted-by":"publisher","first-page":"37","DOI":"10.47194\/ijgor.v2i1.67","article-title":"Comparison of numerical simulation of epidemiological model between Euler method with 4th order Runge Kutta method","volume":"2","author":"Rizky","year":"2021","journal-title":"Int J Glob Operat Res"},{"key":"B4","first-page":"1","article-title":"Numerical study of Kermack-Mckendrik SIR model to predict the outbreak of Ebola virus diseases using Euler and fourth order Runge-Kutta methods","volume":"37","author":"Tareque","year":"2017","journal-title":"Am Sci Res J Eng Technol Sci"},{"key":"B5","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1016\/j.apm.2016.10.003","article-title":"Stability analysis of delayed predator prey model with disease in prey","volume":"12","author":"Gunasundari","year":"2017","journal-title":"Int J Comput Appl. Math"},{"key":"B6","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1155\/2022\/5104350","article-title":"Fractional conformable stochastic integrodifferential equations: existence, uniqueness, and numerical simulations utilizing the shifted legendre spectral collocation algorithm","volume":"2022","author":"Haneen","year":"2022","journal-title":"Math Probl Eng"},{"key":"B7","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1016\/j.cjph.2022.10.002","article-title":"Numerical solutions and geometric attractors of a fractional model of the cancer-immune based on the Atangana-Baleanu-Caputo derivative and the reproducing kernel scheme","volume":"80","author":"Banan","year":"2022","journal-title":"Chin J Phys"},{"key":"B8","doi-asserted-by":"publisher","first-page":"2022","DOI":"10.1007\/s40096-022-00495-9","article-title":"Numerical Hilbert space solution of fractional Sobolev equation in (1+1)-dimensional space","author":"Omar","year":"2022","journal-title":"Math Sci"},{"key":"B9","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.idm.2020.11.002","article-title":"Law of mass action and saturation in SIR model with application to Coronavirus modelling","volume":"6","author":"Kolokolnikov","year":"2021","journal-title":"Infect Dis Model"},{"key":"B10","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.mbs.2013.08.014","article-title":"Spatial spread of an epidemic through public transportation systems with a hub","volume":"246","author":"Xu","year":"2013","journal-title":"Math Biosci"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1101\/2020.02.16.20023465","article-title":"Epidemic analysis of COVID-19 in China by dynamical modeling","author":"Peng","year":"2013","journal-title":"MedRxiv"},{"key":"B12","doi-asserted-by":"publisher","first-page":"140","DOI":"10.31943\/mathline.v6i2.176","article-title":"The Euler, Heun, and fourth order Runge-Kutta solutions to SEIR model for the spread of meningitis disease","volume":"6","author":"Hurit","year":"2021","journal-title":"J Mat Pendidikan Mat"},{"key":"B13","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1155\/2022\/4247800","article-title":"Dynamics of a stochastic epidemic model with vaccination and multiple time-delays for COVID-19 in the UAE","volume":"2022","author":"Alsakaji","year":"2022","journal-title":"Hindawi Compl"},{"key":"B14","author":"Kandasamy","year":"1997","journal-title":"Numerical Methods"},{"key":"B15","doi-asserted-by":"crossref","DOI":"10.1002\/0470868279","volume-title":"Numerical Methods for Ordinary Differential Equation","author":"Butcher","year":"2003"},{"key":"B16","unstructured":"2011"},{"key":"B17","unstructured":"2021"}],"container-title":["Frontiers in Applied Mathematics and Statistics"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2023.1124897\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T09:26:16Z","timestamp":1676453176000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2023.1124897\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,15]]},"references-count":17,"alternative-id":["10.3389\/fams.2023.1124897"],"URL":"https:\/\/doi.org\/10.3389\/fams.2023.1124897","relation":{},"ISSN":["2297-4687"],"issn-type":[{"value":"2297-4687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,15]]},"article-number":"1124897"}}