{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T15:01:50Z","timestamp":1773932510312,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,12]],"date-time":"2024-02-12T00:00:00Z","timestamp":1707696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Northern Border University","award":["NBU-FFR-2024-133-01"],"award-info":[{"award-number":["NBU-FFR-2024-133-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>We derive a reaction\u2013diffusion model with time-delayed nonlocal effects to study an epidemic\u2019s spatial spread numerically. The model describes infected individuals in the latent period using a structured model with diffusion. The epidemic model assumes that infectious individuals are subject to containment measures. To simulate the model in two-dimensional space, we use the continuous Runge\u2013Kutta method of the fourth order and the discrete Runge\u2013Kutta method of the third order with six stages. The numerical results admit the existence of traveling wave solutions for the proposed model. We use the COVID-19 epidemic to conduct numerical experiments and investigate the minimal speed of spread of the traveling wave front. The minimal spreading speeds of COVID-19 are found and discussed. Also, we assess the power of containment measures to contain the epidemic. The results depict a clear drop in the spreading speed of the traveling wave front after applying containment measures to at-risk populations.<\/jats:p>","DOI":"10.3390\/computation12020034","type":"journal-article","created":{"date-parts":[[2024,2,12]],"date-time":"2024-02-12T04:47:45Z","timestamp":1707713265000},"page":"34","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Modeling and Simulating an Epidemic in Two Dimensions with an Application Regarding COVID-19"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9120-3326","authenticated-orcid":false,"given":"Khalaf M.","family":"Alanazi","sequence":"first","affiliation":[{"name":"Mathematics Department, College of Sciences and Arts, Northern Border University, Rafha 76316, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.apnum.2018.08.009","article-title":"Numerical simulations of the spread of rabies in two-dimensional space","volume":"135","author":"Alanazi","year":"2019","journal-title":"Appl. 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