{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T04:03:47Z","timestamp":1773288227608,"version":"3.50.1"},"reference-count":32,"publisher":"SAGE Publications","issue":"12","license":[{"start":{"date-parts":[[2024,12,1]],"date-time":"2024-12-01T00:00:00Z","timestamp":1733011200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational Biology"],"published-print":{"date-parts":[[2024,12,1]]},"abstract":"<jats:p>Since the stochastic age-structured multigroup susceptible-infected-recovering (SIR) epidemic model is nonlinear, the solution of this model is hard to be explicitly represented. It is necessary to construct effective numerical methods so as to predict the number of infections. In addition, the stochastic age-structured multigroup SIR model has features of positivity and boundedness of the solution. Therefore, in this article, in order to ensure that the numerical and analytical solutions must have the same properties, by modifying the classical Euler\u2013Maruyama (EM) scheme, we generate a positivity and boundedness preserving EM (PBPEM) method on temporal space for stochastic age-structured multigroup SIR model, which is proved to have a strong convergence to the true solution over finite time intervals. Moreover, by combining the standard finite element method and the PBPEM method, we propose a full-discrete scheme to show the numerical solutions, as well as analyze the error estimations. Finally, the full-discrete scheme is applied to a general stochastic two-group SIR model and the Chlamydia epidemic model, which shows the superiority of the numerical method.<\/jats:p>","DOI":"10.1089\/cmb.2023.0443","type":"journal-article","created":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T05:07:54Z","timestamp":1727413674000},"page":"1259-1290","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Positivity and Boundedness Preserving Numerical Scheme for a Stochastic Multigroup Susceptible-Infected-Recovering Epidemic Model with Age Structure"],"prefix":"10.1177","volume":"31","author":[{"given":"Han","family":"Ma","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Ningxia University, Yinchuan, P.R. China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanyan","family":"Du","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Ningxia University, Yinchuan, P.R. China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Qingdao University of Technology, Qingdao, P.R. China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5851-0957","authenticated-orcid":false,"given":"Qimin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Ningxia University, Yinchuan, P.R. China."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2024,12,4]]},"reference":[{"key":"e_1_3_5_2_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781420010305"},{"key":"e_1_3_5_3_1","first-page":"521","article-title":"The stability in Lp\n                   and L1\n                     p\n                   of the L2\n                  -projection onto finite element function spaces","volume":"48","author":"Crouzeix M.","year":"1987","unstructured":"Crouzeix M., , Thom\u00e9 V. The stability in Lp and L1p of the L2-projection onto finite element function spaces. Math Comp, 1987; 48:521\u2013532.","journal-title":"Math Comp"},{"key":"e_1_3_5_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/18M1215554"},{"key":"e_1_3_5_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/15M1022124"},{"key":"e_1_3_5_6_1","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2015.12.99"},{"key":"e_1_3_5_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1121627"},{"key":"e_1_3_5_8_1","first-page":"259","article-title":"Global stability of the endemic equilibrium of multigroup SIR epidemic models","volume":"14","author":"Guo H.","year":"2006","unstructured":"Guo H., , Li M. Y., , Shuai Z. Global stability of the endemic equilibrium of multigroup SIR epidemic models. Can Appl Math Q, 2006; 14:259\u2013284.","journal-title":"Can Appl Math Q"},{"key":"e_1_3_5_9_1","doi-asserted-by":"publisher","DOI":"10.1214\/19-AOP1345"},{"key":"e_1_3_5_10_1","unstructured":"Japanese Ministry of Health Labour and Welfare. Reported Cases of Sexually Transmitted Diseases (in Japanese) 2023b. https:\/\/www.mhlw.go.jp\/topics\/2005\/04\/tp0411-1.html [May 11 2023]."},{"key":"e_1_3_5_11_1","unstructured":"Japanese Ministry of Health Labour and Welfare.. The 23nd Life Tables 2023a. https:\/\/www.mhlw.go.jp\/english\/database\/db-hw\/lifetb22nd\/index.html [May 12 2023]."},{"key":"e_1_3_5_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2010.12.042"},{"key":"e_1_3_5_13_1","first-page":"321","article-title":"Global behavior of a multi-group SIR epidemic model with age structure and an application to the chlamydia epidemic in Japan","volume":"79","author":"Kuniya T","year":"2019","unstructured":"Kuniya T. Global behavior of a multi-group SIR epidemic model with age structure and an application to the chlamydia epidemic in Japan. SIAM J Numer Anal, 2019; 79:321\u2013340.","journal-title":"SIAM J Numer Anal"},{"key":"e_1_3_5_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2013.01.044"},{"key":"e_1_3_5_15_1","volume-title":"Nonsmooth Data Error Estimates With Applications to the Study of the Long-time Behavior of Finite Element Solutions of Semilinear Parabolic Problems","author":"Larsson S","year":"1992","unstructured":"Larsson S. Nonsmooth Data Error Estimates With Applications to the Study of the Long-time Behavior of Finite Element Solutions of Semilinear Parabolic Problems. Chalmers: Department of Mathematics, Chalmers Tekniska H\u00f6gskola\/G\u00f6teborgs Universitet; 1992."},{"key":"e_1_3_5_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2019.04.211"},{"key":"e_1_3_5_17_1","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/dry088"},{"key":"e_1_3_5_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2018.03.020"},{"key":"e_1_3_5_19_1","doi-asserted-by":"publisher","DOI":"10.1515\/cmam-2017-0023"},{"key":"e_1_3_5_20_1","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2020.1843074"},{"key":"e_1_3_5_21_1","unstructured":"Portal Site of Official Statistics of Japan.. Population Estimates by Age (5-Year Age Group) and Sex\u2014Total Population Japanese Population. 2023. https:\/\/www.stat.go.jp\/english\/data\/jinsui\/tsuki\/index.html [May 12 2023]."},{"key":"e_1_3_5_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2012.02.052"},{"key":"e_1_3_5_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2021.04.024"},{"key":"e_1_3_5_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-016-0044-7"},{"key":"e_1_3_5_25_1","doi-asserted-by":"publisher","DOI":"10.1142\/S1793524518500687"},{"key":"e_1_3_5_26_1","doi-asserted-by":"publisher","DOI":"10.1080\/00036811.2017.1336545"},{"key":"e_1_3_5_27_1","doi-asserted-by":"crossref","DOI":"10.3934\/dcdsb.2017151","article-title":"Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility","volume":"22","author":"Wang J.","year":"2017","unstructured":"Wang J., , Liu X., , Kuniya T., , Pang J. Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility. Discrete Contin Dyn Syst B, 2017; 22.","journal-title":"Discrete Contin Dyn Syst B"},{"key":"e_1_3_5_28_1","first-page":"78","article-title":"Analysis of an age-structured multi-group heroin epidemic model","volume":"347","author":"Wang J.","year":"2019","unstructured":"Wang J., , Wang J., , Kuniya T. Analysis of an age-structured multi-group heroin epidemic model. Appl Math Comput, 2019; 347:78\u2013100.","journal-title":"Appl Math Comput"},{"key":"e_1_3_5_29_1","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2015.12.1083"},{"key":"e_1_3_5_30_1","first-page":"58","article-title":"Finite element methods and their error analysis for SPDEs driven by Gaussian and non-Gaussian noises","volume":"332","author":"Yang X.","year":"2018","unstructured":"Yang X., , Zhao W. Finite element methods and their error analysis for SPDEs driven by Gaussian and non-Gaussian noises. Appl Math Comput, 2018; 332:58\u201375.","journal-title":"Appl Math Comput"},{"key":"e_1_3_5_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2020.113173"},{"key":"e_1_3_5_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.06.050"},{"key":"e_1_3_5_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2011.07.025"}],"container-title":["Journal of Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1089\/cmb.2023.0443","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1089\/cmb.2023.0443","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1089\/cmb.2023.0443","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:25:13Z","timestamp":1773231913000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1089\/cmb.2023.0443"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,1]]},"references-count":32,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2024,12,1]]}},"alternative-id":["10.1089\/cmb.2023.0443"],"URL":"https:\/\/doi.org\/10.1089\/cmb.2023.0443","relation":{},"ISSN":["1066-5277","1557-8666"],"issn-type":[{"value":"1066-5277","type":"print"},{"value":"1557-8666","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,1]]}}}