{"id":"https://openalex.org/W2913393012","doi":"https://doi.org/10.1155/2019/3859815","title":"State-Dependent Pulse Vaccination and Therapeutic Strategy in an SI Epidemic Model with Nonlinear Incidence Rate","display_name":"State-Dependent Pulse Vaccination and Therapeutic Strategy in an SI Epidemic Model with Nonlinear Incidence Rate","publication_year":2019,"publication_date":"2019-02-06","ids":{"openalex":"https://openalex.org/W2913393012","doi":"https://doi.org/10.1155/2019/3859815","mag":"2913393012","pmid":"https://pubmed.ncbi.nlm.nih.gov/30881479"},"language":"en","primary_location":{"id":"doi:10.1155/2019/3859815","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/3859815","pdf_url":"https://downloads.hindawi.com/journals/cmmm/2019/3859815.pdf","source":{"id":"https://openalex.org/S36980176","display_name":"Computational and Mathematical Methods in Medicine","issn_l":"1748-670X","issn":["1748-670X","1748-6718"],"is_oa":false,"is_in_doaj":false,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Mathematical Methods in Medicine","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/cmmm/2019/3859815.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084572159","display_name":"Kaiyuan Liu","orcid":"https://orcid.org/0000-0002-2127-0267"},"institutions":[{"id":"https://openalex.org/I41147446","display_name":"Anshan Normal University","ror":"https://ror.org/04s5wwh39","country_code":"CN","type":"education","lineage":["https://openalex.org/I41147446"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kaiyuan Liu","raw_affiliation_strings":["College of Mathematics and Information Science, Anshan Normal University, Anshan 114016, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Anshan Normal University, Anshan 114016, China","institution_ids":["https://openalex.org/I41147446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082010998","display_name":"Tongqian Zhang","orcid":"https://orcid.org/0000-0001-9603-3867"},"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":"Tongqian Zhang","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"],"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"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102936938","display_name":"Lansun Chen","orcid":"https://orcid.org/0000-0003-3651-9181"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lansun Chen","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"],"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5082010998"],"corresponding_institution_ids":["https://openalex.org/I80143920"],"apc_list":{"value":2100,"currency":"USD","value_usd":2100},"apc_paid":{"value":2100,"currency":"USD","value_usd":2100},"fwci":3.5522,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.92066312,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"2019","issue":null,"first_page":"1","last_page":"10"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10288","display_name":"Fractional Differential Equations Solutions","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":0.9907000064849854,"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/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.8274762630462646},{"id":"https://openalex.org/keywords/pulse","display_name":"Pulse (music)","score":0.6009078621864319},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5748500227928162},{"id":"https://openalex.org/keywords/impulse","display_name":"Impulse (physics)","score":0.5461089611053467},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.543952226638794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5260498523712158},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5008931159973145},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5001571178436279},{"id":"https://openalex.org/keywords/impulse-response","display_name":"Impulse response","score":0.4242752492427826},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3262050151824951},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3196457028388977},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30746138095855713},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2902025580406189},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2723085284233093},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2503446340560913},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.14760050177574158},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.08328527212142944},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07805564999580383}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.8274762630462646},{"id":"https://openalex.org/C2780167933","wikidata":"https://www.wikidata.org/wiki/Q1550652","display_name":"Pulse (music)","level":3,"score":0.6009078621864319},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5748500227928162},{"id":"https://openalex.org/C70836080","wikidata":"https://www.wikidata.org/wiki/Q837940","display_name":"Impulse (physics)","level":2,"score":0.5461089611053467},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.543952226638794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5260498523712158},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5008931159973145},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5001571178436279},{"id":"https://openalex.org/C72279823","wikidata":"https://www.wikidata.org/wiki/Q1139726","display_name":"Impulse response","level":2,"score":0.4242752492427826},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3262050151824951},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3196457028388977},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30746138095855713},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2902025580406189},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2723085284233093},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2503446340560913},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.14760050177574158},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.08328527212142944},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07805564999580383},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.0}],"mesh":[{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003140","descriptor_name":"Communicable Disease Control","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003140","descriptor_name":"Communicable Disease Control","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003140","descriptor_name":"Communicable Disease Control","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003141","descriptor_name":"Communicable Diseases","qualifier_ui":"Q000453","qualifier_name":"epidemiology","is_major_topic":false},{"descriptor_ui":"D003141","descriptor_name":"Communicable Diseases","qualifier_ui":"Q000453","qualifier_name":"epidemiology","is_major_topic":false},{"descriptor_ui":"D003141","descriptor_name":"Communicable Diseases","qualifier_ui":"Q000453","qualifier_name":"epidemiology","is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004196","descriptor_name":"Disease Outbreaks","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004196","descriptor_name":"Disease Outbreaks","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004196","descriptor_name":"Disease Outbreaks","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007115","descriptor_name":"Immunization Schedule","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007115","descriptor_name":"Immunization Schedule","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007115","descriptor_name":"Immunization Schedule","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D014611","descriptor_name":"Vaccination","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D014611","descriptor_name":"Vaccination","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D014611","descriptor_name":"Vaccination","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D015994","descriptor_name":"Incidence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015994","descriptor_name":"Incidence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015994","descriptor_name":"Incidence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017589","descriptor_name":"Immunization Programs","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017589","descriptor_name":"Immunization Programs","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017589","descriptor_name":"Immunization Programs","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D055552","descriptor_name":"Infectious Disease Medicine","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D055552","descriptor_name":"Infectious Disease Medicine","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D055552","descriptor_name":"Infectious Disease Medicine","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D058872","descriptor_name":"Epidemics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D058872","descriptor_name":"Epidemics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D058872","descriptor_name":"Epidemics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":5,"locations":[{"id":"doi:10.1155/2019/3859815","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/3859815","pdf_url":"https://downloads.hindawi.com/journals/cmmm/2019/3859815.pdf","source":{"id":"https://openalex.org/S36980176","display_name":"Computational and Mathematical Methods in Medicine","issn_l":"1748-670X","issn":["1748-670X","1748-6718"],"is_oa":false,"is_in_doaj":false,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Mathematical Methods in Medicine","raw_type":"journal-article"},{"id":"pmid:30881479","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30881479","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":"Computational and mathematical methods in medicine","raw_type":null},{"id":"pmh:oai:doaj.org/article:17dd07a55722499288368313fb1b440d","is_oa":true,"landing_page_url":"https://doaj.org/article/17dd07a55722499288368313fb1b440d","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":"Computational and Mathematical Methods in Medicine, Vol 2019 (2019)","raw_type":"article"},{"id":"pmh:oai:europepmc.org:5404342","is_oa":true,"landing_page_url":"http://europepmc.org/pmc/articles/PMC6381564","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:6381564","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6381564","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Comput Math Methods Med","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1155/2019/3859815","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/3859815","pdf_url":"https://downloads.hindawi.com/journals/cmmm/2019/3859815.pdf","source":{"id":"https://openalex.org/S36980176","display_name":"Computational and Mathematical Methods in Medicine","issn_l":"1748-670X","issn":["1748-670X","1748-6718"],"is_oa":false,"is_in_doaj":false,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Mathematical Methods in Medicine","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Good health and well-being","score":0.8700000047683716,"id":"https://metadata.un.org/sdg/3"}],"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/G3214160367","display_name":null,"funder_award_id":"No. 11","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/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/G4656895506","display_name":null,"funder_award_id":"11671346","funder_id":"https://openalex.org/F4320322522","funder_display_name":"Shandong University of Science and Technology"},{"id":"https://openalex.org/G5167091242","display_name":null,"funder_award_id":"No. 1","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"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/G6130374233","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/G6902845470","display_name":null,"funder_award_id":"61751317","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/G7608752429","display_name":null,"funder_award_id":"Talent","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7830984251","display_name":null,"funder_award_id":"11671346","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8645068773","display_name":null,"funder_award_id":"61751317","funder_id":"https://openalex.org/F4320322522","funder_display_name":"Shandong University of Science and Technology"},{"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"}],"funders":[{"id":"https://openalex.org/F4320311026","display_name":"Shandong University","ror":"https://ror.org/0207yh398"},{"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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2913393012.pdf","grobid_xml":"https://content.openalex.org/works/W2913393012.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W572972466","https://openalex.org/W1878952130","https://openalex.org/W1981858768","https://openalex.org/W1983504681","https://openalex.org/W1984343531","https://openalex.org/W1984955994","https://openalex.org/W2021925903","https://openalex.org/W2022434170","https://openalex.org/W2030167963","https://openalex.org/W2042391826","https://openalex.org/W2053523645","https://openalex.org/W2053786065","https://openalex.org/W2074733010","https://openalex.org/W2075489080","https://openalex.org/W2076220071","https://openalex.org/W2083824931","https://openalex.org/W2087836556","https://openalex.org/W2107835392","https://openalex.org/W2144301074","https://openalex.org/W2148301044","https://openalex.org/W2152721342","https://openalex.org/W2199017660","https://openalex.org/W2200387372","https://openalex.org/W2216045595","https://openalex.org/W2282405828","https://openalex.org/W2307125864","https://openalex.org/W2344841815","https://openalex.org/W2610570754","https://openalex.org/W2626892378","https://openalex.org/W2725765108","https://openalex.org/W2743084399","https://openalex.org/W2748666568","https://openalex.org/W2783621192","https://openalex.org/W2783808903","https://openalex.org/W2790149985","https://openalex.org/W2792021312","https://openalex.org/W2793347221","https://openalex.org/W2794171901","https://openalex.org/W2798173114","https://openalex.org/W2799693713","https://openalex.org/W2884269718","https://openalex.org/W2884539436","https://openalex.org/W2885315384","https://openalex.org/W2889417563","https://openalex.org/W2891763094","https://openalex.org/W2892037363","https://openalex.org/W3021557197"],"related_works":["https://openalex.org/W2363992932","https://openalex.org/W2910725637","https://openalex.org/W2043723919","https://openalex.org/W2066340280","https://openalex.org/W1593713154","https://openalex.org/W2158263287","https://openalex.org/W2013210442","https://openalex.org/W2051697746","https://openalex.org/W2272518678","https://openalex.org/W2140267235"],"abstract_inverted_index":{"In":[0],"this":[1,25],"paper,":[2],"the":[3,13,16,38,41,46,53,58,61,65,73,80,93,96,123],"state-dependent":[4],"pulse":[5,19,54,74],"vaccination":[6],"and":[7,79,88,101],"therapeutic":[8],"strategy":[9],"are":[10,118],"considered":[11],"in":[12],"control":[14,94],"of":[15,48,60],"disease.":[17],"A":[18],"system":[20,39,75,81],"is":[21,67],"built":[22],"to":[23,121],"model":[24],"process":[26],"based":[27],"on":[28],"an":[29,103],"SI":[30],"ordinary":[31],"differential":[32],"equation":[33],"model.":[34],"At":[35],"first,":[36],"for":[37,52],"neglecting":[40],"impulse":[42],"effect,":[43],"we":[44],"give":[45],"classification":[47],"singular":[49],"points.":[50],"Then":[51],"system,":[55,64],"by":[56,89,115],"using":[57],"theory":[59],"semicontinuous":[62],"dynamic":[63],"dynamics":[66,78],"analyzed.":[68],"Our":[69],"analysis":[70],"shows":[71],"that":[72],"exhibits":[76],"rich":[77],"has":[82],"a":[83],"unique":[84],"order-1":[85,97,107],"homoclinic":[86,98],"cycle,":[87],"choosing":[90],"<i>p</i>":[91,111],"as":[92],"parameter,":[95],"cycle":[99],"disappears":[100],"bifurcates":[102],"orbitally":[104],"asymptotical":[105],"stable":[106],"periodic":[108],"solution":[109],"when":[110],"changes.":[112],"Numerical":[113],"simulations":[114],"maple":[116],"18":[117],"carried":[119],"out":[120],"illustrate":[122],"theoretical":[124],"results.":[125]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":9}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
