{"id":"https://openalex.org/W2172286141","doi":"https://doi.org/10.1142/s021812740902324x","title":"THE SIS MODEL WITH TIME DELAY ON COMPLEX NETWORKS","display_name":"THE SIS MODEL WITH TIME DELAY ON COMPLEX NETWORKS","publication_year":2009,"publication_date":"2009-02-01","ids":{"openalex":"https://openalex.org/W2172286141","doi":"https://doi.org/10.1142/s021812740902324x","mag":"2172286141"},"language":"en","primary_location":{"id":"doi:10.1142/s021812740902324x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740902324x","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5100734030","display_name":"Xin\u2010Jian Xu","orcid":"https://orcid.org/0000-0001-6088-976X"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I60858718","display_name":"University of Aveiro","ror":"https://ror.org/00nt41z93","country_code":"PT","type":"education","lineage":["https://openalex.org/I60858718"]}],"countries":["CN","PT"],"is_corresponding":false,"raw_author_name":"XIN-JIAN XU","raw_affiliation_strings":["Departamento de F\u00edsica da Universidade de Aveiro, 3810-193 Aveiro, Portugal","Department of Mathematics, College of Science, Shanghai University, Baoshan Area, Shanghai 200444, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica da Universidade de Aveiro, 3810-193 Aveiro, Portugal","institution_ids":["https://openalex.org/I60858718"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, Shanghai University, Baoshan Area, Shanghai 200444, P. R. China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024633466","display_name":"Guanrong Chen","orcid":"https://orcid.org/0000-0003-1381-7418"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"GUANRONG CHEN","raw_affiliation_strings":["Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, P. R. China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7101,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.73131149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"19","issue":"02","first_page":"623","last_page":"628"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.979200005531311,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.5792216658592224},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.5418577194213867},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.537975013256073},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4616488516330719},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44320571422576904},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43184414505958557},{"id":"https://openalex.org/keywords/transmission-rate","display_name":"Transmission rate","score":0.42594635486602783},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3847222924232483},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3704426884651184},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3695570230484009},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18509754538536072},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.1785641610622406},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17835861444473267},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.14589035511016846},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.127620130777359},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.11537551879882812},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08336609601974487}],"concepts":[{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.5792216658592224},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.5418577194213867},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.537975013256073},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4616488516330719},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44320571422576904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43184414505958557},{"id":"https://openalex.org/C2989335485","wikidata":"https://www.wikidata.org/wiki/Q17130189","display_name":"Transmission rate","level":3,"score":0.42594635486602783},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3847222924232483},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3704426884651184},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3695570230484009},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18509754538536072},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.1785641610622406},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17835861444473267},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.14589035511016846},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.127620130777359},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.11537551879882812},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08336609601974487},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021812740902324x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740902324x","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3","score":0.8600000143051147}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W2008620264","https://openalex.org/W2030539428","https://openalex.org/W2034413844","https://openalex.org/W2037881439","https://openalex.org/W2038511471","https://openalex.org/W2043890595","https://openalex.org/W2055620707","https://openalex.org/W2071802245","https://openalex.org/W2087451948","https://openalex.org/W2093616570","https://openalex.org/W2096145431","https://openalex.org/W2099953962","https://openalex.org/W2100491128","https://openalex.org/W2100776472","https://openalex.org/W2110919848","https://openalex.org/W2112090702","https://openalex.org/W2121821841","https://openalex.org/W2122328014","https://openalex.org/W2124637492","https://openalex.org/W2136525561","https://openalex.org/W2142661640","https://openalex.org/W2161728228","https://openalex.org/W2320448585","https://openalex.org/W4254962106","https://openalex.org/W4388299012"],"related_works":["https://openalex.org/W2014541560","https://openalex.org/W2117046038","https://openalex.org/W4303188256","https://openalex.org/W2308693247","https://openalex.org/W2083725625","https://openalex.org/W2057373456","https://openalex.org/W268961470","https://openalex.org/W2359342237","https://openalex.org/W2394056119","https://openalex.org/W4327813467"],"abstract_inverted_index":{"We":[0,13,83],"present":[1],"a":[2,49,59],"time-delayed":[3],"SIS":[4],"model":[5],"on":[6],"complex":[7],"networks":[8],"to":[9],"study":[10],"epidemic":[11,42,64],"spreading.":[12],"found":[14,39,56],"that":[15,40,57],"the":[16,33,41,45,63,79],"existence":[17],"of":[18,29],"delay":[19,46,80],"will":[20],"affect,":[21],"and":[22,27,44,75],"oftentimes":[23],"enhance,":[24],"both":[25],"outbreak":[26],"prevalence":[28,65],"infectious":[30],"diseases":[31],"in":[32],"networks.":[34],"For":[35,52],"small-world":[36],"networks,":[37,54],"we":[38,55],"threshold":[43],"time":[47,81],"have":[48],"power-law":[50],"relation.":[51],"scale-free":[53],"for":[58],"given":[60],"transmission":[61],"rate,":[62],"has":[66],"an":[67],"exponential":[68],"form,":[69],"which":[70],"can":[71],"be":[72],"analytically":[73],"obtained,":[74],"it":[76],"decays":[77],"as":[78],"increases.":[82],"confirm":[84],"all":[85],"results":[86],"by":[87],"sufficient":[88],"numerical":[89],"simulations.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}