{"id":"https://openalex.org/W3012394361","doi":"https://doi.org/10.1109/cdc40024.2019.9030236","title":"Time-scale Separation on Networks for Multi-City Epidemics","display_name":"Time-scale Separation on Networks for Multi-City Epidemics","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W3012394361","doi":"https://doi.org/10.1109/cdc40024.2019.9030236","mag":"3012394361"},"language":"en","primary_location":{"id":"doi:10.1109/cdc40024.2019.9030236","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030236","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5039356334","display_name":"Patrick Lewien","orcid":null},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Patrick Lewien","raw_affiliation_strings":["Department of Mechanical Engineering, The University of Melbourne, VIC, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, The University of Melbourne, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060665833","display_name":"Airlie Chapman","orcid":"https://orcid.org/0000-0002-8946-552X"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Airlie Chapman","raw_affiliation_strings":["Department of Mechanical Engineering, The University of Melbourne, VIC, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, The University of Melbourne, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039356334"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":null,"apc_paid":null,"fwci":0.4344,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.63087283,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"746","last_page":"751"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9976999759674072,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9976999759674072,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9968000054359436,"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/T10410","display_name":"COVID-19 epidemiological studies","score":0.9939000010490417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.6593987345695496},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6179664134979248},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6015921831130981},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5426796078681946},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5075749158859253},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.48532575368881226},{"id":"https://openalex.org/keywords/scale-free-network","display_name":"Scale-free network","score":0.475978285074234},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.4525550603866577},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4379040002822876},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.4339880347251892},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.4199678301811218},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4122253358364105},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37969279289245605},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3758503198623657},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.356159508228302},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3341329097747803},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33265987038612366},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19459715485572815},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15629342198371887},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.14039823412895203},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.13095414638519287},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10209536552429199},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.0865170955657959}],"concepts":[{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.6593987345695496},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6179664134979248},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6015921831130981},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5426796078681946},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5075749158859253},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.48532575368881226},{"id":"https://openalex.org/C25580894","wikidata":"https://www.wikidata.org/wiki/Q1071058","display_name":"Scale-free network","level":3,"score":0.475978285074234},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4525550603866577},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4379040002822876},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4339880347251892},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.4199678301811218},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4122253358364105},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37969279289245605},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3758503198623657},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.356159508228302},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3341329097747803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33265987038612366},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19459715485572815},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15629342198371887},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.14039823412895203},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.13095414638519287},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10209536552429199},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0865170955657959},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc40024.2019.9030236","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9030236","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3","score":0.8399999737739563}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W613360614","https://openalex.org/W1932806540","https://openalex.org/W2030205386","https://openalex.org/W2030539428","https://openalex.org/W2035787788","https://openalex.org/W2055581502","https://openalex.org/W2070589563","https://openalex.org/W2088674014","https://openalex.org/W2123326271","https://openalex.org/W2793705641","https://openalex.org/W2963734869","https://openalex.org/W2963815167","https://openalex.org/W3124566197","https://openalex.org/W3142588439","https://openalex.org/W4232371096","https://openalex.org/W4236304509","https://openalex.org/W6672862109"],"related_works":["https://openalex.org/W2074717584","https://openalex.org/W2210722882","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2050693590","https://openalex.org/W2009168760","https://openalex.org/W2944759572","https://openalex.org/W4300989278","https://openalex.org/W4285551356"],"abstract_inverted_index":{"This":[0,94],"paper":[1],"explores":[2],"a":[3,16,53,66],"general":[4],"multiple":[5],"time-scale":[6,41,83,136],"approach":[7,155],"to":[8,99,114],"model":[9],"reduction":[10],"in":[11,43,153],"dynamic":[12],"network-of-network":[13],"systems,":[14],"with":[15],"specific":[17],"treatment":[18],"on":[19,81],"multi-city":[20,151],"epidemics.":[21],"Extensive":[22],"coupling":[23],"between":[24,125],"layers":[25],"of":[26,38,62,102,123,141,148],"networks":[27],"often":[28],"complicates":[29],"and":[30,70,120],"obfuscates":[31],"the":[32,36,39,44,63,82,100,106,121,129,138,149,154,157],"interaction":[33],"dynamics.":[34],"Through":[35],"use":[37],"natural":[40],"differences":[42],"system,":[45],"these":[46],"dynamics":[47,140,152],"can":[48,145],"be":[49,112],"individually":[50],"studied":[51],"under":[52,134],"separation":[54],"principle,":[55],"simplifying":[56],"analysis.":[57],"We":[58,132],"describe":[59],"asymptotic":[60],"stability":[61],"network-of-networks":[64],"through":[65],"composite":[67],"Lyapunov":[68],"function,":[69],"provide":[71],"an":[72,142],"M-matrix":[73],"condition":[74,91],"which":[75],"guarantees":[76],"such":[77,88],"stability.":[78],"Conservative":[79],"bounds":[80],"parameters":[84],"are":[85],"given":[86],"quantitatively":[87],"that":[89,147],"this":[90],"is":[92,96],"satisfied.":[93],"theory":[95],"consequently":[97],"applied":[98],"study":[101],"multicity":[103],"epidemics,":[104],"where":[105],"interactions":[107],"within":[108],"each":[109],"city":[110,144],"may":[111],"assumed":[113],"behave":[115],"at":[116,128],"their":[117],"own":[118],"time-scale,":[119],"movement":[122],"population":[124],"cities":[126],"occurs":[127],"slowest":[130],"time-scale.":[131],"show,":[133],"certain":[135],"conditions,":[137],"isolated":[139],"individual":[143],"approximate":[146],"full":[150],"towards":[156],"disease-free":[158],"equilibrium.":[159]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}