{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:08:29Z","timestamp":1740103709818,"version":"3.37.3"},"reference-count":31,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,8,8]],"date-time":"2020-08-08T00:00:00Z","timestamp":1596844800000},"content-version":"unspecified","delay-in-days":0,"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":["11871179","11771374","135309475"],"award-info":[{"award-number":["11871179","11771374","135309475"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871179","11771374","135309475"],"award-info":[{"award-number":["11871179","11771374","135309475"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds of Heilongjiang Provincial Colleges","award":["11871179","11771374","135309475"],"award-info":[{"award-number":["11871179","11771374","135309475"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,8,8]]},"abstract":"<jats:p>In this paper, we propose a stage-structured predator-prey model with migrations among patches in an <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>n<\/mml:mi><\/mml:math>-patch environment. The net reproduction number for each patch in isolation is obtained along with the net reproduction number of the system of patches, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u211b<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math>. Inequalities describing the relationship among these numbers are also given. Furthermore, threshold dynamics determined by <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u211b<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math> is established: the predator dies out if <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u211b<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>&lt;<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math> while the predator persists if <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u211b<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>&gt;<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>. Focusing on the case with two patches, we obtain that the dispersal decreases the net reproduction number <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">\u211b<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math>. By numerical simulations, we find that the dispersal may be a good thing or a bad thing because the dispersal could make the predator population thrive or extinct, and hence we might seek steady state in the ecological environment by controlling parameters related to the prey and the predator.<\/jats:p>","DOI":"10.1155\/2020\/6028019","type":"journal-article","created":{"date-parts":[[2020,8,8]],"date-time":"2020-08-08T23:31:12Z","timestamp":1596929472000},"page":"1-13","source":"Crossref","is-referenced-by-count":0,"title":["A Stage-Structured Predator-Prey Model in a Patchy Environment"],"prefix":"10.1155","volume":"2020","author":[{"given":"Xuejuan","family":"Lu","sequence":"first","affiliation":[{"name":"College of Science, Qiqihar University, Qiqihar, Heilongjiang 161006, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2896-5627","authenticated-orcid":true,"given":"Yuming","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7919-0801","authenticated-orcid":true,"given":"Shengqiang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Tiangong University, Tianjin 300387, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1017\/s1464793104006645"},{"year":"2003","key":"2"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.es.21.110190.002313"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.ecolsys.34.011802.132428"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1137\/100817954"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1142\/s0218339006001933"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.2307\/3384"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2017046"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1086\/282900"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/s0092-8240(86)90009-1"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(94)90038-8"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2016.03.015"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/bf03167461"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2016.21.737"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2016.03.005"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2016.10.035"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/s0025-5564(02)00108-6"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-006-9169-6"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-015-0084-6"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2002.11.001"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.4039\/entm9745fv"},{"issue":"4","key":"22","first-page":"421","volume":"4","year":"1996","journal-title":"Canadian Applied Math Quarterly"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/s0022-247x(03)00428-1"},{"issue":"1","key":"24","first-page":"175","volume":"17","year":"2009","journal-title":"Canadian Applied Mathematics Quarterly"},{"year":"2001","key":"25"},{"year":"1985","key":"26"},{"year":"1991","key":"27"},{"year":"2010","key":"28"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1137\/0524026"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1023\/a:1009044515567"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2012.01.004"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/6028019.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/6028019.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/6028019.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,8]],"date-time":"2020-08-08T23:31:20Z","timestamp":1596929480000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/6028019\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,8]]},"references-count":31,"alternative-id":["6028019","6028019"],"URL":"https:\/\/doi.org\/10.1155\/2020\/6028019","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,8,8]]}}}