{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:18:52Z","timestamp":1753881532023,"version":"3.41.2"},"reference-count":21,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T00:00:00Z","timestamp":1614038400000},"content-version":"vor","delay-in-days":53,"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":["61702439"],"award-info":[{"award-number":["61702439"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003472","name":"Harbin Institute of Technology","doi-asserted-by":"publisher","award":["IDGA1010200107"],"award-info":[{"award-number":["IDGA1010200107"]}],"id":[{"id":"10.13039\/501100003472","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Exact solutions of epidemic models are critical for identifying the severity and mitigation possibility for epidemics. However, solving complex models can be difficult when interfering conditions from the real\u2010world are incorporated into the models. In this paper, we focus on the generally unsolvable adaptive susceptible\u2010infected\u2010susceptible (ASIS) epidemic model, a typical example of a class of epidemic models that characterize the complex interplays between the virus spread and network structural evolution. We propose two methods based on mean\u2010field approximation, i.e., the first\u2010order mean\u2010field approximation (FOMFA) and higher\u2010order mean\u2010field approximation (HOMFA), to derive the exact solutions to ASIS models. Both methods demonstrate the capability of accurately approximating the metastable\u2010state statistics of the model, such as the infection fraction and network density, with low computational cost. These methods are potentially powerful tools in understanding, mitigating, and controlling disease outbreaks and infodemics.<\/jats:p>","DOI":"10.1155\/2021\/6637761","type":"journal-article","created":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T19:37:33Z","timestamp":1614109053000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["High\u2010Order Mean\u2010Field Approximations for Adaptive Susceptible\u2010Infected\u2010Susceptible Model in Finite\u2010Size Networks"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3044-9047","authenticated-orcid":false,"given":"Kai","family":"Wang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8342-4623","authenticated-orcid":false,"given":"Xiao Fan","family":"Liu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7279-1038","authenticated-orcid":false,"given":"Dongchao","family":"Guo","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,2,23]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1103\/revmodphys.87.925"},{"key":"e_1_2_9_2_2","doi-asserted-by":"crossref","unstructured":"YangW. 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Analysis of malicious flows via SIS epidemic model in CCN Proceedings of the 2018 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS) April 2018 Honolulu HI USA 748\u2013753 https:\/\/doi.org\/10.1109\/INFCOMW.2018.8406860 2-s2.0-85050665649.","DOI":"10.1109\/INFCOMW.2018.8406860"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.86.3200"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.208701"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.85.036108"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-10-5287-3"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2014.07.001"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNET.2008.925623"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1145\/1284680.1284681"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.85.056111"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.88.042802"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.92.030801"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.86.026116"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.86.016116"},{"key":"e_1_2_9_15_2","doi-asserted-by":"crossref","unstructured":"ChenZ. 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Divide and conquer: leveraging topology in control of epidemic information dynamics Proceedings of the 2016 IEEE Global Communications Conference (GLOBECOM) December 2016 Washington DC USA 1\u20136 https:\/\/doi.org\/10.1109\/GLOCOM.2016.7841747 2-s2.0-85015457085.","DOI":"10.1109\/GLOCOM.2016.7841747"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1145\/2635673"},{"key":"e_1_2_9_20_2","doi-asserted-by":"crossref","unstructured":"MarbukhV. Economics of networked infrastructures at the edge of undesirable contagion: a case of SIS infection Proceedings of the 2018 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS) April 2018 Honolulu HI USA 1\u20132.","DOI":"10.1109\/INFCOMW.2018.8406916"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-10-5287-3_11"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6637761.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6637761.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/6637761","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T21:32:01Z","timestamp":1723239121000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/6637761"}},"subtitle":[],"editor":[{"given":"Honglei","family":"Xu","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/6637761"],"URL":"https:\/\/doi.org\/10.1155\/2021\/6637761","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2020-10-03","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-02-11","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-02-23","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"6637761"}}