{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:54:00Z","timestamp":1753887240324,"version":"3.41.2"},"reference-count":25,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,1,9]],"date-time":"2019-01-09T00:00:00Z","timestamp":1546992000000},"content-version":"vor","delay-in-days":8,"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":["11771373"],"award-info":[{"award-number":["11771373"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>This paper investigates a three\u2010patch Rift Valley fever virus transmission model with periodic coefficients. The basic reproduction number <jats:italic>R<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic>0<\/jats:sub>(<jats:italic>i<\/jats:italic> = 1,2,3) is calculated for the model by using the next infection operator method. The threshold conditions on the extinction and permanence in the mean of the disease with probability one. The Rift Valley fever disease will be permanent in the <jats:italic>j<\/jats:italic>\u2010th (<jats:italic>j<\/jats:italic> = 1,2,3) patch if <jats:italic>j<\/jats:italic> \u2265 <jats:italic>i<\/jats:italic>, <jats:italic>R<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic>0<\/jats:sub> &gt; 1 and dies out in the <jats:italic>j<\/jats:italic>\u2010th patch if <jats:italic>j<\/jats:italic> &lt; <jats:italic>i<\/jats:italic>. The numerical simulations are given to confirm the theoretical results.<\/jats:p>","DOI":"10.1155\/2019\/7896946","type":"journal-article","created":{"date-parts":[[2019,1,9]],"date-time":"2019-01-09T23:32:01Z","timestamp":1547076721000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Threshold Dynamics in a Periodic Three\u2010Patch Rift Valley Fever Virus Transmission Model"],"prefix":"10.1155","volume":"2019","author":[{"given":"Buyu","family":"Wen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4285-3277","authenticated-orcid":false,"given":"Zhidong","family":"Teng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenlin","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,1,9]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10441-011-9132-2"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/path.1700340418"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1080\/17513758.2012.733427"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511610493"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.2460\/javma.232.4.514"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0108172"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0130838"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pntd.0003388"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/138757"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.puhe.2015.07.034"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-014-9998-7"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2012.04.029"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-013-9818-5"},{"key":"e_1_2_9_14_2","first-page":"1","article-title":"An epidemiological model of Rift Valley fever","volume":"2007","author":"Gaff H.","year":"2007","journal-title":"Electronic Journal of Differential Equations"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/627586"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2015.05.005"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/841367"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-007-9231-z"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2006.01.085"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-008-9111-8"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21761-1"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(02)00108-6"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511530043"},{"key":"e_1_2_9_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2014.05.079"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2017.10.011"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/7896946.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/7896946.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2019\/7896946","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T11:38:52Z","timestamp":1723030732000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2019\/7896946"}},"subtitle":[],"editor":[{"given":"Peter","family":"Giesl","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1155\/2019\/7896946"],"URL":"https:\/\/doi.org\/10.1155\/2019\/7896946","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2019,1]]},"assertion":[{"value":"2018-04-29","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-08-29","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-01-09","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"7896946"}}