{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T11:12:33Z","timestamp":1774955553748,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2018,2,28]],"date-time":"2018-02-28T00:00:00Z","timestamp":1519776000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"NSERC and CIHR of Canada"},{"DOI":"10.13039\/501100001809","name":"the National Natural Sciences Foundation of China","doi-asserted-by":"crossref","award":["11301491"],"award-info":[{"award-number":["11301491"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Sciences Foundation of China","doi-asserted-by":"crossref","award":["11331009"],"award-info":[{"award-number":["11331009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003398","name":"Shanxi Scholarship Council of China","doi-asserted-by":"publisher","award":["2014-020"],"award-info":[{"award-number":["2014-020"]}],"id":[{"id":"10.13039\/501100003398","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the One Hundred Talents Project of Shanxi Province"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Bull Math Biol"],"published-print":{"date-parts":[[2018,4]]},"DOI":"10.1007\/s11538-018-0404-8","type":"journal-article","created":{"date-parts":[[2018,2,28]],"date-time":"2018-02-28T18:05:51Z","timestamp":1519841151000},"page":"840-863","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Two-patch model for the spread of West Nile virus"],"prefix":"10.1007","volume":"80","author":[{"given":"Juping","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chris","family":"Cosner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huaiping","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,2,28]]},"reference":[{"key":"404_CR1","doi-asserted-by":"publisher","first-page":"1553","DOI":"10.1007\/s00285-013-0677-3","volume":"68","author":"A Abdelrazec","year":"2014","unstructured":"Abdelrazec A, Lenhart S, Zhu HP (2014) Transmission Dynamics of West Nile virus in mosquito and Corvids and non-Corvids. J Math Biol 68:1553\u20131582","journal-title":"J Math Biol"},{"key":"404_CR2","doi-asserted-by":"publisher","first-page":"1577","DOI":"10.1086\/508754","volume":"194","author":"JF Anderson","year":"2006","unstructured":"Anderson JF, Main AJ (2006) Importance of vertical and horizontal transmission of West Nile virus by Culex pipiens in the Northeastern United States. J Infect Dis 194:1577\u20131579","journal-title":"J Infect Dis"},{"key":"404_CR3","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1093\/imammb\/dqi003","volume":"22","author":"J Arino","year":"2005","unstructured":"Arino J, Davis JR, Hartley D, Jordan R, Miller JM, van den Driessche P (2005) A multi-species epidemic model with spatial dynamics. Math Med Biol 22:129\u2013142","journal-title":"Math Med Biol"},{"key":"404_CR4","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.mbs.2005.09.002","volume":"206","author":"J Arino","year":"2006","unstructured":"Arino J, Jordan R, van den Driessche P (2006) Quarantine in a multi-species epidemics model with spatial dynamics. Math Biosci 206:46\u201360","journal-title":"Math Biosci"},{"key":"404_CR5","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.mbs.2008.08.010","volume":"216","author":"P Auger","year":"2008","unstructured":"Auger P, Kouokam E, Sallet G, Tchuente M, Tsanou B (2008) The Ross-Macdonald model in a patchy environment. Math Biosci 216:123\u2013131","journal-title":"Math Biosci"},{"key":"404_CR6","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1016\/S1473-3099(02)00368-7","volume":"2","author":"GL Campbell","year":"2002","unstructured":"Campbell GL, Marfin AA, Lanciotti RS, Gubler DJ (2002) West Nile virus. Lancet Infect Dis 2:519\u2013529","journal-title":"Lancet Infect Dis"},{"key":"404_CR7","series-title":"Lecture notes in biomathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-70514-7","volume-title":"Mathematical structures of epidemic systems","author":"V Capasso","year":"1993","unstructured":"Capasso V (1993) Mathematical structures of epidemic systems, vol 97. Lecture notes in biomathematics. Springer, Berlin"},{"key":"404_CR8","doi-asserted-by":"publisher","first-page":"550","DOI":"10.1016\/j.jtbi.2009.02.016","volume":"258","author":"C Cosner","year":"2009","unstructured":"Cosner C, Beier JC, Cantrell RS, Impoinvil D, Kapitanski L, Potts MD, Troyo A, Ruan S (2009) The effect of human movement on the persistence of vector-borne diseases. J Theor Biol 258:550\u2013560","journal-title":"J Theor Biol"},{"key":"404_CR9","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1016\/j.bulm.2004.11.008","volume":"67","author":"G Cruz-Pacheco","year":"2005","unstructured":"Cruz-Pacheco G, Esteva L, Monta\u00f1o-Hirose JA, Vargas C (2005) Modelling the dynamics of West Nile virus. Bull Math Biol 67:1157\u20131172","journal-title":"Bull Math Biol"},{"key":"404_CR10","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/BF00178324","volume":"28","author":"O Diekmann","year":"1990","unstructured":"Diekmann O, Heesterbeek JAP, Metz JAJ (1990) On the definition and the computation of the basic reproduction ratio $$R_0$$ R 0 in models for infectious diseases in heterogeneous populations. J Math Biol 28:365\u2013382","journal-title":"J Math Biol"},{"key":"404_CR11","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1155\/2003\/575341","volume":"14","author":"MA Drebot","year":"2003","unstructured":"Drebot MA, Barker R et al (2003) West Nile virus surveillance and diagnostics: a Canadian perspective. Can J Infect Dis 14:105\u2013114","journal-title":"Can J Infect Dis"},{"key":"404_CR12","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/0035-9203(86)90199-9","volume":"80","author":"C Dye","year":"1986","unstructured":"Dye C, Hasibeder G (1986) Population dynamics of mosquito-borne disease: effects of flies which bite some people more frequently than others. T R Soc Trop Med Hyg 80:69\u201377","journal-title":"T R Soc Trop Med Hyg"},{"key":"404_CR13","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1137\/110850761","volume":"72","author":"DZ Gao","year":"2012","unstructured":"Gao DZ, Ruan SG (2012) A multipatch malaria model with logistic growth populations. SIAM J Appl Math 72:819\u2013841","journal-title":"SIAM J Appl Math"},{"key":"404_CR14","doi-asserted-by":"publisher","first-page":"743","DOI":"10.1603\/0022-2585-40.6.743","volume":"40","author":"LB Goddard","year":"2003","unstructured":"Goddard LB, Roth AE, Reisen WK, Scott TW (2003) Vertical transmission of West Nile virus by three California Culex (Diptera: Culicidae) species. J Med Entomol 40:743\u2013746","journal-title":"J Med Entomol"},{"key":"404_CR15","first-page":"259","volume":"14","author":"HB Guo","year":"2006","unstructured":"Guo HB, Li MY, Shuai ZS (2006) Global stability of the endemic equilibrium of multigroup SIR epidemic models. Can Appl Math Q 14:259\u2013284","journal-title":"Can Appl Math Q"},{"key":"404_CR16","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/0025-5564(94)00066-9","volume":"128","author":"KP Hadeler","year":"1995","unstructured":"Hadeler KP, Castillo-Chavez C (1995) A core group model for disease transmission. Math Biosci 128:41\u201355","journal-title":"Math Biosci"},{"key":"404_CR17","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/S0025-5564(97)00027-8","volume":"146","author":"KP Hadeler","year":"1997","unstructured":"Hadeler KP, van den Driessche P (1997) Backward bifurcation in epidemic control. Math Biosci 146:15\u201335","journal-title":"Math Biosci"},{"key":"404_CR18","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/0040-5809(88)90003-2","volume":"33","author":"G Hasibeder","year":"1988","unstructured":"Hasibeder G, Dye C (1988) Population dynamics of mosquito-borne disease: persistence in a completely heterogeneous environment. Theor Popul Biol 33:31\u201353","journal-title":"Theor Popul Biol"},{"key":"404_CR19","unstructured":"http:\/\/www.northlineexpress.com\/outdoor-patio\/mosquito-control\/mosquito-faqs.html$#$ how-far-can-mosquitoes-fly"},{"issue":"1","key":"404_CR20","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s11538-005-9018-z","volume":"68","author":"M Lewis","year":"2006","unstructured":"Lewis M, Renclawowicz J, van den Driessche P (2006) Traveling waves and spread rates for a West Nile virus model. Bull Math Biol 68(1):3\u201323","journal-title":"Bull Math Biol"},{"key":"404_CR21","doi-asserted-by":"publisher","first-page":"1381","DOI":"10.1007\/s00285-017-1124-7","volume":"75","author":"ZG Lin","year":"2017","unstructured":"Lin ZG, Zhu HP (2017) Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary. J Math Biol 75:1381\u20131409","journal-title":"J Math Biol"},{"key":"404_CR22","doi-asserted-by":"crossref","first-page":"145","DOI":"10.3934\/mbe.2006.3.145","volume":"3","author":"R Liu","year":"2006","unstructured":"Liu R, Shuai J, Wu J, Zhu H (2006) Modeling spatial spread of West Nile virus and impact of directional dispersal of birds. Math Biosci Eng 3:145\u2013160","journal-title":"Math Biosci Eng"},{"key":"404_CR23","doi-asserted-by":"publisher","first-page":"392","DOI":"10.3201\/eid0804.010217","volume":"8","author":"M Malkinson","year":"2002","unstructured":"Malkinson M, Banet C, Weisman Y, Pokamunski S, King R, Drouet MT, Deubel V (2002) Introduction of West Nile virus in the Middle East by migrating white storks. Emerg Infect Dis 8:392\u2013397","journal-title":"Emerg Infect Dis"},{"key":"404_CR24","doi-asserted-by":"publisher","first-page":"319","DOI":"10.3201\/eid0604.000401","volume":"6","author":"JH Rappole","year":"2000","unstructured":"Rappole JH, Derrickson SR, Hubalek Z (2000) Migratory birds and spread of West Nile virus in the Western Hemisphere. Emerg Infect Dis 6:319\u2013328","journal-title":"Emerg Infect Dis"},{"key":"404_CR25","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1006\/bulm.2001.0231","volume":"63","author":"DJ Rodriguez","year":"2001","unstructured":"Rodriguez DJ, Torres-Sorando L (2001) Models of infectious diseases in spatially heterogeneous environments. Bull Math Biol 63:547\u2013571","journal-title":"Bull Math Biol"},{"key":"404_CR26","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1137\/0152030","volume":"52","author":"CP Simon","year":"1992","unstructured":"Simon CP, Jacquez JA (1992) Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations. SIAM J Appl Math 52:541\u2013576","journal-title":"SIAM J Appl Math"},{"key":"404_CR27","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1186\/1475-2875-3-13","volume":"3","author":"DL Smith","year":"2004","unstructured":"Smith DL, McKenzie FE (2004) Statics and dynamics of malaria infection in Anopheles mosquitoes. Malar J 3:13\u201326","journal-title":"Malar J"},{"key":"404_CR28","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/S0304-3800(97)00135-X","volume":"104","author":"L Torres-Sorando","year":"1997","unstructured":"Torres-Sorando L, Rodriguez DJ (1997) Models of spatio-temporal dynamics in malaria. Ecol Modelling 104:231\u2013240","journal-title":"Ecol Modelling"},{"key":"404_CR29","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","volume":"180","author":"P Driessche van den","year":"2002","unstructured":"van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180:29\u201348","journal-title":"Math Biosci"}],"container-title":["Bulletin of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11538-018-0404-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-018-0404-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-018-0404-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,28]],"date-time":"2020-10-28T21:10:19Z","timestamp":1603919419000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11538-018-0404-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,28]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,4]]}},"alternative-id":["404"],"URL":"https:\/\/doi.org\/10.1007\/s11538-018-0404-8","relation":{},"ISSN":["0092-8240","1522-9602"],"issn-type":[{"value":"0092-8240","type":"print"},{"value":"1522-9602","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,28]]},"assertion":[{"value":"5 August 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 February 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 February 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}