{"id":"https://openalex.org/W1622308394","doi":"https://doi.org/10.1137/120872942","title":"Basic Reproduction Numbers for Reaction-Diffusion Epidemic Models","display_name":"Basic Reproduction Numbers for Reaction-Diffusion Epidemic Models","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1622308394","doi":"https://doi.org/10.1137/120872942","mag":"1622308394"},"language":"en","primary_location":{"id":"doi:10.1137/120872942","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120872942","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077454585","display_name":"Wendi Wang","orcid":"https://orcid.org/0000-0003-4741-7789"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wendi Wang","raw_affiliation_strings":["Southwest University, P.R. China"],"affiliations":[{"raw_affiliation_string":"Southwest University, P.R. China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108578833","display_name":"Xiao\u2010Qiang Zhao","orcid":"https://orcid.org/0000-0002-3026-2656"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiao-Qiang Zhao","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077454585"],"corresponding_institution_ids":["https://openalex.org/I142108993"],"apc_list":null,"apc_paid":null,"fwci":7.8659,"has_fulltext":false,"cited_by_count":537,"citation_normalized_percentile":{"value":0.97553692,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"11","issue":"4","first_page":"1652","last_page":"1673"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9868999719619751,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7872279286384583},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"Basic reproduction number","score":0.7544575333595276},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.7405798435211182},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.6395652294158936},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.553964376449585},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5415130257606506},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5412310361862183},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47832345962524414},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.4429623782634735},{"id":"https://openalex.org/keywords/reproduction","display_name":"Reproduction","score":0.434021532535553},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4180387854576111},{"id":"https://openalex.org/keywords/principal","display_name":"Principal (computer security)","score":0.4119337797164917},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.35350361466407776},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.326971173286438},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2242681086063385},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.16860440373420715},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1477178931236267},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09677985310554504},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.09513196349143982}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7872279286384583},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.7544575333595276},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.7405798435211182},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.6395652294158936},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.553964376449585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5415130257606506},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5412310361862183},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47832345962524414},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.4429623782634735},{"id":"https://openalex.org/C59659247","wikidata":"https://www.wikidata.org/wiki/Q11990","display_name":"Reproduction","level":2,"score":0.434021532535553},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4180387854576111},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.4119337797164917},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.35350361466407776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.326971173286438},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2242681086063385},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.16860440373420715},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1477178931236267},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09677985310554504},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.09513196349143982},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120872942","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120872942","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Good health and well-being","score":0.8399999737739563,"id":"https://metadata.un.org/sdg/3"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W93771389","https://openalex.org/W1973861336","https://openalex.org/W1975141707","https://openalex.org/W1978518692","https://openalex.org/W1991258950","https://openalex.org/W1993397183","https://openalex.org/W1996144618","https://openalex.org/W1996970583","https://openalex.org/W2004880157","https://openalex.org/W2008847296","https://openalex.org/W2011125691","https://openalex.org/W2020116213","https://openalex.org/W2032417357","https://openalex.org/W2035271803","https://openalex.org/W2041572706","https://openalex.org/W2046985721","https://openalex.org/W2049318707","https://openalex.org/W2054113533","https://openalex.org/W2056513959","https://openalex.org/W2059395503","https://openalex.org/W2065644774","https://openalex.org/W2067241000","https://openalex.org/W2093076707","https://openalex.org/W2108565494","https://openalex.org/W2112680994","https://openalex.org/W2120262351","https://openalex.org/W2122128564","https://openalex.org/W2136714512","https://openalex.org/W2145068255","https://openalex.org/W2160117222","https://openalex.org/W2324618167"],"related_works":["https://openalex.org/W2366002891","https://openalex.org/W4295814686","https://openalex.org/W2370645916","https://openalex.org/W4380902525","https://openalex.org/W236190221","https://openalex.org/W2379779959","https://openalex.org/W2333822231","https://openalex.org/W2320270721","https://openalex.org/W4388854896","https://openalex.org/W1622308394"],"abstract_inverted_index":{"The":[0],"theory":[1],"of":[2,52,58],"the":[3,26,56],"principal":[4],"eigenvalue":[5,11],"is":[6],"developed":[7],"for":[8,36],"an":[9],"elliptic":[10],"problem":[12],"associated":[13],"with":[14,20,40],"a":[15,49],"linear":[16],"parabolic":[17],"cooperative":[18],"system":[19],"some":[21],"zero":[22],"diffusion":[23],"coefficients.":[24],"Then":[25],"basic":[27],"reproduction":[28],"number":[29],"and":[30,61],"its":[31],"computation":[32],"formulae":[33],"are":[34,46],"established":[35],"reaction-diffusion":[37],"epidemic":[38],"models":[39],"compartmental":[41],"structure.":[42],"These":[43],"theoretical":[44],"results":[45],"applied":[47],"to":[48,54],"spatial":[50,59],"model":[51],"rabies":[53],"study":[55],"influence":[57],"heterogeneity":[60],"population":[62],"mobility":[63],"on":[64],"disease":[65],"transmission.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":16},{"year":2025,"cited_by_count":70},{"year":2024,"cited_by_count":80},{"year":2023,"cited_by_count":69},{"year":2022,"cited_by_count":51},{"year":2021,"cited_by_count":62},{"year":2020,"cited_by_count":49},{"year":2019,"cited_by_count":48},{"year":2018,"cited_by_count":23},{"year":2017,"cited_by_count":30},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
