{"id":"https://openalex.org/W4296019425","doi":"https://doi.org/10.3390/sym14091919","title":"Dynamics of a Novel IVRD Pandemic Model of a Large Population over a Long Time with Efficient Numerical Methods","display_name":"Dynamics of a Novel IVRD Pandemic Model of a Large Population over a Long Time with Efficient Numerical Methods","publication_year":2022,"publication_date":"2022-09-13","ids":{"openalex":"https://openalex.org/W4296019425","doi":"https://doi.org/10.3390/sym14091919"},"language":"en","primary_location":{"id":"doi:10.3390/sym14091919","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091919","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1919/pdf?version=1663748511","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/9/1919/pdf?version=1663748511","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089657756","display_name":"Maheswari Rangasamy","orcid":"https://orcid.org/0000-0002-4403-1752"},"institutions":[{"id":"https://openalex.org/I4387155381","display_name":"Sri Eshwar College of Engineering","ror":"https://ror.org/02f1z8215","country_code":null,"type":"education","lineage":["https://openalex.org/I4387155381"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Maheswari Rangasamy","raw_affiliation_strings":["Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore 641202, India"],"raw_orcid":"https://orcid.org/0000-0002-4403-1752","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore 641202, India","institution_ids":["https://openalex.org/I4387155381"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022457417","display_name":"Nazek Alessa","orcid":"https://orcid.org/0000-0003-3283-4870"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Nazek Alessa","raw_affiliation_strings":["Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-3283-4870","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056608178","display_name":"Prasantha Bharathi Dhandapani","orcid":"https://orcid.org/0000-0002-3152-1592"},"institutions":[{"id":"https://openalex.org/I4387155381","display_name":"Sri Eshwar College of Engineering","ror":"https://ror.org/02f1z8215","country_code":null,"type":"education","lineage":["https://openalex.org/I4387155381"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Prasantha Bharathi Dhandapani","raw_affiliation_strings":["Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore 641202, India"],"raw_orcid":"https://orcid.org/0000-0002-3152-1592","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore 641202, India","institution_ids":["https://openalex.org/I4387155381"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075501481","display_name":"K. Loganathan","orcid":"https://orcid.org/0000-0002-6435-2916"},"institutions":[{"id":"https://openalex.org/I73779912","display_name":"Manipal University Jaipur","ror":"https://ror.org/040h76494","country_code":null,"type":"education","lineage":["https://openalex.org/I73779912"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Karuppusamy Loganathan","raw_affiliation_strings":["Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur 303007, India","Research and Development Wing, Live4Research, Tiruppur 638106, India"],"raw_orcid":"https://orcid.org/0000-0002-6435-2916","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur 303007, India","institution_ids":["https://openalex.org/I73779912"]},{"raw_affiliation_string":"Research and Development Wing, Live4Research, Tiruppur 638106, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5075501481"],"corresponding_institution_ids":["https://openalex.org/I73779912"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.3755,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78656283,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"9","first_page":"1919","last_page":"1919"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9990000128746033,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9969000220298767,"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":0.9101999998092651,"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/epidemic-model","display_name":"Epidemic model","score":0.7016545534133911},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"Basic reproduction number","score":0.6620696783065796},{"id":"https://openalex.org/keywords/rabies","display_name":"Rabies","score":0.6479341983795166},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5633741617202759},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5120287537574768},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48316091299057007},{"id":"https://openalex.org/keywords/pandemic","display_name":"Pandemic","score":0.4767095446586609},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.4450047016143799},{"id":"https://openalex.org/keywords/disease","display_name":"Disease","score":0.4412718415260315},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.42200490832328796},{"id":"https://openalex.org/keywords/coronavirus-disease-2019","display_name":"Coronavirus disease 2019 (COVID-19)","score":0.33280766010284424},{"id":"https://openalex.org/keywords/virology","display_name":"Virology","score":0.32633015513420105},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.2686536908149719},{"id":"https://openalex.org/keywords/infectious-disease","display_name":"Infectious disease (medical specialty)","score":0.1882716417312622},{"id":"https://openalex.org/keywords/environmental-health","display_name":"Environmental health","score":0.127623051404953}],"concepts":[{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.7016545534133911},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.6620696783065796},{"id":"https://openalex.org/C2776849203","wikidata":"https://www.wikidata.org/wiki/Q39222","display_name":"Rabies","level":2,"score":0.6479341983795166},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5633741617202759},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5120287537574768},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48316091299057007},{"id":"https://openalex.org/C89623803","wikidata":"https://www.wikidata.org/wiki/Q12184","display_name":"Pandemic","level":5,"score":0.4767095446586609},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.4450047016143799},{"id":"https://openalex.org/C2779134260","wikidata":"https://www.wikidata.org/wiki/Q12136","display_name":"Disease","level":2,"score":0.4412718415260315},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.42200490832328796},{"id":"https://openalex.org/C3008058167","wikidata":"https://www.wikidata.org/wiki/Q84263196","display_name":"Coronavirus disease 2019 (COVID-19)","level":4,"score":0.33280766010284424},{"id":"https://openalex.org/C159047783","wikidata":"https://www.wikidata.org/wiki/Q7215","display_name":"Virology","level":1,"score":0.32633015513420105},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.2686536908149719},{"id":"https://openalex.org/C524204448","wikidata":"https://www.wikidata.org/wiki/Q788926","display_name":"Infectious disease (medical specialty)","level":3,"score":0.1882716417312622},{"id":"https://openalex.org/C99454951","wikidata":"https://www.wikidata.org/wiki/Q932068","display_name":"Environmental health","level":1,"score":0.127623051404953},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14091919","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091919","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1919/pdf?version=1663748511","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e82162489bfa4e9da59152a54d15bde9","is_oa":true,"landing_page_url":"https://doaj.org/article/e82162489bfa4e9da59152a54d15bde9","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":"Symmetry, Vol 14, Iss 9, p 1919 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/9/1919/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14091919","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry; Volume 14; Issue 9; Pages: 1919","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14091919","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091919","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1919/pdf?version=1663748511","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","score":0.8600000143051147,"display_name":"Good health and well-being"}],"awards":[{"id":"https://openalex.org/G5943188291","display_name":null,"funder_award_id":"PNURSP2022R59","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"}],"funders":[{"id":"https://openalex.org/F4320322484","display_name":"Princess Nourah Bint Abdulrahman University","ror":"https://ror.org/05b0cyh02"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4296019425.pdf","grobid_xml":"https://content.openalex.org/works/W4296019425.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1574717195","https://openalex.org/W2050297638","https://openalex.org/W2556784265","https://openalex.org/W2779051987","https://openalex.org/W2892265093","https://openalex.org/W2901375502","https://openalex.org/W2963641381","https://openalex.org/W2991370870","https://openalex.org/W3009876049","https://openalex.org/W3010693502","https://openalex.org/W3010863549","https://openalex.org/W3011238444","https://openalex.org/W3011427855","https://openalex.org/W3011561368","https://openalex.org/W3013226575","https://openalex.org/W3022714712","https://openalex.org/W3025352604","https://openalex.org/W3042895113","https://openalex.org/W3091776190","https://openalex.org/W3099401800","https://openalex.org/W3106778318","https://openalex.org/W3132964890","https://openalex.org/W3134431775","https://openalex.org/W3135512661","https://openalex.org/W3162070856","https://openalex.org/W4210680464","https://openalex.org/W4233423810","https://openalex.org/W4285392674","https://openalex.org/W6662774108","https://openalex.org/W6730176618","https://openalex.org/W6791054450"],"related_works":["https://openalex.org/W4320351350","https://openalex.org/W2230721379","https://openalex.org/W2376250553","https://openalex.org/W3138234900","https://openalex.org/W2356839139","https://openalex.org/W4388177052","https://openalex.org/W3113377908","https://openalex.org/W2032448025","https://openalex.org/W4293088316","https://openalex.org/W4282960359"],"abstract_inverted_index":{"The":[0],"model":[1,48,78,132,174],"of":[2,60,98,114,123,130,163,186],"any":[3,124],"epidemic":[4,171,187],"illness":[5],"is":[6,39,104,133,144],"evolved":[7],"from":[8,83],"the":[9,20,24,35,42,71,93,100,111,121,139,161,184,189],"current":[10],"susceptibility.":[11],"We":[12],"aim":[13],"to":[14,23,91,109,203],"construct":[15],"a":[16,47,76,107],"model,":[17],"based":[18],"on":[19,34,120],"literature,":[21],"different":[22],"conventional":[25],"examinations":[26],"in":[27,169,180,183],"epidemiology,":[28],"i.e.,":[29],"what":[30],"will":[31,167],"occur":[32],"depends":[33],"susceptible":[36],"cases,":[37,142],"which":[38,143],"not":[40,64,145],"always":[41],"case;":[43],"one":[44],"must":[45],"consider":[46],"with":[49,106,117,138],"aspects":[50,115],"such":[51,150],"as":[52,80,151],"infections,":[53],"recoveries,":[54],"deaths,":[55],"and":[56,175,193,200],"vaccinated":[57],"populations.":[58],"Much":[59],"this":[61,131,157],"information":[62],"may":[63],"be":[65,178],"available.":[66],"So":[67],"without":[68],"artificially":[69],"assuming":[70],"unknown":[72],"aspects,":[73],"we":[74,135],"frame":[75],"new":[77],"known":[79],"IVRD.":[81],"Apart":[82],"qualitative":[84],"evaluation,":[85],"numerical":[86],"evaluation":[87],"has":[88],"been":[89],"completed":[90],"aid":[92],"results.":[94],"A":[95,147],"novel":[96,128],"approach":[97],"calculating":[99],"fundamental":[101],"reproduction/transmission":[102],"range":[103],"presented,":[105],"view":[108],"estimating":[110],"largest":[112],"number":[113],"possible,":[116],"minimal":[118],"restrictions":[119],"spread":[122],"disease.":[125],"An":[126],"additional":[127],"aspect":[129],"that":[134],"include":[136],"vaccines":[137],"actively":[140],"infected":[141,210],"common.":[146],"few":[148],"infections":[149],"rabies,":[152,198],"ebola,":[153,199],"etc.,":[154],"can":[155,177],"apply":[156],"model.":[158,172],"In":[159],"general,":[160],"concept":[162],"symmetry":[164],"or":[165],"asymmetry":[166],"exist":[168],"every":[170],"This":[173],"method":[176],"applied":[179],"scientific":[181],"research":[182],"fields":[185],"modeling,":[188],"medical":[190],"sciences,":[191],"virology,":[192],"other":[194],"areas,":[195],"particularly":[196],"concerning":[197],"similar":[201],"diseases,":[202],"show":[204],"how":[205],"immunity":[206],"develops":[207],"after":[208],"being":[209],"by":[211],"these":[212],"viruses.":[213]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
