{"id":"https://openalex.org/W2306789923","doi":"https://doi.org/10.1007/s11424-015-3243-9","title":"Global stability for a heroin model with age-dependent susceptibility","display_name":"Global stability for a heroin model with age-dependent susceptibility","publication_year":2015,"publication_date":"2015-06-06","ids":{"openalex":"https://openalex.org/W2306789923","doi":"https://doi.org/10.1007/s11424-015-3243-9","mag":"2306789923"},"language":"en","primary_location":{"id":"doi:10.1007/s11424-015-3243-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-015-3243-9","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","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/A5046520540","display_name":"Bin Fang","orcid":"https://orcid.org/0000-0003-1955-6626"},"institutions":[{"id":"https://openalex.org/I4210104311","display_name":"Institute of Scientific and Technical Information of China","ror":"https://ror.org/01b2av652","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210104311","https://openalex.org/I4210120069","https://openalex.org/I4210127390"]},{"id":"https://openalex.org/I130750295","display_name":"Xinyang Normal University","ror":"https://ror.org/0190x2a66","country_code":"CN","type":"education","lineage":["https://openalex.org/I130750295"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bin Fang","raw_affiliation_strings":["Beijing Institute of Information and Control, Beijing, 100037, China","Department of Mathematics, Xinyang Normal University, Xinyang, 464000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Institute of Information and Control, Beijing, 100037, China","institution_ids":["https://openalex.org/I4210104311"]},{"raw_affiliation_string":"Department of Mathematics, Xinyang Normal University, Xinyang, 464000, China","institution_ids":["https://openalex.org/I130750295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100697759","display_name":"Xuezhi Li","orcid":"https://orcid.org/0009-0002-4972-6198"},"institutions":[{"id":"https://openalex.org/I130750295","display_name":"Xinyang Normal University","ror":"https://ror.org/0190x2a66","country_code":"CN","type":"education","lineage":["https://openalex.org/I130750295"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuezhi Li","raw_affiliation_strings":["Department of Mathematics, Xinyang Normal University, Xinyang, 464000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Xinyang Normal University, Xinyang, 464000, China","institution_ids":["https://openalex.org/I130750295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036215265","display_name":"Maia Martcheva","orcid":"https://orcid.org/0000-0001-8968-1663"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maia Martcheva","raw_affiliation_strings":["Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL, 32611\u20138105, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL, 32611\u20138105, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101482995","display_name":"Liming Cai","orcid":"https://orcid.org/0000-0002-2113-8821"},"institutions":[{"id":"https://openalex.org/I130750295","display_name":"Xinyang Normal University","ror":"https://ror.org/0190x2a66","country_code":"CN","type":"education","lineage":["https://openalex.org/I130750295"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liming Cai","raw_affiliation_strings":["Department of Mathematics, Xinyang Normal University, Xinyang, 464000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Xinyang Normal University, Xinyang, 464000, China","institution_ids":["https://openalex.org/I130750295"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5046520540"],"corresponding_institution_ids":["https://openalex.org/I130750295","https://openalex.org/I4210104311"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.0427,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.87956963,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"28","issue":"6","first_page":"1243","last_page":"1257"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10410","display_name":"COVID-19 epidemiological studies","score":0.9890999794006348,"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"}},{"id":"https://openalex.org/T11764","display_name":"Evolution and Genetic Dynamics","score":0.983299970626831,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7856826782226562},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.7674695253372192},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"Basic reproduction number","score":0.7156369090080261},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5892524719238281},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5580525398254395},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5578076839447021},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.530786395072937},{"id":"https://openalex.org/keywords/reproduction","display_name":"Reproduction","score":0.5006232261657715},{"id":"https://openalex.org/keywords/heroin-addiction","display_name":"Heroin addiction","score":0.47865307331085205},{"id":"https://openalex.org/keywords/heroin","display_name":"Heroin","score":0.4660645127296448},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.35360345244407654},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3257490396499634},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.28729191422462463},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23569267988204956},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.17190545797348022},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.14677608013153076},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12619352340698242},{"id":"https://openalex.org/keywords/drug","display_name":"Drug","score":0.10962510108947754},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.06548801064491272}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7856826782226562},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.7674695253372192},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.7156369090080261},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5892524719238281},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5580525398254395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5578076839447021},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.530786395072937},{"id":"https://openalex.org/C59659247","wikidata":"https://www.wikidata.org/wiki/Q11990","display_name":"Reproduction","level":2,"score":0.5006232261657715},{"id":"https://openalex.org/C2909052318","wikidata":"https://www.wikidata.org/wiki/Q1639178","display_name":"Heroin addiction","level":4,"score":0.47865307331085205},{"id":"https://openalex.org/C2778903686","wikidata":"https://www.wikidata.org/wiki/Q60168","display_name":"Heroin","level":3,"score":0.4660645127296448},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.35360345244407654},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3257490396499634},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.28729191422462463},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23569267988204956},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.17190545797348022},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.14677608013153076},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12619352340698242},{"id":"https://openalex.org/C2780035454","wikidata":"https://www.wikidata.org/wiki/Q8386","display_name":"Drug","level":2,"score":0.10962510108947754},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.06548801064491272},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C98274493","wikidata":"https://www.wikidata.org/wiki/Q128406","display_name":"Pharmacology","level":1,"score":0.0},{"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:10.1007/s11424-015-3243-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-015-3243-9","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","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":0.8399999737739563}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W228144990","https://openalex.org/W1511286968","https://openalex.org/W1895307243","https://openalex.org/W1963895250","https://openalex.org/W1966397236","https://openalex.org/W1972712963","https://openalex.org/W1993220987","https://openalex.org/W1996363933","https://openalex.org/W2011771253","https://openalex.org/W2016334322","https://openalex.org/W2023617216","https://openalex.org/W2043651266","https://openalex.org/W2060225663","https://openalex.org/W2079871064","https://openalex.org/W2084084346","https://openalex.org/W2091229236","https://openalex.org/W2102775287","https://openalex.org/W2110161208","https://openalex.org/W2120986881","https://openalex.org/W2144862516","https://openalex.org/W2149772822","https://openalex.org/W2159436611","https://openalex.org/W2161728228","https://openalex.org/W2236277094","https://openalex.org/W2315398832","https://openalex.org/W2480341355","https://openalex.org/W4388299012"],"related_works":["https://openalex.org/W2388257287","https://openalex.org/W2153734122","https://openalex.org/W2071231746","https://openalex.org/W2908688458","https://openalex.org/W2051622558","https://openalex.org/W2912506578","https://openalex.org/W2306789923","https://openalex.org/W2734649795","https://openalex.org/W2378841998","https://openalex.org/W2884265924"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2}],"updated_date":"2026-06-02T09:04:35.204637","created_date":"2025-10-10T00:00:00"}