{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:45:48Z","timestamp":1760147148532,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,12]],"date-time":"2023-01-12T00:00:00Z","timestamp":1673481600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basque Government","award":["IT1555-22","KK-2022\/00090","PID2021-1235430B-C21\/C22"],"award-info":[{"award-number":["IT1555-22","KK-2022\/00090","PID2021-1235430B-C21\/C22"]}]},{"name":"MCIN\/AEI","award":["IT1555-22","KK-2022\/00090","PID2021-1235430B-C21\/C22"],"award-info":[{"award-number":["IT1555-22","KK-2022\/00090","PID2021-1235430B-C21\/C22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, the transmission dynamical model of the deadly infectious disease named Ebola is investigated. This disease identified in the Democratic Republic of Congo (DRC) and Sudan (now South Sudan) and was identified in 1976. The novelty of the model under discussion is the inclusion of advection and diffusion in each compartmental equation. The addition of these two terms makes the model more general. Similar to a simple population dynamic system, the prescribed model also has two equilibrium points and an important threshold, known as the basic reproductive number. The current work comprises the existence and uniqueness of the solution, the numerical analysis of the model, and finally, the graphical simulations. In the section on the existence and uniqueness of the solutions, the optimal existence is assessed in a closed and convex subset of function space. For the numerical study, a nonstandard finite difference (NSFD) scheme is adopted to approximate the solution of the continuous mathematical model. The main reason for the adoption of this technique is delineated in the form of the positivity of the state variables, which is necessary for any population model. The positivity of the applied scheme is verified by the concept of M-matrices. Since the numerical method gives a discrete system of difference equations corresponding to a continuous system, some other relevant properties are also needed to describe it. In this respect, the consistency and stability of the designed technique are corroborated by using Taylor\u2019s series expansion and Von Neumann\u2019s stability criteria, respectively. To authenticate the proposed NSFD method, two other illustrious techniques are applied for the sake of comparison. In the end, numerical simulations are also performed that show the efficiency of the prescribed technique, while the existing techniques fail to do so.<\/jats:p>","DOI":"10.3390\/axioms12010079","type":"journal-article","created":{"date-parts":[[2023,1,13]],"date-time":"2023-01-13T02:57:33Z","timestamp":1673578653000},"page":"79","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Analysis of a Modified System of Infectious Disease in a Closed and Convex Subset of a Function Space with Numerical Study"],"prefix":"10.3390","volume":"12","author":[{"given":"Tahira Sumbal","family":"Shaikh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Lahore College for Women University, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-1424","authenticated-orcid":false,"given":"Ali","family":"Akg\u00fcl","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Mathematics, Lebanese American University, Beirut 1102-2801, Lebanon"},{"name":"Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey"},{"name":"Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, 99138 Nicosia, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Aziz ur","family":"Rehman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1742-585X","authenticated-orcid":false,"given":"Nauman","family":"Ahmed","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Lahore, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6929-8093","authenticated-orcid":false,"given":"Muhammad Sajid","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Department of Humanities & Basic Sciences, MCS, National University of Sciences and Technology, Islamabad 44010, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naveed","family":"Shahid","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Lahore, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2165-3479","authenticated-orcid":false,"given":"Muhammad","family":"Rafiq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, 99138 Nicosia, Turkey"},{"name":"Department of Mathematics, Faculty of Science and Technology, University of Central Punjab, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"De la Sen","sequence":"additional","affiliation":[{"name":"Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Bizkaia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1803","DOI":"10.3389\/fimmu.2018.01803","article-title":"Advances in designing and developing vaccines, drugs, and therapies to counter Ebola virus","volume":"9","author":"Dhama","year":"2018","journal-title":"Front. 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