{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T08:53:43Z","timestamp":1772268823367,"version":"3.50.1"},"reference-count":52,"publisher":"Public Library of Science (PLoS)","issue":"2","license":[{"start":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T00:00:00Z","timestamp":1739491200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2301627"],"award-info":[{"award-number":["2301627"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Research Projects of the Education Office of Jilin Province, China","award":["JJKH20250046KJ, JJKH20241240KJ"],"award-info":[{"award-number":["JJKH20250046KJ, JJKH20241240KJ"]}]},{"name":"Technology Development Program of Jilin Province, China","award":["20210508024RQ"],"award-info":[{"award-number":["20210508024RQ"]}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>With the ongoing evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and its increasing adaptation to humans, several variants of concern (VOCs) and variants of interest (VOIs) have been identified since late 2020. These include Alpha, Beta, Gamma, Delta, Omicron parent lineage, and other variants. These variants may show distinct levels of virulence, antigenicity, and infectivity, which require specific defense and control measures. In this study, we propose an <jats:inline-formula id=\"pcbi.1012778.e001\"><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"pcbi.1012778.e001g\" mimetype=\"image\" position=\"anchor\" xlink:href=\"info:doi\/10.1371\/journal.pcbi.1012778.e001\" xlink:type=\"simple\"\/><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" id=\"m001\"><mml:mi>S<\/mml:mi><mml:msub><mml:mrow><mml:mi>I<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>\u2026<\/mml:mo><mml:msub><mml:mrow><mml:mi>I<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mi>R<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula> infectious disease model to simulate the spread of SARS-CoV-2 variants among the human population. We combine the proposed epidemic model and reported infected data of variants with physical information neural networks (PINNs) to develop a novel mechanism called VOCs-informed neural network (VOCs-INN). In our experiments, we found that this algorithm can accurately fit the reported data of the British Columbia (BC) province and its five internal health agencies in Canada. Furthermore, it can simulate observed or unobserved dynamics, infer time-dependent parameters, and enable short-term predictions. The experimental results also reveal variations in the intensity of control strategies implemented across these regions. VOCs-INN performs well in fitting and forecasting when analyzing long-term or multi-wave data.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012778","type":"journal-article","created":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T18:38:54Z","timestamp":1739558334000},"page":"e1012778","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":3,"title":["Using a multi-strain infectious disease model with physical information neural networks to study the time dependence of SARS-CoV-2 variants of concern"],"prefix":"10.1371","volume":"21","author":[{"given":"Wenxuan","family":"Li","sequence":"first","affiliation":[]},{"given":"Xu","family":"Chen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4354-2665","authenticated-orcid":true,"given":"Suli","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Chiyu","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Guyue","family":"Liu","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2025,2,14]]},"reference":[{"key":"pcbi.1012778.ref001"},{"key":"pcbi.1012778.ref002","first-page":"1","article-title":"Global stability of the endemic equilibrium of a tuberculosis model with immigration and treatment","volume":"19","author":"H Guo","year":"2011","journal-title":"Canad Appl Math Quart."},{"key":"pcbi.1012778.ref003"},{"issue":"2","key":"pcbi.1012778.ref004","doi-asserted-by":"crossref","first-page":"3763","DOI":"10.3934\/math.2023188","article-title":"A higher order Galerkin time discretization scheme for the novel mathematical model of COVID-19","volume":"8","author":"M Jawad","year":"2023","journal-title":"Math"},{"issue":"1","key":"pcbi.1012778.ref005","first-page":"85","article-title":"Study of fractional order SIR model with MH type treatment rate and its stability analysis","volume":"2","author":"S Paul","year":"2024","journal-title":"Bullet Biomath."},{"issue":"10","key":"pcbi.1012778.ref006","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1007\/s11538-022-01064-w","article-title":"Assessing age-specific vaccination strategies and post-vaccination reopening policies for COVID-19 control using SEIR modeling approach","volume":"84","author":"X Wang","year":"2022","journal-title":"Bull Math Biol"},{"issue":"04","key":"pcbi.1012778.ref007","doi-asserted-by":"crossref","first-page":"2350040","DOI":"10.1142\/S1793524523500407","article-title":"A stochastic SIS epidemic infectious diseases model with double stochastic perturbations","volume":"17","author":"X Chen","year":"2024","journal-title":"Int J Biomath."},{"key":"pcbi.1012778.ref008"},{"issue":"4","key":"pcbi.1012778.ref009","first-page":"581","article-title":"Mathematical modeling of the dynamics of COVID-19 variants of concern: asymptotic and finite-time perspectives","volume":"7","author":"A-S Ciupeanu","year":"2022","journal-title":"Infect Dis Model"},{"key":"pcbi.1012778.ref010"},{"issue":"3","key":"pcbi.1012778.ref011","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1109\/JPROC.2021.3060483","article-title":"Explaining deep neural networks and beyond: a review of methods and applications","volume":"109","author":"W Samek","year":"2021","journal-title":"Proc IEEE"},{"key":"pcbi.1012778.ref012","article-title":"A low-cost deep neural network-based autonomous car. 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