{"id":"https://openalex.org/W2028680067","doi":"https://doi.org/10.1137/120876642","title":"Global Stability of Infectious Disease Models Using Lyapunov Functions","display_name":"Global Stability of Infectious Disease Models Using Lyapunov Functions","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2028680067","doi":"https://doi.org/10.1137/120876642","mag":"2028680067"},"language":"en","primary_location":{"id":"doi:10.1137/120876642","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120876642","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":true,"oa_status":"green","oa_url":"https://stars.library.ucf.edu/facultybib2010/4700","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076385958","display_name":"Zhisheng Shuai","orcid":"https://orcid.org/0000-0002-9599-6589"},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Zhisheng Shuai","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada","institution_ids":["https://openalex.org/I212119943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049802779","display_name":"P. van den Driessche","orcid":"https://orcid.org/0000-0003-1485-8326"},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"P. van den Driessche","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada","institution_ids":["https://openalex.org/I212119943"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076385958"],"corresponding_institution_ids":["https://openalex.org/I212119943"],"apc_list":null,"apc_paid":null,"fwci":12.4515,"has_fulltext":false,"cited_by_count":431,"citation_normalized_percentile":{"value":0.98974239,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"73","issue":"4","first_page":"1513","last_page":"1532"},"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9941999912261963,"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"}},{"id":"https://openalex.org/T10044","display_name":"Protein Structure and Dynamics","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"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/lyapunov-function","display_name":"Lyapunov function","score":0.7540349960327148},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6399123072624207},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6199657320976257},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6112156510353088},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5825949311256409},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5153507590293884},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43227988481521606},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33708804845809937},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2559071183204651},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.11224392056465149}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7540349960327148},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6399123072624207},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6199657320976257},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6112156510353088},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5825949311256409},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5153507590293884},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43227988481521606},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33708804845809937},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2559071183204651},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.11224392056465149},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120876642","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120876642","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"},{"id":"pmh:oai:stars.library.ucf.edu:facultybib2010-5699","is_oa":true,"landing_page_url":"https://stars.library.ucf.edu/facultybib2010/4700","pdf_url":null,"source":{"id":"https://openalex.org/S4210172555","display_name":"Journal of International Crisis and Risk Communication Research","issn_l":"2576-0017","issn":["2576-0017","2576-0025"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Bibliography 2010s","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:stars.library.ucf.edu:facultybib2010-5699","is_oa":true,"landing_page_url":"https://stars.library.ucf.edu/facultybib2010/4700","pdf_url":null,"source":{"id":"https://openalex.org/S4210172555","display_name":"Journal of International Crisis and Risk Communication Research","issn_l":"2576-0017","issn":["2576-0017","2576-0025"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Bibliography 2010s","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W94176095","https://openalex.org/W138083112","https://openalex.org/W567930972","https://openalex.org/W1479863711","https://openalex.org/W1500921805","https://openalex.org/W1510122527","https://openalex.org/W1853209780","https://openalex.org/W1964273550","https://openalex.org/W1968972679","https://openalex.org/W1970718404","https://openalex.org/W1985782993","https://openalex.org/W1988160370","https://openalex.org/W1992640600","https://openalex.org/W1996757718","https://openalex.org/W1998590186","https://openalex.org/W2002220178","https://openalex.org/W2010825494","https://openalex.org/W2011557321","https://openalex.org/W2012967905","https://openalex.org/W2028378134","https://openalex.org/W2038090279","https://openalex.org/W2038195874","https://openalex.org/W2041572706","https://openalex.org/W2048946655","https://openalex.org/W2054353417","https://openalex.org/W2055605553","https://openalex.org/W2059239694","https://openalex.org/W2079067287","https://openalex.org/W2101758302","https://openalex.org/W2112680994","https://openalex.org/W2123302884","https://openalex.org/W2160057076","https://openalex.org/W2161499589","https://openalex.org/W2161728228","https://openalex.org/W2167887891","https://openalex.org/W2494397142","https://openalex.org/W2799004609","https://openalex.org/W3141151088"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2030955003","https://openalex.org/W2374426356","https://openalex.org/W1977987201","https://openalex.org/W2059628530","https://openalex.org/W2164487476","https://openalex.org/W3194517843","https://openalex.org/W2106169668","https://openalex.org/W2534107666"],"abstract_inverted_index":{"Two":[0],"systematic":[1],"methods":[2],"are":[3,18,60,82],"presented":[4],"to":[5,21,36,62,84],"guide":[6],"the":[7,31,38,42,64,68,75,86],"construction":[8],"of":[9,41,67,88],"Lyapunov":[10],"functions":[11],"for":[12],"general":[13],"infectious":[14],"disease":[15,72],"models":[16,73,81],"and":[17,55,77],"thus":[19],"applicable":[20],"establish":[22],"their":[23],"global":[24,39,65],"dynamics.":[25],"Specifically,":[26],"a":[27,46],"matrix-theoretic":[28],"method":[29,48],"using":[30],"Perron":[32],"eigenvector":[33],"is":[34],"applied":[35],"prove":[37,63],"stability":[40,66],"disease-free":[43],"equilibrium,":[44],"while":[45],"graph-theoretic":[47],"based":[49],"on":[50],"Kirchhoff's":[51],"matrix":[52],"tree":[53],"theorem":[54],"two":[56,78],"new":[57,79],"combinatorial":[58],"identities":[59],"used":[61,83],"endemic":[69],"equilibrium.":[70],"Several":[71],"in":[74],"literature":[76],"cholera":[80],"demonstrate":[85],"applications":[87],"these":[89],"methods.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":29},{"year":2025,"cited_by_count":49},{"year":2024,"cited_by_count":42},{"year":2023,"cited_by_count":47},{"year":2022,"cited_by_count":49},{"year":2021,"cited_by_count":58},{"year":2020,"cited_by_count":57},{"year":2019,"cited_by_count":34},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":21},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":7}],"updated_date":"2026-08-12T07:12:00.856984","created_date":"2025-10-10T00:00:00"}