{"id":"https://openalex.org/W3028252730","doi":"https://doi.org/10.1155/2020/8268950","title":"Analysis of a Diffusive Heroin Epidemic Model in a Heterogeneous Environment","display_name":"Analysis of a Diffusive Heroin Epidemic Model in a Heterogeneous Environment","publication_year":2020,"publication_date":"2020-05-20","ids":{"openalex":"https://openalex.org/W3028252730","doi":"https://doi.org/10.1155/2020/8268950","mag":"3028252730"},"language":"lv","primary_location":{"id":"doi:10.1155/2020/8268950","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/8268950","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/8268950.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2020/8268950.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056132441","display_name":"Jinliang Wang","orcid":"https://orcid.org/0000-0002-9646-2765"},"institutions":[{"id":"https://openalex.org/I55022517","display_name":"Heilongjiang University","ror":"https://ror.org/04zyhq975","country_code":"CN","type":"education","lineage":["https://openalex.org/I55022517"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinliang Wang","raw_affiliation_strings":["School of Mathematical Science, Heilongjiang University, Harbin 150080, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Heilongjiang University, Harbin 150080, China","institution_ids":["https://openalex.org/I55022517"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063575002","display_name":"Hongquan Sun","orcid":"https://orcid.org/0000-0002-3960-3568"},"institutions":[{"id":"https://openalex.org/I134626604","display_name":"Jiujiang University","ror":"https://ror.org/0066vpg85","country_code":"CN","type":"education","lineage":["https://openalex.org/I134626604"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongquan Sun","raw_affiliation_strings":["School of Science, Jiujiang University, Jiujiang 332005, China"],"affiliations":[{"raw_affiliation_string":"School of Science, Jiujiang University, Jiujiang 332005, China","institution_ids":["https://openalex.org/I134626604"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063575002"],"corresponding_institution_ids":["https://openalex.org/I134626604"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.7212,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.74203623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"12"},"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":0.9995999932289124,"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":0.9995999932289124,"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":0.9932000041007996,"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":0.9890000224113464,"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/algorithm","display_name":"Algorithm","score":0.5674266219139099},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3944961428642273}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5674266219139099},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3944961428642273}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2020/8268950","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/8268950","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/8268950.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:8268950","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2020/8268950.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:99d37999c8154c5fa552b8d10ec0b33f","is_oa":true,"landing_page_url":"https://doaj.org/article/99d37999c8154c5fa552b8d10ec0b33f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"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":"Complexity, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/8268950","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/8268950","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/8268950.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3","score":0.8399999737739563}],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2476221792","display_name":null,"funder_award_id":"Heilongjiang","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2554158904","display_name":null,"funder_award_id":"GJJ190923","funder_id":"https://openalex.org/F4320325626","funder_display_name":"Education Department of Jiangxi Province"},{"id":"https://openalex.org/G3274520935","display_name":null,"funder_award_id":"2018002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3848755737","display_name":null,"funder_award_id":"LC2018002","funder_id":"https://openalex.org/F4320323085","funder_display_name":"Natural Science Foundation of Heilongjiang Province"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4139225467","display_name":null,"funder_award_id":"C2018002","funder_id":"https://openalex.org/F4320323085","funder_display_name":"Natural Science Foundation of Heilongjiang Province"},{"id":"https://openalex.org/G5860893155","display_name":null,"funder_award_id":"LH2019A021","funder_id":"https://openalex.org/F4320323085","funder_display_name":"Natural Science Foundation of Heilongjiang Province"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6289341725","display_name":null,"funder_award_id":"11871179","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7346218018","display_name":null,"funder_award_id":"11871","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7487091920","display_name":null,"funder_award_id":"GJJ190923","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7752304157","display_name":null,"funder_award_id":"11871179","funder_id":"https://openalex.org/F4320323085","funder_display_name":"Natural Science Foundation of Heilongjiang Province"},{"id":"https://openalex.org/G8114210943","display_name":null,"funder_award_id":"LC2018002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8976936471","display_name":null,"funder_award_id":"GJJ190923","funder_id":"https://openalex.org/F4320323085","funder_display_name":"Natural Science Foundation of Heilongjiang Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323085","display_name":"Natural Science Foundation of Heilongjiang Province","ror":null},{"id":"https://openalex.org/F4320325626","display_name":"Education Department of Jiangxi Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3028252730.pdf","grobid_xml":"https://content.openalex.org/works/W3028252730.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W217894125","https://openalex.org/W1622308394","https://openalex.org/W1964385385","https://openalex.org/W1976180149","https://openalex.org/W1978518692","https://openalex.org/W1996363933","https://openalex.org/W2001801852","https://openalex.org/W2016334322","https://openalex.org/W2043651266","https://openalex.org/W2046573764","https://openalex.org/W2046985721","https://openalex.org/W2047926127","https://openalex.org/W2067241000","https://openalex.org/W2072573489","https://openalex.org/W2072867280","https://openalex.org/W2102775287","https://openalex.org/W2120986881","https://openalex.org/W2235655169","https://openalex.org/W2324618167","https://openalex.org/W2494123768","https://openalex.org/W2562091157","https://openalex.org/W2741909209","https://openalex.org/W2743044718","https://openalex.org/W2782333862","https://openalex.org/W2782533806","https://openalex.org/W2897122385","https://openalex.org/W2903438637","https://openalex.org/W2909752832","https://openalex.org/W2912464825","https://openalex.org/W2964680114","https://openalex.org/W2972118775","https://openalex.org/W2973391458","https://openalex.org/W2994745434","https://openalex.org/W2999690744","https://openalex.org/W3010952028","https://openalex.org/W3099348273","https://openalex.org/W3104961365"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829"],"abstract_inverted_index":{"This":[0],"paper":[1,17],"is":[2,18,38,57],"concerned":[3],"with":[4],"a":[5,10,63],"reaction-diffusion":[6],"heroin":[7,45,55,115],"model":[8],"in":[9],"bound":[11],"domain.":[12],"The":[13],"objective":[14],"of":[15,75,82,114],"this":[16],"to":[19,100],"explore":[20],"the":[21,72,101,104,112],"threshold":[22,26],"dynamics":[23],"based":[24],"on":[25,110],"parameter":[27],"and":[28,36,60,79],"basic":[29],"reproduction":[30],"number":[31],"(BRN)":[32],"<mml:math":[33,42,52,76],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[34,43,53,77],"id=\"M1\"><mml:msub><mml:mrow><mml:mi>\u211c</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>,":[35],"it":[37],"proved":[39],"that":[40,71,98],"if":[41,51],"id=\"M2\"><mml:msub><mml:mrow><mml:mi>\u211c</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>&lt;</mml:mo><mml:mn>1</mml:mn></mml:math>,":[44],"spread":[46,56],"will":[47],"be":[48],"extinct,":[49],"while":[50],"id=\"M3\"><mml:msub><mml:mrow><mml:mi>\u211c</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo><mml:mn>1</mml:mn></mml:math>,":[54],"uniformly":[58],"persistent":[59],"there":[61],"exists":[62],"positive":[64,84,92],"heroin-spread":[65],"steady":[66,85],"state.":[67],"We":[68],"also":[69],"obtain":[70],"explicit":[73],"formula":[74],"id=\"M4\"><mml:msub><mml:mrow><mml:mi>\u211c</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>":[78],"global":[80],"attractiveness":[81],"constant":[83],"state":[86],"(PSS)":[87],"when":[88],"all":[89],"parameters":[90],"are":[91],"constants.":[93],"Our":[94],"simulation":[95],"results":[96],"reveal":[97],"compared":[99],"homogeneous":[102],"setting,":[103],"spatial":[105],"heterogeneity":[106],"has":[107],"essential":[108],"impacts":[109],"increasing":[111],"risk":[113],"spread.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}