{"id":"https://openalex.org/W2962976446","doi":"https://doi.org/10.1109/tac.2019.2898515","title":"Analysis and Control of a Continuous-Time Bi-Virus Model","display_name":"Analysis and Control of a Continuous-Time Bi-Virus Model","publication_year":2019,"publication_date":"2019-02-12","ids":{"openalex":"https://openalex.org/W2962976446","doi":"https://doi.org/10.1109/tac.2019.2898515","mag":"2962976446"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2019.2898515","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2898515","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5100396338","display_name":"Ji Liu","orcid":"https://orcid.org/0000-0003-2871-9888"},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ji Liu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Stony Brook University, Centereach, USA"],"raw_orcid":"https://orcid.org/0000-0003-2871-9888","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Stony Brook University, Centereach, USA","institution_ids":["https://openalex.org/I59553526"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085597072","display_name":"Philip E. Par\u00e9","orcid":"https://orcid.org/0000-0002-4095-7320"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Philip E. Pare","raw_affiliation_strings":["Division of Decision and Control Systems, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-4095-7320","affiliations":[{"raw_affiliation_string":"Division of Decision and Control Systems, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110629459","display_name":"Angelia Nedi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Angelia Nedic","raw_affiliation_strings":["School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, USA"],"raw_orcid":"https://orcid.org/0000-0001-9365-6321","affiliations":[{"raw_affiliation_string":"School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, USA","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101932271","display_name":"Choon Yik Tang","orcid":"https://orcid.org/0000-0001-6145-301X"},"institutions":[{"id":"https://openalex.org/I8692664","display_name":"University of Oklahoma","ror":"https://ror.org/02aqsxs83","country_code":"US","type":"education","lineage":["https://openalex.org/I8692664"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Choon Yik Tang","raw_affiliation_strings":["School of Electrical and Computer Engineering, University of Oklahoma, Norman, USA"],"raw_orcid":"https://orcid.org/0000-0001-6145-301X","affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, University of Oklahoma, Norman, USA","institution_ids":["https://openalex.org/I8692664"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043282337","display_name":"Carolyn L. Beck","orcid":"https://orcid.org/0000-0003-4880-6380"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Carolyn L. Beck","raw_affiliation_strings":["Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Champaign, USA"],"raw_orcid":"https://orcid.org/0000-0003-4880-6380","affiliations":[{"raw_affiliation_string":"Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Champaign, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019604570","display_name":"Tamer Ba\u015far","orcid":"https://orcid.org/0000-0003-4406-7875"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tamer Basar","raw_affiliation_strings":["Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Champaign, USA"],"raw_orcid":"https://orcid.org/0000-0003-4406-7875","affiliations":[{"raw_affiliation_string":"Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Champaign, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":13.0649,"has_fulltext":false,"cited_by_count":118,"citation_normalized_percentile":{"value":0.99172608,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"64","issue":"12","first_page":"4891","last_page":"4906"},"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":0.9991000294685364,"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":0.9991000294685364,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9962000250816345,"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":0.9944999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/virus","display_name":"Virus","score":0.6039162874221802},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5629347562789917},{"id":"https://openalex.org/keywords/impossibility","display_name":"Impossibility","score":0.5442817211151123},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.4711645543575287},{"id":"https://openalex.org/keywords/computer-virus","display_name":"Computer virus","score":0.46722444891929626},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4368076026439667},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4281825125217438},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.4274417757987976},{"id":"https://openalex.org/keywords/virology","display_name":"Virology","score":0.4146375060081482},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.39096033573150635},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.39001813530921936},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3843584656715393},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3280276656150818},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14662638306617737},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11153769493103027},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10918009281158447},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.09760740399360657},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0824081301689148}],"concepts":[{"id":"https://openalex.org/C2522874641","wikidata":"https://www.wikidata.org/wiki/Q808","display_name":"Virus","level":2,"score":0.6039162874221802},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5629347562789917},{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.5442817211151123},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4711645543575287},{"id":"https://openalex.org/C19407854","wikidata":"https://www.wikidata.org/wiki/Q485","display_name":"Computer virus","level":2,"score":0.46722444891929626},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4368076026439667},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4281825125217438},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.4274417757987976},{"id":"https://openalex.org/C159047783","wikidata":"https://www.wikidata.org/wiki/Q7215","display_name":"Virology","level":1,"score":0.4146375060081482},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.39096033573150635},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.39001813530921936},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3843584656715393},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3280276656150818},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14662638306617737},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11153769493103027},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10918009281158447},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.09760740399360657},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0824081301689148},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2019.2898515","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2898515","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being","score":0.8299999833106995}],"awards":[{"id":"https://openalex.org/G3441682284","display_name":null,"funder_award_id":"DMS 13-12907","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4559779936","display_name":null,"funder_award_id":"W911NF-16-1-0485","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6371249099","display_name":null,"funder_award_id":"ECCS 15-09302","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G750930579","display_name":null,"funder_award_id":"CCF 11-11342","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8325026323","display_name":null,"funder_award_id":"N00014-16-1-2710","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8824011968","display_name":null,"funder_award_id":"N00014-12-1-0998","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8925639116","display_name":null,"funder_award_id":"CNS 15-44953","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W196409072","https://openalex.org/W1481661614","https://openalex.org/W1501825524","https://openalex.org/W1510170991","https://openalex.org/W1828315746","https://openalex.org/W1964585873","https://openalex.org/W1985782993","https://openalex.org/W1991365171","https://openalex.org/W1994507967","https://openalex.org/W2005504141","https://openalex.org/W2008072444","https://openalex.org/W2038195874","https://openalex.org/W2040938924","https://openalex.org/W2050331367","https://openalex.org/W2061949976","https://openalex.org/W2063366119","https://openalex.org/W2068899084","https://openalex.org/W2090502749","https://openalex.org/W2099440098","https://openalex.org/W2102365618","https://openalex.org/W2110852762","https://openalex.org/W2111725629","https://openalex.org/W2112494680","https://openalex.org/W2118820208","https://openalex.org/W2144301074","https://openalex.org/W2148301044","https://openalex.org/W2155039147","https://openalex.org/W2156928189","https://openalex.org/W2161499589","https://openalex.org/W2163595839","https://openalex.org/W2169017746","https://openalex.org/W2292530634","https://openalex.org/W2292780929","https://openalex.org/W2314043858","https://openalex.org/W2440001402","https://openalex.org/W2594150684","https://openalex.org/W2962976446","https://openalex.org/W2963160040","https://openalex.org/W2963815167","https://openalex.org/W2964009245","https://openalex.org/W2964101545","https://openalex.org/W3035235874","https://openalex.org/W3105940665","https://openalex.org/W4295016751","https://openalex.org/W4388299012","https://openalex.org/W6607972483","https://openalex.org/W6651925351","https://openalex.org/W6698775190","https://openalex.org/W6718465079"],"related_works":["https://openalex.org/W2384156839","https://openalex.org/W4321602641","https://openalex.org/W2394251275","https://openalex.org/W4241392912","https://openalex.org/W2596801716","https://openalex.org/W4387391601","https://openalex.org/W2141614742","https://openalex.org/W2369846953","https://openalex.org/W2362926696","https://openalex.org/W915072206"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"a":[3,15,59,85,104,181,192],"distributed":[4,196],"continuous-time":[5],"bi-virus":[6],"model":[7],"in":[8,177],"which":[9,65,89,161],"two":[10,43,78,125,141,167],"competing":[11],"viruses":[12,44,72,142],"spread":[13,45,143],"over":[14,46,144],"network":[16,27,102],"consisting":[17],"of":[18,21,25,34,165,171,180,195],"multiple":[19],"groups":[20],"individuals.":[22],"Limiting":[23],"behaviors":[24],"the":[26,32,35,42,52,56,62,81,100,108,121,134,140,145,150,163,166,178],"are":[28,175],"characterized":[29],"by":[30],"analyzing":[31],"equilibria":[33,79,119,174],"system":[36,53,151],"and":[37,84,124,136,185],"their":[38],"stability.":[39],"Specifically,":[40],"when":[41],"possibly":[47],"different":[48],"directed":[49,147],"infection":[50,137,148],"graphs,":[51],"may":[54,152],"have":[55,153],"following:":[57],"first,":[58],"unique":[60],"equilibrium,":[61],"healthy":[63,82,122],"state,":[64,88],"is":[66,90,189],"globally":[67,92],"stable,":[68,93],"implying":[69,94],"that":[70,95],"both":[71],"will":[73,98,111],"eventually":[74],"be":[75,112],"eradicated,":[76,113],"second,":[77],"including":[80,120],"state":[83,123],"dominant":[86,126],"virus":[87,97,110,127],"almost":[91],"one":[96],"pervade":[99],"entire":[101],"causing":[103],"single-virus":[105],"epidemic":[106,159],"while":[107],"other":[109],"or":[114,155],"third,":[115],"at":[116],"least":[117],"three":[118],"states,":[128],"depending":[129],"on":[130,133],"certain":[131,193],"conditions":[132],"healing":[135],"rates.":[138],"When":[139],"same":[146],"graph,":[149],"zero":[154],"infinitely":[156],"many":[157],"coexisting":[158],"equilibria,":[160],"represents":[162],"pervasion":[164],"viruses.":[168],"Sensitivity":[169],"properties":[170],"some":[172],"nontrivial":[173],"investigated":[176],"context":[179],"decentralized":[182],"control":[183],"technique,":[184],"an":[186],"impossibility":[187],"result":[188],"given":[190],"for":[191],"type":[194],"feedback":[197],"controller.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":21},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":18},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-16T09:24:06.705377","created_date":"2025-10-10T00:00:00"}
