{"id":"https://openalex.org/W2008686523","doi":"https://doi.org/10.1137/060672522","title":"Asymptotic Profiles of the Steady States for an SIS Epidemic Patch Model","display_name":"Asymptotic Profiles of the Steady States for an SIS Epidemic Patch Model","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2008686523","doi":"https://doi.org/10.1137/060672522","mag":"2008686523"},"language":"en","primary_location":{"id":"doi:10.1137/060672522","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060672522","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","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/A5089903310","display_name":"Linda J. S. Allen","orcid":"https://orcid.org/0000-0002-8692-708X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. J. S. Allen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021063042","display_name":"Benjamin M. Bolker","orcid":"https://orcid.org/0000-0002-2127-0443"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. M. Bolker","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108749023","display_name":"Y. Lou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Y. Lou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5064306510","display_name":"Andrew L. Nevai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. L. Nevai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2021,"has_fulltext":false,"cited_by_count":242,"citation_normalized_percentile":{"value":0.90775889,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"67","issue":"5","first_page":"1283","last_page":"1309"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9990000128746033,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"Basic reproduction number","score":0.6929168105125427},{"id":"https://openalex.org/keywords/extinction","display_name":"Extinction (optical mineralogy)","score":0.5867802500724792},{"id":"https://openalex.org/keywords/spatial-heterogeneity","display_name":"Spatial heterogeneity","score":0.5261009931564331},{"id":"https://openalex.org/keywords/persistence","display_name":"Persistence (discontinuity)","score":0.4893028438091278},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44622793793678284},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.42526113986968994},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.42202818393707275},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3297160267829895},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2753618061542511},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.23470336198806763},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.23363274335861206},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.22685423493385315},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.22233238816261292},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.11717653274536133}],"concepts":[{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.6929168105125427},{"id":"https://openalex.org/C101991246","wikidata":"https://www.wikidata.org/wiki/Q5422078","display_name":"Extinction (optical mineralogy)","level":2,"score":0.5867802500724792},{"id":"https://openalex.org/C180478619","wikidata":"https://www.wikidata.org/wiki/Q7574066","display_name":"Spatial heterogeneity","level":2,"score":0.5261009931564331},{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.4893028438091278},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44622793793678284},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.42526113986968994},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.42202818393707275},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3297160267829895},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2753618061542511},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.23470336198806763},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.23363274335861206},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.22685423493385315},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.22233238816261292},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.11717653274536133},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/060672522","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060672522","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Good health and well-being","score":0.8600000143051147,"id":"https://metadata.un.org/sdg/3"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W62720732","https://openalex.org/W1500921805","https://openalex.org/W1579743691","https://openalex.org/W1583499676","https://openalex.org/W1640687854","https://openalex.org/W1654578212","https://openalex.org/W1851248039","https://openalex.org/W1965433670","https://openalex.org/W1977642252","https://openalex.org/W1991258950","https://openalex.org/W1993397183","https://openalex.org/W1994078094","https://openalex.org/W1996144618","https://openalex.org/W1998590186","https://openalex.org/W2001454048","https://openalex.org/W2012590521","https://openalex.org/W2022888574","https://openalex.org/W2033017709","https://openalex.org/W2041572706","https://openalex.org/W2045967620","https://openalex.org/W2049352128","https://openalex.org/W2070589563","https://openalex.org/W2082904576","https://openalex.org/W2084933402","https://openalex.org/W2093223643","https://openalex.org/W2112680994","https://openalex.org/W2112900204","https://openalex.org/W2128436420","https://openalex.org/W2128978199","https://openalex.org/W2151917856","https://openalex.org/W2284792865","https://openalex.org/W2324758086","https://openalex.org/W2327049868","https://openalex.org/W2332788889","https://openalex.org/W3108418035"],"related_works":["https://openalex.org/W1995895161","https://openalex.org/W2352063914","https://openalex.org/W1822185412","https://openalex.org/W2047377442","https://openalex.org/W2017131795","https://openalex.org/W1517471410","https://openalex.org/W2084404356","https://openalex.org/W1976578070","https://openalex.org/W2372259772","https://openalex.org/W2967747686"],"abstract_inverted_index":{"Spatial":[0],"heterogeneity,":[1,139],"habitat":[2,140,286],"connectivity,":[3,141,287],"and":[4,15,46,60,70,116,142,149,179,248,288],"rates":[5,62,143],"of":[6,17,29,144,162,184,227,241,255,285],"movement":[7,145],"can":[8,49,249],"have":[9,251,276,298],"large":[10],"impacts":[11],"on":[12,244,258],"the":[13,26,30,76,92,102,119,155,160,163,169,182,196,212,225,272],"persistence":[14,148],"extinction":[16],"infectious":[18],"diseases.":[19],"These":[20,296],"factors":[21],"are":[22,66,281,291],"shown":[23,99],"to":[24,146,159,218,231],"determine":[25,74],"asymptotic":[27],"profile":[28],"steady":[31],"states":[32,209],"in":[33,43,56,271,283],"a":[34,130,189,219,238,252],"frequency-dependent":[35],"SIS":[36],"(susceptible-infected-susceptible)":[37],"epidemic":[38],"model":[39,93],"with":[40],"n":[41],"patches":[42,65,247,270],"which":[44],"susceptible":[45,228,242,256,277],"infected":[47,185],"individuals":[48,186,229,243,257,278],"both":[50],"move":[51],"between":[52],"patches.":[53,264],"Patch":[54],"differences":[55,72],"local":[57],"disease":[58,147,302],"transmission":[59],"recovery":[61],"characterize":[63],"whether":[64,75,268],"low-risk":[67,82,167,246],"or":[68,79,83,279],"high-risk,":[69],"these":[71,289],"collectively":[73],"spatial":[77,138,164],"domain,":[78],"habitat,":[80],"is":[81,94,97,105,112,122,172,199],"high-risk.":[84],"The":[85,151,206],"basic":[86,156],"reproduction":[87,157],"number":[88,158,240,254],"${\\cal":[89],"R}_0$":[90],"for":[91,193,267,301],"determined.":[95],"It":[96],"then":[98],"that":[100,117,210],"when":[101,118,211],"disease-free":[103,120,170,197,222,235,274],"equilibrium":[104,121,171,198,214,223,236,275],"stable":[106,173],"(${\\cal":[107,124,174,202],"R}_0":[108,125,175,203],"<":[109,176],"1$)":[110,127,177],"it":[111,216],"globally":[113],"asymptotically":[114],"stable,":[115],"unstable":[123,201],">":[126,204],"there":[128],"exists":[129],"unique":[131],"endemic":[132,213],"equilibrium.":[133],"Two":[134],"main":[135],"theorems":[136],"link":[137],"extinction.":[150],"first":[152],"theorem":[153,208],"relates":[154],"heterogeneity":[161],"domain.":[165],"For":[166],"domains,":[168,195],"if":[178,181],"only":[180],"mobility":[183,226],"lies":[187],"above":[188],"threshold":[190],"value,":[191],"but":[192,260],"high-risk":[194,263,269],"always":[200],"1$).":[205],"second":[207],"exists,":[215],"tends":[217,230],"spatially":[220],"inhomogeneous":[221],"as":[224],"zero.":[232],"This":[233],"limiting":[234,273],"has":[237],"positive":[239,253],"all":[245],"also":[250],"some,":[259],"not":[261,280],"all,":[262],"Sufficient":[265],"conditions":[266,290],"given":[282],"terms":[284],"illustrated":[292],"using":[293],"numerical":[294],"examples.":[295],"results":[297],"important":[299],"implications":[300],"control.":[303]},"counts_by_year":[{"year":2026,"cited_by_count":13},{"year":2025,"cited_by_count":33},{"year":2024,"cited_by_count":27},{"year":2023,"cited_by_count":26},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":25},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":7}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}