{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T06:17:06Z","timestamp":1772691426551,"version":"3.50.1"},"reference-count":37,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:p>This paper generally addresses the study of the spatial outspreading of contagious infectious diseases. A spatial deterministic mathematical model that consists of five coupled nonlinear systems of partial differential equations is introduced. The population is divided into various classes, such as susceptible, exposed, infectious, noninfectious infected, and recovered, and described on a plague domain that changes with time. The space and time affect the distribution of velocity, which is unspecified in the model. The moving domain boundary describes the epidemic wavefront. Theoretical analysis has been applied to the SEINRS model and examines the existence of endemic equilibrium. The existence and termination of the disease have been determined by the fundamental reproduction number, which is achieved by using the next-generation matrix procedure. A numerical simulation is carried out to study the temporal and spatial dynamics of an epidemic model for various scenarios, together with a sensible epidemic setting, which shows that the system achieves endemic equilibrium after some days, with a fundamental reproduction number greater than one. Additionally, a case study on the initial COVID-19 epidemic in Italy has been carried out, allowing us to successfully apply our model to actual data and acquire essential insights into the dynamics, which predict the time duration for the virus to disseminate throughout the country, nearly aligning with the actual observed. The model\u2019s fit was confirmed with [Formula: see text], indicating 98.1% accuracy in predicting cumulative instances. To simulate different populations and areas, the model is very adaptable. The anticipation is that this model can exceed the spatial prediction of epidemic models.<\/jats:p>","DOI":"10.1142\/s179396232550076x","type":"journal-article","created":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T07:40:26Z","timestamp":1763624426000},"source":"Crossref","is-referenced-by-count":0,"title":["Dynamics of SEINRS deterministic epidemic model in spatiotemporal heterogeneous medium with spatially finite domain"],"prefix":"10.1142","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6242-0658","authenticated-orcid":false,"given":"Najeeb Alam","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Karachi, Karachi 75270, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-4563-327X","authenticated-orcid":false,"given":"Araib","family":"Aqee","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Karachi, Karachi 75270, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3873-1410","authenticated-orcid":false,"given":"Dilber Uzun","family":"Ozsahin","sequence":"additional","affiliation":[{"name":"Department of Medical Diagnostic Imaging, College of Health Science, University of Sharjah, Sharjah 27272, UAE"},{"name":"Research Institute for Medical and Health Sciences, University of Sharjah, Sharjah 27272, UAE"},{"name":"Operational Research Center in Healthcare, Near East University, Nicosia\/TRNC, Mersin 10, Mersin 99138, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5438-5407","authenticated-orcid":false,"given":"Hijaz","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Operational Research Center in Healthcare, Near East University, Nicosia\/TRNC, Mersin 10, Mersin 99138, Turkey"},{"name":"Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea"},{"name":"VIZJA University, Okopowa 59, Warsaw 01-043, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9448-2650","authenticated-orcid":false,"given":"Asmat","family":"Ara","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Karachi, Karachi 75270, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-2302-9379","authenticated-orcid":false,"given":"Muhammad","family":"Ayaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Karachi, Karachi 75270, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-6092-5021","authenticated-orcid":false,"given":"Nadeem Alam","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Iqra University, Karachi, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,12,19]]},"reference":[{"key":"S179396232550076XBIB001","doi-asserted-by":"publisher","DOI":"10.1201\/b16343"},{"key":"S179396232550076XBIB002","doi-asserted-by":"publisher","DOI":"10.3389\/fimmu.2019.00549"},{"key":"S179396232550076XBIB003","volume-title":"An Introduction to Epidemiology","author":"Timmreck T. C.","year":"2002"},{"key":"S179396232550076XBIB004","doi-asserted-by":"publisher","DOI":"10.12703\/r\/11-2"},{"key":"S179396232550076XBIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218348X21501826"},{"key":"S179396232550076XBIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2021.104564"},{"key":"S179396232550076XBIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijid.2020.11.154"},{"key":"S179396232550076XBIB008","first-page":"1","volume":"2013","author":"Weiss H. H.","year":"2013","journal-title":"Math. Mater."},{"key":"S179396232550076XBIB009","unstructured":"Beckley R., Modeling epidemics with differential equations, Tennessee State University Internal Report, 2013."},{"key":"S179396232550076XBIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s11831-021-09634-2"},{"key":"S179396232550076XBIB011","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/ac2b16"},{"key":"S179396232550076XBIB012","doi-asserted-by":"publisher","DOI":"10.1017\/jpr.2020.15"},{"key":"S179396232550076XBIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2008.12.032"},{"key":"S179396232550076XBIB014","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/186437"},{"key":"S179396232550076XBIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecocom.2020.100855"},{"key":"S179396232550076XBIB016","volume-title":"Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation","volume":"5","author":"Diekmann O.","year":"2000"},{"key":"S179396232550076XBIB017","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-012-0330-5"},{"key":"S179396232550076XBIB018","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5193(85)80276-9"},{"issue":"1255","key":"S179396232550076XBIB019","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1098\/rspb.1986.0078","volume":"229","author":"Murray J. D.","year":"1986","journal-title":"Proc. R. Soc. Lond. Ser. B: Biol. Sci."},{"key":"S179396232550076XBIB020","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2021.01.006"},{"key":"S179396232550076XBIB021","first-page":"1046","volume":"6","author":"Zhuang Q.","year":"2021","journal-title":"Infect. Dis. Model."},{"key":"S179396232550076XBIB022","doi-asserted-by":"publisher","DOI":"10.1038\/s41591-020-1046-6"},{"issue":"10","key":"S179396232550076XBIB023","first-page":"55","volume":"3","author":"Kilpatrick A.","year":"2010","journal-title":"Nat. Educ. Knowl."},{"key":"S179396232550076XBIB024","doi-asserted-by":"publisher","DOI":"10.1098\/rsos.220064"},{"key":"S179396232550076XBIB025","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-021-03435-4"},{"key":"S179396232550076XBIB026","volume":"15","author":"Bodson M.","year":"2019","journal-title":"A Tutorial Presentation ( Ingl\u00e9s) [Explicaci\u00f3n del criterio de Routh-Hurwitz. Un tutorial de presentaci\u00f3n]"},{"key":"S179396232550076XBIB027","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/1217\/1\/012056"},{"key":"S179396232550076XBIB028","doi-asserted-by":"publisher","DOI":"10.1016\/0959-4388(93)90206-E"},{"key":"S179396232550076XBIB029","doi-asserted-by":"publisher","DOI":"10.1016\/j.epidem.2021.100528"},{"key":"S179396232550076XBIB030","doi-asserted-by":"publisher","DOI":"10.1186\/s41256-020-00170-3"},{"key":"S179396232550076XBIB031","unstructured":"https:\/\/www.worlddata.info\/europe\/italy."},{"key":"S179396232550076XBIB032","doi-asserted-by":"publisher","DOI":"10.1016\/j.rico.2022.100119"},{"key":"S179396232550076XBIB033","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/accf46"},{"key":"S179396232550076XBIB034","unstructured":"https:\/\/www.worldometers.info\/coronavirus\/country\/italy\/#graph-cases-daily."},{"issue":"1","key":"S179396232550076XBIB035","first-page":"120","volume":"15","author":"Massad E.","year":"2010","journal-title":"Trop. Med. Int. Health"},{"key":"S179396232550076XBIB036","unstructured":"https:\/\/www.worldometers.info\/coronavirus\/."},{"key":"S179396232550076XBIB037","doi-asserted-by":"publisher","DOI":"10.17654\/0974324324019"}],"container-title":["International Journal of Modeling, Simulation, and Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S179396232550076X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T04:23:50Z","timestamp":1772684630000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S179396232550076X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,19]]},"references-count":37,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["10.1142\/S179396232550076X"],"URL":"https:\/\/doi.org\/10.1142\/s179396232550076x","relation":{},"ISSN":["1793-9623","1793-9615"],"issn-type":[{"value":"1793-9623","type":"print"},{"value":"1793-9615","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,19]]},"article-number":"2550076"}}