{"id":"https://openalex.org/W2113105229","doi":"https://doi.org/10.1137/090757009","title":"On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics","display_name":"On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2113105229","doi":"https://doi.org/10.1137/090757009","mag":"2113105229","pmid":"https://pubmed.ncbi.nlm.nih.gov/21785515"},"language":"en","primary_location":{"id":"doi:10.1137/090757009","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090757009","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3140286","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085827512","display_name":"Hongyu Miao","orcid":"https://orcid.org/0000-0002-4131-3164"},"institutions":[{"id":"https://openalex.org/I5388228","display_name":"University of Rochester","ror":"https://ror.org/022kthw22","country_code":"US","type":"education","lineage":["https://openalex.org/I5388228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hongyu Miao","raw_affiliation_strings":["Department of Biostatistics and Computational Biology, University of Rochester School of Medicine and Dentistry, 601 Elmwood Avenue, Box 630, Rochester, New York 14642, USA","hongyu_miao@urmc.rochester.edu and hwu@bst.rochester.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Biostatistics and Computational Biology, University of Rochester School of Medicine and Dentistry, 601 Elmwood Avenue, Box 630, Rochester, New York 14642, USA","institution_ids":["https://openalex.org/I5388228"]},{"raw_affiliation_string":"hongyu_miao@urmc.rochester.edu and hwu@bst.rochester.edu#TAB#","institution_ids":["https://openalex.org/I5388228"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091665121","display_name":"Xiaohua Xia","orcid":"https://orcid.org/0000-0002-3413-4731"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaohua Xia","raw_affiliation_strings":["xxia@postino.up.ac.za#TAB#"],"affiliations":[{"raw_affiliation_string":"xxia@postino.up.ac.za#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058338534","display_name":"Alan S. Perelson","orcid":"https://orcid.org/0000-0002-2455-0002"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alan S. Perelson","raw_affiliation_strings":["asp@lanl.gov#TAB#"],"affiliations":[{"raw_affiliation_string":"asp@lanl.gov#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045155778","display_name":"Hulin Wu","orcid":"https://orcid.org/0000-0002-5809-5407"},"institutions":[{"id":"https://openalex.org/I5388228","display_name":"University of Rochester","ror":"https://ror.org/022kthw22","country_code":"US","type":"education","lineage":["https://openalex.org/I5388228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hulin Wu","raw_affiliation_strings":["University of Rochester"],"affiliations":[{"raw_affiliation_string":"University of Rochester","institution_ids":["https://openalex.org/I5388228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5085827512"],"corresponding_institution_ids":["https://openalex.org/I5388228"],"apc_list":null,"apc_paid":null,"fwci":24.8343,"has_fulltext":false,"cited_by_count":614,"citation_normalized_percentile":{"value":0.99737107,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"53","issue":"1","first_page":"3","last_page":"39"},"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":0.998199999332428,"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":0.998199999332428,"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":0.9936000108718872,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9900000095367432,"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/identifiability","display_name":"Identifiability","score":0.9592388868331909},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.9449247717857361},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6960654258728027},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.567726194858551},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5171817541122437},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4418134093284607},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36027848720550537},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.23538818955421448},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.12095066905021667},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08308044075965881},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07172468304634094}],"concepts":[{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.9592388868331909},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.9449247717857361},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6960654258728027},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.567726194858551},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5171817541122437},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4418134093284607},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36027848720550537},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.23538818955421448},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.12095066905021667},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08308044075965881},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07172468304634094},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/090757009","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090757009","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},{"id":"pmid:21785515","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21785515","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM review. Society for Industrial and Applied Mathematics","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:3140286","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3140286","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Rev Soc Ind Appl Math","raw_type":"Text"},{"id":"pmh:oai:repository.up.ac.za:2263/19604","is_oa":false,"landing_page_url":"http://hdl.handle.net/2263/19604","pdf_url":null,"source":{"id":"https://openalex.org/S4306401870","display_name":"UpSpace Institutional Repository (University of Pretoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I69552723","host_organization_name":"University of Pretoria","host_organization_lineage":["https://openalex.org/I69552723"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:pubmedcentral.nih.gov:3140286","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3140286","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Rev Soc Ind Appl Math","raw_type":"Text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being","score":0.8100000023841858}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":120,"referenced_works":["https://openalex.org/W12655809","https://openalex.org/W19125392","https://openalex.org/W103156936","https://openalex.org/W128790735","https://openalex.org/W193859048","https://openalex.org/W217529161","https://openalex.org/W576422698","https://openalex.org/W1479979375","https://openalex.org/W1486996222","https://openalex.org/W1503543307","https://openalex.org/W1514872062","https://openalex.org/W1522687244","https://openalex.org/W1542865006","https://openalex.org/W1549386224","https://openalex.org/W1549690076","https://openalex.org/W1574498833","https://openalex.org/W1575978816","https://openalex.org/W1581560749","https://openalex.org/W1584835303","https://openalex.org/W1589370794","https://openalex.org/W1598593415","https://openalex.org/W1600765471","https://openalex.org/W1601426486","https://openalex.org/W1887006513","https://openalex.org/W1909787060","https://openalex.org/W1965324089","https://openalex.org/W1967819897","https://openalex.org/W1967988563","https://openalex.org/W1968205521","https://openalex.org/W1968399352","https://openalex.org/W1973381652","https://openalex.org/W1978548185","https://openalex.org/W1980416356","https://openalex.org/W1980662086","https://openalex.org/W1989466762","https://openalex.org/W1994695086","https://openalex.org/W1997275627","https://openalex.org/W1997774242","https://openalex.org/W1998932188","https://openalex.org/W2001060170","https://openalex.org/W2003195392","https://openalex.org/W2003945397","https://openalex.org/W2004433740","https://openalex.org/W2006370534","https://openalex.org/W2008365461","https://openalex.org/W2009749531","https://openalex.org/W2011630381","https://openalex.org/W2014620040","https://openalex.org/W2018301734","https://openalex.org/W2019069710","https://openalex.org/W2020102996","https://openalex.org/W2027734689","https://openalex.org/W2029641002","https://openalex.org/W2029784397","https://openalex.org/W2030524855","https://openalex.org/W2031434350","https://openalex.org/W2033980528","https://openalex.org/W2036693704","https://openalex.org/W2040890176","https://openalex.org/W2042195578","https://openalex.org/W2042628558","https://openalex.org/W2043170493","https://openalex.org/W2044028647","https://openalex.org/W2044403736","https://openalex.org/W2048110904","https://openalex.org/W2048234055","https://openalex.org/W2051203581","https://openalex.org/W2051269276","https://openalex.org/W2054519334","https://openalex.org/W2055761669","https://openalex.org/W2058899256","https://openalex.org/W2064059889","https://openalex.org/W2067265199","https://openalex.org/W2067296217","https://openalex.org/W2071448055","https://openalex.org/W2072667966","https://openalex.org/W2072924064","https://openalex.org/W2074016482","https://openalex.org/W2074216670","https://openalex.org/W2074333823","https://openalex.org/W2080504923","https://openalex.org/W2081599914","https://openalex.org/W2082536486","https://openalex.org/W2085944542","https://openalex.org/W2094547604","https://openalex.org/W2097246026","https://openalex.org/W2098649922","https://openalex.org/W2099604946","https://openalex.org/W2100659437","https://openalex.org/W2102669993","https://openalex.org/W2105626102","https://openalex.org/W2108834847","https://openalex.org/W2109977701","https://openalex.org/W2116090803","https://openalex.org/W2121590359","https://openalex.org/W2126571583","https://openalex.org/W2128005489","https://openalex.org/W2128506325","https://openalex.org/W2128543792","https://openalex.org/W2136343012","https://openalex.org/W2136840897","https://openalex.org/W2138826235","https://openalex.org/W2140571318","https://openalex.org/W2140998418","https://openalex.org/W2144622325","https://openalex.org/W2150303830","https://openalex.org/W2170219825","https://openalex.org/W2171968193","https://openalex.org/W2312457402","https://openalex.org/W2332782972","https://openalex.org/W2333635821","https://openalex.org/W2480657587","https://openalex.org/W2483775066","https://openalex.org/W2611050160","https://openalex.org/W2612686320","https://openalex.org/W2797320655","https://openalex.org/W2887527214","https://openalex.org/W2987025408","https://openalex.org/W3160954918","https://openalex.org/W4253175466"],"related_works":["https://openalex.org/W2113105229","https://openalex.org/W2517973022","https://openalex.org/W4283316300","https://openalex.org/W1543121148","https://openalex.org/W3082668976","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4382202915","https://openalex.org/W3161724164"],"abstract_inverted_index":{"Ordinary":[0],"differential":[1],"equations":[2],"(ODE)":[3],"are":[4,83,124,141],"a":[5,16,31],"powerful":[6],"tool":[7,33],"for":[8,79,95],"modeling":[9,132],"dynamic":[10],"processes":[11],"with":[12],"wide":[13],"applications":[14],"in":[15,34,40,55,68,72,100,152],"variety":[17],"of":[18,135],"scientific":[19],"fields.":[20],"Over":[21],"the":[22,65,101],"last":[23],"2":[24],"decades,":[25,106],"ODEs":[26],"have":[27],"also":[28,125],"emerged":[29],"as":[30],"prevailing":[32],"various":[35],"biomedical":[36],"research":[37,123],"fields,":[38],"especially":[39],"infectious":[41],"disease":[42],"modeling.":[43],"In":[44,87],"practice,":[45],"it":[46],"is":[47,64],"important":[48],"and":[49,75,114,121,138],"necessary":[50],"to":[51,104,143,146],"determine":[52],"unknown":[53,70],"parameters":[54,71],"ODE":[56,73,81,97],"models":[57,74,82,98],"based":[58],"on":[59],"experimental":[60],"data.":[61],"Identifiability":[62],"analysis":[63,77,93,113,150],"first":[66],"step":[67],"determing":[69],"such":[76],"techniques":[78],"nonlinear":[80,96],"still":[84],"under":[85],"development.":[86],"this":[88],"article,":[89],"we":[90],"review":[91],"identifiability":[92,109,112,116,149],"methodologies":[94],"developed":[99],"past":[102],"one":[103],"two":[105],"including":[107],"structural":[108],"analysis,":[110],"practical":[111],"sensitivity-based":[115],"analysis.":[117],"Some":[118],"advanced":[119],"topics":[120],"ongoing":[122],"briefly":[126],"reviewed.":[127],"Finally,":[128],"some":[129],"examples":[130],"from":[131],"viral":[133],"dynamics":[134],"HIV,":[136],"influenza":[137],"hepatitis":[139],"viruses":[140],"given":[142],"illustrate":[144],"how":[145],"apply":[147],"these":[148],"methods":[151],"practice.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":11},{"year":2025,"cited_by_count":52},{"year":2024,"cited_by_count":59},{"year":2023,"cited_by_count":52},{"year":2022,"cited_by_count":66},{"year":2021,"cited_by_count":63},{"year":2020,"cited_by_count":57},{"year":2019,"cited_by_count":38},{"year":2018,"cited_by_count":50},{"year":2017,"cited_by_count":29},{"year":2016,"cited_by_count":36},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":26},{"year":2013,"cited_by_count":27},{"year":2012,"cited_by_count":14}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}