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After proving the existence and uniqueness of the global solution to the system, we developed sufficient conditions for the existence of an stationary ergodic distribution of the positive solutions.\nThen we gave sufficient conditions for extinction of the diseases which is based on the basic reproduction number in its corresponding deterministic system.<\/jats:p>","DOI":"10.1515\/mcma-2024-2010","type":"journal-article","created":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T18:04:25Z","timestamp":1722621865000},"page":"269-280","source":"Crossref","is-referenced-by-count":0,"title":["Dynamics of a multigroup stochastic SIQR epidemic model"],"prefix":"10.1515","volume":"30","author":[{"given":"Sanaz","family":"Lamei","sequence":"first","affiliation":[{"name":"Faculty of Mathematical Sciences , University of Guilan , Rasht , Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mozhgan","family":"Akbari","sequence":"additional","affiliation":[{"name":"Faculty of Mathematical Sciences , University of Guilan , Rasht , Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,8,3]]},"reference":[{"key":"2024083008370657633_j_mcma-2024-2010_ref_001","unstructured":"E.  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Lajmanovich and J. A.  Yorke,\nA deterministic model for gonorrhea in a nonhomogeneous population,\nMath. Biosci. 28 (1976), no. 3\u20134, 221\u2013236.","DOI":"10.1016\/0025-5564(76)90125-5"},{"key":"2024083008370657633_j_mcma-2024-2010_ref_012","doi-asserted-by":"crossref","unstructured":"Q.  Liu and D.  Jiang,\nDynamics of a multigroup SIRS epidemic model with random perturbations and varying total population size,\nCommun. Pure Appl. Anal. 19 (2020), no. 2, 1089\u20131110.","DOI":"10.3934\/cpaa.2020050"},{"key":"2024083008370657633_j_mcma-2024-2010_ref_013","doi-asserted-by":"crossref","unstructured":"Q.  Liu, D.  Jiang, T.  Hayat and A.  Alsaedi,\nDynamics of a stochastic multigroup SIQR epidemic model with standard incidence rates,\nJ. Franklin Inst. 356 (2019), no. 5, 2960\u20132993.","DOI":"10.1016\/j.jfranklin.2019.01.038"},{"key":"2024083008370657633_j_mcma-2024-2010_ref_014","unstructured":"X.  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Phenom. 15 (2020), Paper No. 24.","DOI":"10.1051\/mmnp\/2020006"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2010\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2010\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T08:37:44Z","timestamp":1725007064000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2010\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,3]]},"references-count":17,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,6,18]]},"published-print":{"date-parts":[[2024,9,1]]}},"alternative-id":["10.1515\/mcma-2024-2010"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2024-2010","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"type":"print","value":"0929-9629"},{"type":"electronic","value":"1569-3961"}],"subject":[],"published":{"date-parts":[[2024,8,3]]}}}