{"id":"https://openalex.org/W3169045385","doi":"https://doi.org/10.1155/2021/6612451","title":"A Virus Propagation Model and Optimal Control Strategy in the Point\u2010to\u2010Group Network to Information Security Investment","display_name":"A Virus Propagation Model and Optimal Control Strategy in the Point\u2010to\u2010Group Network to Information Security Investment","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3169045385","doi":"https://doi.org/10.1155/2021/6612451","mag":"3169045385"},"language":"en","primary_location":{"id":"doi:10.1155/2021/6612451","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6612451","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6612451.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/2021/6612451.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025160756","display_name":"Liping Feng","orcid":null},"institutions":[{"id":"https://openalex.org/I28992388","display_name":"Xinzhou Teachers University","ror":"https://ror.org/01175g155","country_code":"CN","type":"education","lineage":["https://openalex.org/I28992388"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liping Feng","raw_affiliation_strings":["Computer Science Department, Xinzhou Teachers University, Xinzhou, Shanxi 034000, China"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Xinzhou Teachers University, Xinzhou, Shanxi 034000, China","institution_ids":["https://openalex.org/I28992388"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075582280","display_name":"Ruifeng Han","orcid":"https://orcid.org/0000-0002-8256-4074"},"institutions":[{"id":"https://openalex.org/I28992388","display_name":"Xinzhou Teachers University","ror":"https://ror.org/01175g155","country_code":"CN","type":"education","lineage":["https://openalex.org/I28992388"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruifeng Han","raw_affiliation_strings":["Computer Science Department, Xinzhou Teachers University, Xinzhou, Shanxi 034000, China"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Xinzhou Teachers University, Xinzhou, Shanxi 034000, China","institution_ids":["https://openalex.org/I28992388"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100332078","display_name":"Hongbin Wang","orcid":"https://orcid.org/0000-0001-8559-5960"},"institutions":[{"id":"https://openalex.org/I28992388","display_name":"Xinzhou Teachers University","ror":"https://ror.org/01175g155","country_code":"CN","type":"education","lineage":["https://openalex.org/I28992388"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongbin Wang","raw_affiliation_strings":["Computer Science Department, Xinzhou Teachers University, Xinzhou, Shanxi 034000, China"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Xinzhou Teachers University, Xinzhou, Shanxi 034000, China","institution_ids":["https://openalex.org/I28992388"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059038276","display_name":"Qingshan Zhao","orcid":"https://orcid.org/0000-0002-3767-1102"},"institutions":[{"id":"https://openalex.org/I28992388","display_name":"Xinzhou Teachers University","ror":"https://ror.org/01175g155","country_code":"CN","type":"education","lineage":["https://openalex.org/I28992388"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qingshan Zhao","raw_affiliation_strings":["Computer Science Department, Xinzhou Teachers University, Xinzhou, Shanxi 034000, China"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Xinzhou Teachers University, Xinzhou, Shanxi 034000, China","institution_ids":["https://openalex.org/I28992388"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064771543","display_name":"FU Cheng-li","orcid":null},"institutions":[{"id":"https://openalex.org/I28992388","display_name":"Xinzhou Teachers University","ror":"https://ror.org/01175g155","country_code":"CN","type":"education","lineage":["https://openalex.org/I28992388"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chengli Fu","raw_affiliation_strings":["Computer Science Department, Xinzhou Teachers University, Xinzhou, Shanxi 034000, China"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Xinzhou Teachers University, Xinzhou, Shanxi 034000, China","institution_ids":["https://openalex.org/I28992388"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036591099","display_name":"Qi Han","orcid":"https://orcid.org/0000-0002-3264-9571"},"institutions":[{"id":"https://openalex.org/I168337820","display_name":"Chongqing University of Science and Technology","ror":"https://ror.org/03n3v6d52","country_code":"CN","type":"education","lineage":["https://openalex.org/I168337820"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qi Han","raw_affiliation_strings":["School of Intelligent Technology and Engineering, Chongqing University of Science &Technology, Chongqing 401331, China"],"affiliations":[{"raw_affiliation_string":"School of Intelligent Technology and Engineering, Chongqing University of Science &Technology, Chongqing 401331, China","institution_ids":["https://openalex.org/I168337820"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5036591099"],"corresponding_institution_ids":["https://openalex.org/I168337820"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.3201,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.59950284,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"2021","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10400","display_name":"Network Security and Intrusion Detection","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10400","display_name":"Network Security and Intrusion Detection","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6546880006790161},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5846577286720276},{"id":"https://openalex.org/keywords/computer-virus","display_name":"Computer virus","score":0.5551968812942505},{"id":"https://openalex.org/keywords/information-security","display_name":"Information security","score":0.5234750509262085},{"id":"https://openalex.org/keywords/pontryagins-minimum-principle","display_name":"Pontryagin's minimum principle","score":0.5149405598640442},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5028857588768005},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.46328917145729065},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45396339893341064},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.423051118850708},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29381096363067627},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.22001710534095764},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.13733068108558655},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11741891503334045}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6546880006790161},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5846577286720276},{"id":"https://openalex.org/C19407854","wikidata":"https://www.wikidata.org/wiki/Q485","display_name":"Computer virus","level":2,"score":0.5551968812942505},{"id":"https://openalex.org/C527648132","wikidata":"https://www.wikidata.org/wiki/Q189900","display_name":"Information security","level":2,"score":0.5234750509262085},{"id":"https://openalex.org/C141803461","wikidata":"https://www.wikidata.org/wiki/Q3491629","display_name":"Pontryagin's minimum principle","level":3,"score":0.5149405598640442},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5028857588768005},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.46328917145729065},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45396339893341064},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.423051118850708},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29381096363067627},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.22001710534095764},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.13733068108558655},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11741891503334045},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2021/6612451","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6612451","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6612451.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:6612451","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2021/6612451.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:672614bb42f54e509bec04d3a624b522","is_oa":true,"landing_page_url":"https://doaj.org/article/672614bb42f54e509bec04d3a624b522","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":"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 2021 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2021/6612451","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6612451","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6612451.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":[{"id":"https://metadata.un.org/sdg/3","score":0.7400000095367432,"display_name":"Good health and well-being"}],"awards":[{"id":"https://openalex.org/G1312266557","display_name":null,"funder_award_id":"KJQN201901537","funder_id":"https://openalex.org/F4320321884","funder_display_name":"Shanxi Scholarship Council of China"},{"id":"https://openalex.org/G2029860109","display_name":null,"funder_award_id":"2020-139","funder_id":"https://openalex.org/F4320324805","funder_display_name":"Chongqing Municipal Education Commission"},{"id":"https://openalex.org/G2238127691","display_name":null,"funder_award_id":"2020-139","funder_id":"https://openalex.org/F4320321884","funder_display_name":"Shanxi Scholarship Council of China"},{"id":"https://openalex.org/G3041674181","display_name":null,"funder_award_id":"19YJCZH047","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G5047028600","display_name":null,"funder_award_id":"KJQN201901","funder_id":"https://openalex.org/F4320324805","funder_display_name":"Chongqing Municipal Education Commission"},{"id":"https://openalex.org/G5329375900","display_name":null,"funder_award_id":"KJZD-K201901504","funder_id":"https://openalex.org/F4320324805","funder_display_name":"Chongqing Municipal Education Commission"},{"id":"https://openalex.org/G6560976173","display_name":null,"funder_award_id":"19YJCZH047","funder_id":"https://openalex.org/F4320324805","funder_display_name":"Chongqing Municipal Education Commission"},{"id":"https://openalex.org/G673143809","display_name":null,"funder_award_id":"KJQN201901537","funder_id":"https://openalex.org/F4320324805","funder_display_name":"Chongqing Municipal Education Commission"},{"id":"https://openalex.org/G7110126378","display_name":null,"funder_award_id":"KJZD-K201901504","funder_id":"https://openalex.org/F4320321884","funder_display_name":"Shanxi Scholarship Council of China"},{"id":"https://openalex.org/G7754760962","display_name":null,"funder_award_id":"2020KJ025","funder_id":"https://openalex.org/F4320321884","funder_display_name":"Shanxi Scholarship Council of China"}],"funders":[{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320321884","display_name":"Shanxi Scholarship Council of China","ror":"https://ror.org/04atp4p48"},{"id":"https://openalex.org/F4320324805","display_name":"Chongqing Municipal Education Commission","ror":"https://ror.org/031nm5713"},{"id":"https://openalex.org/F4320328124","display_name":"Xinzhou Teachers University","ror":"https://ror.org/01175g155"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3169045385.pdf","grobid_xml":"https://content.openalex.org/works/W3169045385.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1519581288","https://openalex.org/W1972096044","https://openalex.org/W1973288976","https://openalex.org/W1980421658","https://openalex.org/W1989312118","https://openalex.org/W2025801449","https://openalex.org/W2040360392","https://openalex.org/W2043729270","https://openalex.org/W2056075452","https://openalex.org/W2065509599","https://openalex.org/W2108050790","https://openalex.org/W2153692272","https://openalex.org/W2193023643","https://openalex.org/W2231018406","https://openalex.org/W2324540553","https://openalex.org/W2510253580","https://openalex.org/W2562909103","https://openalex.org/W2587683584","https://openalex.org/W2618406327","https://openalex.org/W2779767788","https://openalex.org/W2793251195","https://openalex.org/W2995444071","https://openalex.org/W3002700665","https://openalex.org/W3120064894","https://openalex.org/W4211202937","https://openalex.org/W4251267463","https://openalex.org/W6645410467","https://openalex.org/W6647661980"],"related_works":["https://openalex.org/W2962746246","https://openalex.org/W1967384683","https://openalex.org/W4285534277","https://openalex.org/W3031081244","https://openalex.org/W162218241","https://openalex.org/W4302321938","https://openalex.org/W4292923857","https://openalex.org/W3209004265","https://openalex.org/W1643670820","https://openalex.org/W15954510"],"abstract_inverted_index":{"Epidemiological":[0],"dynamics":[1],"is":[2,21,47,61,68],"a":[3,51,72],"vital":[4],"method":[5],"in":[6,30,41,57,109],"studying":[7],"the":[8,25,36,64,96],"spread":[9,55,108],"of":[10],"computer":[11,53],"network":[12,78],"viruses.":[13],"In":[14],"this":[15],"paper,":[16],"an":[17,43],"optimal":[18,44,65,85],"control":[19,45,66,75,86],"measure":[20,67],"proposed":[22],"based":[23],"on":[24],"SEIR":[26],"virus":[27,54,82,107],"propagation":[28],"model":[29,56],"point\u2010to\u2010group":[31,58,110],"information":[32,59,111],"networks.":[33],"First,":[34],"considering":[35],"need":[37],"for":[38,105],"antivirus":[39],"measures":[40,104],"reality,":[42],"problem":[46],"introduced,":[48],"and":[49,77,95],"then":[50],"controlled":[52],"networks":[60,112],"established.":[62],"Second,":[63],"formulated":[69],"by":[70,81,91],"making":[71],"tradeoff":[73],"between":[74],"cost":[76],"loss":[79],"caused":[80],"intrusion.":[83],"Third,":[84],"strategies":[87],"are":[88,113],"theoretically":[89],"investigated":[90],"Pontryagin\u2019s":[92],"maximum":[93],"principle":[94],"Hamiltonian":[97],"function.":[98],"Finally,":[99],"through":[100],"numerical":[101],"simulations,":[102],"effective":[103],"controlling":[106],"proposed.":[114]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}