{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T00:18:43Z","timestamp":1787617123980,"version":"build-2736575974"},"reference-count":40,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>The theory of the principal eigenvalue is developed for an elliptic eigenvalue problem associated with a linear parabolic cooperative system with some zero diffusion coefficients. Then the basic reproduction number and its computation formulae are established for reaction-diffusion epidemic models with compartmental structure. These theoretical results are applied to a spatial model of rabies to study the influence of spatial heterogeneity and population mobility on disease transmission.<\/jats:p>","DOI":"10.1137\/120872942","type":"journal-article","created":{"date-parts":[[2012,12,13]],"date-time":"2012-12-13T11:28:11Z","timestamp":1355398091000},"page":"1652-1673","source":"Crossref","is-referenced-by-count":521,"title":["Basic Reproduction Numbers for Reaction-Diffusion Epidemic Models"],"prefix":"10.1137","volume":"11","author":[{"given":"Wendi","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao-Qiang","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,12,13]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1038\/289765a0"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2008.21.1"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-011-0418-4"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/050629082"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/BF00167155"},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"R. S. Cantrell and C. Cosner,\n                      Spatial Ecology via Reaction-Diffusion Equations\n                      , Wiley Ser. Math. Comput. Biol., John Wiley and Sons, Chichester, UK, 2003.","DOI":"10.1002\/0470871296"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1086\/341518"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2009.02.016"},{"key":"atypb9","first-page":"61","author":"Desch W.","year":"1986","journal-title":"Heidelberg"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00178324"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1006\/tpbi.2001.1553"},{"key":"atypb12","doi-asserted-by":"publisher","unstructured":"Z. Guo, F. Wang, and X. Zou,\n                      Threshold dynamics of an infective disease model with a fixed latent period and non-local infections\n                      , J. Math. Biol., to appear; DOI: 10.1007\/s00285-011-0500-y.","DOI":"10.1007\/s00285-011-0500-y"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/BF00250649"},{"key":"atypb14","unstructured":"P. Hess,\n                      Periodic-Parabolic Boundary Value Problems and Positivity\n                      , Pitman Res. Notes in Math. 247, Longman Scientific and Technical, Harlow, UK, 1991."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009048616476"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(98)10057-3"},{"key":"atypb17","unstructured":"T. Kato,\n                      Perturbation Theory for Linear Operators\n                      , Springer-Verlag, Berlin, Heidelberg, 1976."},{"key":"atypb18","first-page":"3","volume":"3","author":"Krein M. G.","year":"1948","journal-title":"Usp. Mat. Nauk"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-009-0280-9"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-005-9018-z"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/BF03167595"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-010-0346-8"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/100802189"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.1986.0078"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1137\/060651318"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/25\/5\/1451"},{"key":"atypb27","first-page":"168","author":"Real L. A.","year":"2006","journal-title":"UK"},{"key":"atypb28","first-page":"595","author":"Rosatte R. C.","year":"2007","journal-title":"New York"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2006.3.205"},{"key":"atypb30","first-page":"439","volume":"131","author":"Slate D.","year":"2008","journal-title":"Dev. Biol. (Basel)"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.042400799"},{"key":"atypb32","unstructured":"H. L. Smith,\n                      Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems\n                      , Math. Surveys Monogr. 41, AMS, Providence, RI, 1995."},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.1998.4.73"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1137\/080732870"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(02)00108-6"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(03)00428-1"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2003.11.014"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2002.11.001"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1137\/090775890"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-011-0482-9"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/120872942","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:41:57Z","timestamp":1787236917000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/120872942"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":40,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1137\/120872942"],"URL":"https:\/\/doi.org\/10.1137\/120872942","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]}}}