{"id":"https://openalex.org/W2767477371","doi":"https://doi.org/10.1155/2017/4861391","title":"Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis","display_name":"Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2767477371","doi":"https://doi.org/10.1155/2017/4861391","mag":"2767477371"},"language":"en","primary_location":{"id":"doi:10.1155/2017/4861391","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/4861391","pdf_url":"http://downloads.hindawi.com/journals/complexity/2017/4861391.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":"http://downloads.hindawi.com/journals/complexity/2017/4861391.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090076014","display_name":"Haokun Qi","orcid":"https://orcid.org/0000-0001-5931-1776"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haokun Qi","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102841238","display_name":"Lidan Liu","orcid":"https://orcid.org/0009-0004-1877-2436"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lidan Liu","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019874854","display_name":"Xinzhu Meng","orcid":"https://orcid.org/0000-0002-6553-9686"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xinzhu Meng","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China"],"raw_orcid":"https://orcid.org/0000-0002-6553-9686","affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019874854"],"corresponding_institution_ids":["https://openalex.org/I80143920"],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":{"value":2550,"currency":"USD","value_usd":2550},"fwci":11.4595,"has_fulltext":true,"cited_by_count":64,"citation_normalized_percentile":{"value":0.98807101,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"2017","issue":null,"first_page":"1","last_page":"14"},"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":1.0,"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":1.0,"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":0.9965999722480774,"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/T10410","display_name":"COVID-19 epidemiological studies","score":0.9940999746322632,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.8026489019393921},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.678620457649231},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6330419182777405},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5554149746894836},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5449172854423523},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5349116921424866},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5314556360244751},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.42247089743614197},{"id":"https://openalex.org/keywords/extinction","display_name":"Extinction (optical mineralogy)","score":0.4198110103607178},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3304007649421692},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.14267119765281677},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11418017745018005},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06658220291137695}],"concepts":[{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.8026489019393921},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.678620457649231},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6330419182777405},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5554149746894836},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5449172854423523},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5349116921424866},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5314556360244751},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.42247089743614197},{"id":"https://openalex.org/C101991246","wikidata":"https://www.wikidata.org/wiki/Q5422078","display_name":"Extinction (optical mineralogy)","level":2,"score":0.4198110103607178},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3304007649421692},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.14267119765281677},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11418017745018005},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06658220291137695},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2017/4861391","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/4861391","pdf_url":"http://downloads.hindawi.com/journals/complexity/2017/4861391.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:4861391","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2017/4861391.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:cc369a7d55754f7dad96772268dca6c0","is_oa":true,"landing_page_url":"https://doaj.org/article/cc369a7d55754f7dad96772268dca6c0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2017 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2017/4861391","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/4861391","pdf_url":"http://downloads.hindawi.com/journals/complexity/2017/4861391.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":[{"score":0.8700000047683716,"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3"}],"awards":[{"id":"https://openalex.org/G2313466449","display_name":null,"funder_award_id":"2014TDJH102","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G2440385044","display_name":null,"funder_award_id":"ZR2015AQ001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4258052625","display_name":null,"funder_award_id":"ZR2015AQ001","funder_id":"https://openalex.org/F4320322522","funder_display_name":"Shandong University of Science and Technology"},{"id":"https://openalex.org/G5501176208","display_name":"\u57fa\u4e8e\u5c3a\u5ea6\u9009\u62e9\u6027\u6536\u83b7\u7684\u6e14\u4e1a\u8d44\u6e90\u7684\u7ed3\u6784\u8fdb\u5316\u53ca\u52a8\u529b\u5b66\u7814\u7a76","funder_award_id":"11371230","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7108638857","display_name":null,"funder_award_id":"2014TDJH102","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7712711274","display_name":null,"funder_award_id":"11371230","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G7747215673","display_name":null,"funder_award_id":"ZR2015AQ001","funder_id":"https://openalex.org/F4320338074","funder_display_name":"Government of Shandong Province"},{"id":"https://openalex.org/G7904745116","display_name":null,"funder_award_id":"2014TDJH102","funder_id":"https://openalex.org/F4320338074","funder_display_name":"Government of Shandong Province"},{"id":"https://openalex.org/G8714477604","display_name":null,"funder_award_id":"ZR2015AQ001","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G879360056","display_name":null,"funder_award_id":"2014TDJH102","funder_id":"https://openalex.org/F4320322522","funder_display_name":"Shandong University of Science and Technology"},{"id":"https://openalex.org/G8900774048","display_name":null,"funder_award_id":"11371230","funder_id":"https://openalex.org/F4320338074","funder_display_name":"Government of Shandong Province"},{"id":"https://openalex.org/G8963529913","display_name":null,"funder_award_id":"11371230","funder_id":"https://openalex.org/F4320322522","funder_display_name":"Shandong University of Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322522","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320338074","display_name":"Government of Shandong Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2767477371.pdf","grobid_xml":"https://content.openalex.org/works/W2767477371.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1966106405","https://openalex.org/W1969134016","https://openalex.org/W1969178891","https://openalex.org/W1970495714","https://openalex.org/W1972079349","https://openalex.org/W1984546358","https://openalex.org/W1990179652","https://openalex.org/W1995156941","https://openalex.org/W1995180626","https://openalex.org/W2000978918","https://openalex.org/W2015897674","https://openalex.org/W2018296903","https://openalex.org/W2043300220","https://openalex.org/W2071526905","https://openalex.org/W2074733010","https://openalex.org/W2081182561","https://openalex.org/W2083824931","https://openalex.org/W2084810114","https://openalex.org/W2095406041","https://openalex.org/W2110610296","https://openalex.org/W2148301044","https://openalex.org/W2189910507","https://openalex.org/W2200387372","https://openalex.org/W2216045595","https://openalex.org/W2309143556","https://openalex.org/W2323936621","https://openalex.org/W2415278744","https://openalex.org/W2415858019","https://openalex.org/W2514658470","https://openalex.org/W2530404738","https://openalex.org/W2565828960","https://openalex.org/W2573759052","https://openalex.org/W2609294964","https://openalex.org/W2626892378","https://openalex.org/W2652668669","https://openalex.org/W2725765108","https://openalex.org/W2743084399","https://openalex.org/W2759246731","https://openalex.org/W2759660148","https://openalex.org/W2964132972"],"related_works":["https://openalex.org/W2147581087","https://openalex.org/W1973691824","https://openalex.org/W2587085640","https://openalex.org/W4386071021","https://openalex.org/W2054394682","https://openalex.org/W2291447000","https://openalex.org/W3003614869","https://openalex.org/W3195354540","https://openalex.org/W171914860","https://openalex.org/W4249297485"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,42,45,51,57],"dynamics":[3],"of":[4,41,50,59],"a":[5],"nonautonomous":[6,60],"stochastic":[7,22,61],"SIS":[8],"epidemic":[9,17],"model":[10],"with":[11],"nonlinear":[12],"incidence":[13],"rate":[14],"and":[15,25],"double":[16],"hypothesis.":[18],"By":[19],"constructing":[20],"suitable":[21],"Lyapunov":[23],"functions":[24],"using":[26,56],"Has\u2019minskii":[27],"theory,":[28],"we":[29],"prove":[30],"that":[31],"there":[32],"exists":[33],"at":[34],"least":[35],"one":[36],"nontrivial":[37],"positive":[38],"periodic":[39],"solution":[40],"system.":[43],"Moreover,":[44],"sufficient":[46],"conditions":[47],"for":[48],"extinction":[49],"disease":[52],"are":[53,67],"obtained":[54],"by":[55],"theory":[58],"differential":[62],"equations.":[63],"Finally,":[64],"numerical":[65],"simulations":[66],"utilized":[68],"to":[69],"illustrate":[70],"our":[71],"theoretical":[72],"analysis.":[73]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":29},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
