{"id":"https://openalex.org/W2964801363","doi":"https://doi.org/10.3233/jcm-190028","title":"Mathematical modeling of hepatitis B infection with vaccination and optimal control interventions","display_name":"Mathematical modeling of hepatitis B infection with vaccination and optimal control interventions","publication_year":2019,"publication_date":"2019-08-06","ids":{"openalex":"https://openalex.org/W2964801363","doi":"https://doi.org/10.3233/jcm-190028","mag":"2964801363"},"language":"en","primary_location":{"id":"doi:10.3233/jcm-190028","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jcm-190028","pdf_url":null,"source":{"id":"https://openalex.org/S2765058733","display_name":"Journal of Computational Methods in Sciences and Engineering","issn_l":"1472-7978","issn":["1472-7978","1875-8983"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Methods in Sciences and Engineering","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/A5003720374","display_name":"Saif Ullah","orcid":"https://orcid.org/0000-0002-4338-6850"},"institutions":[{"id":"https://openalex.org/I36001604","display_name":"University of Peshawar","ror":"https://ror.org/02t2qwf81","country_code":"PK","type":"education","lineage":["https://openalex.org/I36001604"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saif Ullah","raw_affiliation_strings":["Department of Mathematics, University of Peshawar, Peshawar, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Peshawar, Peshawar, Pakistan","institution_ids":["https://openalex.org/I36001604"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057536424","display_name":"Muhammad Altaf Khan","orcid":"https://orcid.org/0000-0002-4483-7879"},"institutions":[{"id":"https://openalex.org/I3132053282","display_name":"City University of Science and Information Technology","ror":"https://ror.org/02jsdya97","country_code":"PK","type":"education","lineage":["https://openalex.org/I3132053282"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Altaf Khan","raw_affiliation_strings":["Department of Mathematics, City University of Science and Information Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Science and Information Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I3132053282"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007970705","display_name":"Muhammad Farooq","orcid":"https://orcid.org/0000-0002-0352-7401"},"institutions":[{"id":"https://openalex.org/I36001604","display_name":"University of Peshawar","ror":"https://ror.org/02t2qwf81","country_code":"PK","type":"education","lineage":["https://openalex.org/I36001604"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Farooq","raw_affiliation_strings":["Department of Mathematics, University of Peshawar, Peshawar, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Peshawar, Peshawar, Pakistan","institution_ids":["https://openalex.org/I36001604"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057536424"],"corresponding_institution_ids":["https://openalex.org/I3132053282"],"apc_list":null,"apc_paid":null,"fwci":0.6663,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.74169524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"20","issue":"1","first_page":"331","last_page":"349"},"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":0.9975000023841858,"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":0.9975000023841858,"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":0.996399998664856,"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/T10340","display_name":"Hepatitis B Virus Studies","score":0.9832000136375427,"subfield":{"id":"https://openalex.org/subfields/2713","display_name":"Epidemiology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/vaccination","display_name":"Vaccination","score":0.7764849662780762},{"id":"https://openalex.org/keywords/psychological-intervention","display_name":"Psychological intervention","score":0.6257085800170898},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.49963808059692383},{"id":"https://openalex.org/keywords/virology","display_name":"Virology","score":0.4312742352485657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3418382406234741},{"id":"https://openalex.org/keywords/nursing","display_name":"Nursing","score":0.05046460032463074}],"concepts":[{"id":"https://openalex.org/C22070199","wikidata":"https://www.wikidata.org/wiki/Q192995","display_name":"Vaccination","level":2,"score":0.7764849662780762},{"id":"https://openalex.org/C27415008","wikidata":"https://www.wikidata.org/wiki/Q7256382","display_name":"Psychological intervention","level":2,"score":0.6257085800170898},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.49963808059692383},{"id":"https://openalex.org/C159047783","wikidata":"https://www.wikidata.org/wiki/Q7215","display_name":"Virology","level":1,"score":0.4312742352485657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3418382406234741},{"id":"https://openalex.org/C159110408","wikidata":"https://www.wikidata.org/wiki/Q121176","display_name":"Nursing","level":1,"score":0.05046460032463074}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jcm-190028","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jcm-190028","pdf_url":null,"source":{"id":"https://openalex.org/S2765058733","display_name":"Journal of Computational Methods in Sciences and Engineering","issn_l":"1472-7978","issn":["1472-7978","1875-8983"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Methods in Sciences and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W231975775","https://openalex.org/W1531885435","https://openalex.org/W1975966394","https://openalex.org/W2008175699","https://openalex.org/W2010501535","https://openalex.org/W2042371484","https://openalex.org/W2044163391","https://openalex.org/W2071966334","https://openalex.org/W2083449041","https://openalex.org/W2104969243","https://openalex.org/W2112680994","https://openalex.org/W2125307802","https://openalex.org/W2152803686","https://openalex.org/W2157040936","https://openalex.org/W2738800615","https://openalex.org/W2747872722","https://openalex.org/W2762778406","https://openalex.org/W2787979548","https://openalex.org/W2794522234","https://openalex.org/W3150815371","https://openalex.org/W6652900655"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W3031052312","https://openalex.org/W4389568370","https://openalex.org/W3032375762","https://openalex.org/W1995515455","https://openalex.org/W2080531066","https://openalex.org/W3108674512","https://openalex.org/W1506200166","https://openalex.org/W1489783725","https://openalex.org/W2148612803"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,25,38,64,103,115],"formulate":[4],"a":[5,44],"mathematical":[6],"model":[7,28,42],"to":[8,81,122],"analyze":[9],"the":[10,17,27,41,52,83,89,105,110,117,125],"impact":[11],"of":[12,20,69,79,127],"hospitalization":[13],"and":[14,30,60,99,108],"vaccination":[15],"on":[16],"transmission":[18],"dynamics":[19],"hepatitis":[21,90],"B":[22,91],"infection.":[23,92],"Initially,":[24],"evaluate":[26],"equilibria":[29],"basic":[31,53],"reproduction":[32,54],"number.":[33],"Further,":[34],"using":[35,61,95],"Lyapunov":[36],"function":[37],"prove":[39],"that":[40,86],"has":[43],"globally":[45],"asymptotically":[46],"stable":[47],"infection":[48],"free":[49],"equilibrium":[50],"when":[51,72],"number":[55],"is":[56],"less":[57],"than":[58],"1,":[59],"geometric":[62],"approach":[63],"show":[65],"global":[66],"asymptotic":[67],"stability":[68],"endemic":[70],"equilibrium,":[71],"\u211b0>":[73],"1.":[74],"We":[75],"perform":[76,116],"sensitivity":[77],"analysis":[78],"\u211b0":[80],"identify":[82],"dominant":[84],"parameters":[85],"seriously":[87],"affect":[88],"After":[93],"that,":[94],"optimal":[96],"control":[97,106,128],"theory":[98],"Pontryagin\u2019s":[100],"maximum":[101],"principle,":[102],"develop":[104],"problem":[107],"illustrate":[109],"necessary":[111],"optimality":[112],"conditions.":[113],"Finally,":[114],"numerical":[118],"simulations":[119],"in":[120],"order":[121],"point":[123],"out":[124],"effectiveness":[126],"interventions.":[129]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}
