{"id":"https://openalex.org/W4407980148","doi":"https://doi.org/10.1155/ijmm/3238188","title":"Mathematical Simulation of Optimal Control Measures to Avoid Chickenpox Infection","display_name":"Mathematical Simulation of Optimal Control Measures to Avoid Chickenpox Infection","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4407980148","doi":"https://doi.org/10.1155/ijmm/3238188"},"language":"en","primary_location":{"id":"doi:10.1155/ijmm/3238188","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmm/3238188","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/3238188","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/3238188","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047373638","display_name":"Nada A. Almuallem","orcid":"https://orcid.org/0000-0001-7714-0173"},"institutions":[{"id":"https://openalex.org/I4210099699","display_name":"University of Jeddah","ror":"https://ror.org/015ya8798","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210099699"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Nada A. Almuallem","raw_affiliation_strings":["Department of Mathematics and Statistics ,  Faculty of Science ,  University of Jeddah , P.O. Box 80327,  Jeddah ,  Saudi Arabia , uj.edu.sa"],"raw_orcid":"https://orcid.org/0000-0001-7714-0173","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics ,  Faculty of Science ,  University of Jeddah , P.O. Box 80327,  Jeddah ,  Saudi Arabia , uj.edu.sa","institution_ids":["https://openalex.org/I4210099699"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082512122","display_name":"Hegagi Mohamed Ali","orcid":"https://orcid.org/0000-0003-0159-6726"},"institutions":[{"id":"https://openalex.org/I4210136004","display_name":"University of Bisha","ror":"https://ror.org/040548g92","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210136004"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Hegagi Mohamed Ali","raw_affiliation_strings":["Department of Mathematics ,  College of Science ,  University of Bisha , P.O. Box 551,  Bisha ,  61922 ,  Saudi Arabia , ub.edu.sa"],"raw_orcid":"https://orcid.org/0000-0003-0159-6726","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  College of Science ,  University of Bisha , P.O. Box 551,  Bisha ,  61922 ,  Saudi Arabia , ub.edu.sa","institution_ids":["https://openalex.org/I4210136004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017277498","display_name":"Essam M. Elsaid","orcid":"https://orcid.org/0000-0003-4557-473X"},"institutions":[{"id":"https://openalex.org/I4210136004","display_name":"University of Bisha","ror":"https://ror.org/040548g92","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210136004"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Essam M. Elsaid","raw_affiliation_strings":["Department of Mathematics ,  College of Science ,  University of Bisha , P.O. Box 551,  Bisha ,  61922 ,  Saudi Arabia , ub.edu.sa"],"raw_orcid":"https://orcid.org/0000-0003-4557-473X","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  College of Science ,  University of Bisha , P.O. Box 551,  Bisha ,  61922 ,  Saudi Arabia , ub.edu.sa","institution_ids":["https://openalex.org/I4210136004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037514328","display_name":"Mohamed R. Eid","orcid":"https://orcid.org/0000-0003-2479-9809"},"institutions":[{"id":"https://openalex.org/I118590987","display_name":"Northern Border University","ror":"https://ror.org/03j9tzj20","country_code":"SA","type":"education","lineage":["https://openalex.org/I118590987"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Mohamed R. Eid","raw_affiliation_strings":["Center for Scientific Research and Entrepreneurship ,  Northern Border University ,  Arar ,  73213 ,  Saudi Arabia , nbu.edu.sa"],"raw_orcid":"https://orcid.org/0000-0003-2479-9809","affiliations":[{"raw_affiliation_string":"Center for Scientific Research and Entrepreneurship ,  Northern Border University ,  Arar ,  73213 ,  Saudi Arabia , nbu.edu.sa","institution_ids":["https://openalex.org/I118590987"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077723213","display_name":"W. S. Hassanin","orcid":"https://orcid.org/0000-0002-3446-7018"},"institutions":[{"id":"https://openalex.org/I84058292","display_name":"Helwan University","ror":"https://ror.org/00h55v928","country_code":"EG","type":"education","lineage":["https://openalex.org/I84058292"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"W. S. Hassanin","raw_affiliation_strings":["Department of Mathematics ,  Faculty of Science ,  Helwan University , P.O. Box 11795,  Cairo ,  Egypt , helwan.edu.eg"],"raw_orcid":"https://orcid.org/0000-0002-3446-7018","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Faculty of Science ,  Helwan University , P.O. Box 11795,  Cairo ,  Egypt , helwan.edu.eg","institution_ids":["https://openalex.org/I84058292"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5037514328"],"corresponding_institution_ids":["https://openalex.org/I118590987"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.7365,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63338727,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"2025","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11495","display_name":"Animal Virus Infections Studies","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1103","display_name":"Animal Science and Zoology"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T11495","display_name":"Animal Virus Infections Studies","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1103","display_name":"Animal Science and Zoology"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11560","display_name":"Animal Disease Management and Epidemiology","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1102","display_name":"Agronomy and Crop Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12047","display_name":"Viral Infections and Vectors","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2725","display_name":"Infectious Diseases"},"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/mathematics","display_name":"Mathematics","score":0.781488299369812},{"id":"https://openalex.org/keywords/chickenpox","display_name":"Chickenpox","score":0.7175947427749634},{"id":"https://openalex.org/keywords/virology","display_name":"Virology","score":0.1908589005470276},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.15642568469047546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.781488299369812},{"id":"https://openalex.org/C2776334287","wikidata":"https://www.wikidata.org/wiki/Q44727","display_name":"Chickenpox","level":3,"score":0.7175947427749634},{"id":"https://openalex.org/C159047783","wikidata":"https://www.wikidata.org/wiki/Q7215","display_name":"Virology","level":1,"score":0.1908589005470276},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.15642568469047546},{"id":"https://openalex.org/C2522874641","wikidata":"https://www.wikidata.org/wiki/Q808","display_name":"Virus","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/ijmm/3238188","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmm/3238188","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/3238188","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:3238188","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/ijmms/2025/3238188.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:7ed74954523a4d9889965740d44c6418","is_oa":true,"landing_page_url":"https://doaj.org/article/7ed74954523a4d9889965740d44c6418","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":"International Journal of Mathematics and Mathematical Sciences, Vol 2025 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/ijmm/3238188","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmm/3238188","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/3238188","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2034002651","display_name":null,"funder_award_id":"NBU-FFR-2025-3021-01","funder_id":"https://openalex.org/F4320328654","funder_display_name":"Northern Border University"},{"id":"https://openalex.org/G5791967564","display_name":null,"funder_award_id":"NBU-FFR-2024-","funder_id":"https://openalex.org/F4320328654","funder_display_name":"Northern Border University"}],"funders":[{"id":"https://openalex.org/F4320319621","display_name":"University of Bisha","ror":"https://ror.org/040548g92"},{"id":"https://openalex.org/F4320328654","display_name":"Northern Border University","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4407980148.pdf"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W1537506907","https://openalex.org/W1972671317","https://openalex.org/W2001509918","https://openalex.org/W2011744567","https://openalex.org/W2016946107","https://openalex.org/W2053239897","https://openalex.org/W2078283035","https://openalex.org/W2095135381","https://openalex.org/W2111025883","https://openalex.org/W2112680994","https://openalex.org/W2113133070","https://openalex.org/W2124920694","https://openalex.org/W2135233586","https://openalex.org/W2157424927","https://openalex.org/W2160762786","https://openalex.org/W2185418802","https://openalex.org/W2200415821","https://openalex.org/W2215796543","https://openalex.org/W2468128278","https://openalex.org/W2483924580","https://openalex.org/W2565334299","https://openalex.org/W2616848645","https://openalex.org/W2913440201","https://openalex.org/W2916951179","https://openalex.org/W2970866782","https://openalex.org/W2980602518","https://openalex.org/W2994625392","https://openalex.org/W2995444875","https://openalex.org/W3040345151","https://openalex.org/W3154843831","https://openalex.org/W3164869052","https://openalex.org/W3209174574","https://openalex.org/W3211063647","https://openalex.org/W3215574672","https://openalex.org/W4210417410","https://openalex.org/W4214905596","https://openalex.org/W4224268074","https://openalex.org/W4283836812","https://openalex.org/W4302609762","https://openalex.org/W4306318406","https://openalex.org/W4311143489","https://openalex.org/W4312519515","https://openalex.org/W4321767981","https://openalex.org/W4387745589","https://openalex.org/W4390582280","https://openalex.org/W4392011616","https://openalex.org/W4394993168","https://openalex.org/W4399223750","https://openalex.org/W4400508381","https://openalex.org/W6686546775","https://openalex.org/W6931336814"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4372335389","https://openalex.org/W3049544254","https://openalex.org/W4386807056","https://openalex.org/W2771627015","https://openalex.org/W2806311786","https://openalex.org/W83518725","https://openalex.org/W4242318820","https://openalex.org/W2413220549","https://openalex.org/W2971370707"],"abstract_inverted_index":{"This":[0],"work":[1],"presents":[2],"a":[3,109],"comprehensive":[4],"mathematical":[5],"analysis":[6,64],"of":[7,19,65,72,75,86,99,132],"the":[8,20,24,51,63,66,70,73,84,96,100,130,134],"chickenpox":[9,105,135],"transmission":[10],"model,":[11],"including":[12],"positivity,":[13],"existence,":[14],"invariant":[15],"region,":[16],"and":[17,40,43,58,69,107,117],"uniqueness":[18],"solution.":[21],"We":[22],"enhance":[23],"model":[25,102],"by":[26],"introducing":[27],"optimal":[28,76,87],"control":[29,34,77,88,119,143],"measures":[30,37,45],"using":[31,78],"two":[32],"time\u2010dependent":[33],"variables:":[35],"prevention":[36],"like":[38,46],"vaccination":[39],"movement":[41],"constraints,":[42],"isolation":[44],"quarantine.":[47],"The":[48,121],"study":[49],"evaluates":[50],"basic":[52],"reproduction":[53],"number":[54],",":[55],"equilibrium":[56],"points,":[57],"stability.":[59],"New":[60],"contributions":[61],"include":[62],"model\u2019s":[67],"bifurcations":[68],"proof":[71],"existence":[74],"Fleming\u2019s":[79],"theorem.":[80],"Numerical":[81],"simulations":[82],"demonstrate":[83],"effectiveness":[85],"strategies":[89],"in":[90,103],"reducing":[91],"infection.":[92],"These":[93],"results":[94,122],"highlight":[95],"practical":[97],"importance":[98],"proposed":[101],"mitigating":[104],"outbreaks":[106],"provide":[108],"basis":[110],"for":[111],"future":[112],"extensions":[113],"to":[114,125,128,140],"fractional":[115],"systems":[116],"additional":[118],"variables.":[120],"led":[123],"us":[124],"conclude":[126],"that,":[127],"reduce":[129],"danger":[131],"catching":[133],"virus,":[136],"it":[137],"is":[138],"imperative":[139],"apply":[141],"suggested":[142],"measures.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}
