{"id":"https://openalex.org/W2083969438","doi":"https://doi.org/10.2478/amcs-2013-0027","title":"An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection","display_name":"An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W2083969438","doi":"https://doi.org/10.2478/amcs-2013-0027","mag":"2083969438"},"language":"en","primary_location":{"id":"doi:10.2478/amcs-2013-0027","is_oa":true,"landing_page_url":"https://doi.org/10.2478/amcs-2013-0027","pdf_url":"https://sciendo.com/pdf/10.2478/amcs-2013-0027","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://sciendo.com/pdf/10.2478/amcs-2013-0027","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045968437","display_name":"Hasim A. Obaid","orcid":null},"institutions":[{"id":"https://openalex.org/I869660684","display_name":"University of the Western Cape","ror":"https://ror.org/00h2vm590","country_code":"ZA","type":"education","lineage":["https://openalex.org/I869660684"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Hasim A. Obaid","raw_affiliation_strings":["Department of Mathematics & Applied Mathematics, University of the Western Cape, Bellville 7535, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Applied Mathematics, University of the Western Cape, Bellville 7535, South Africa","institution_ids":["https://openalex.org/I869660684"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078943906","display_name":"Rachid Ouifki","orcid":"https://orcid.org/0000-0001-7697-1792"},"institutions":[{"id":"https://openalex.org/I26092322","display_name":"Stellenbosch University","ror":"https://ror.org/05bk57929","country_code":"ZA","type":"education","lineage":["https://openalex.org/I26092322"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Rachid Ouifki","raw_affiliation_strings":["DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis, Stellenbosch University, Stellenbosch 7600, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis, Stellenbosch University, Stellenbosch 7600, South Africa","institution_ids":["https://openalex.org/I26092322"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078740069","display_name":"Kailash C. Patidar","orcid":"https://orcid.org/0000-0003-4738-637X"},"institutions":[{"id":"https://openalex.org/I869660684","display_name":"University of the Western Cape","ror":"https://ror.org/00h2vm590","country_code":"ZA","type":"education","lineage":["https://openalex.org/I869660684"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Kailash C. Patidar","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa#TAB#","institution_ids":["https://openalex.org/I869660684"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":1.6635,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.85131293,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"23","issue":"2","first_page":"357","last_page":"372"},"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":0.9979000091552734,"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":0.9979000091552734,"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":0.9922000169754028,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9915000200271606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6251518726348877},{"id":"https://openalex.org/keywords/human-immunodeficiency-virus","display_name":"Human immunodeficiency virus (HIV)","score":0.6110533475875854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5148293375968933},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4891107678413391},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.47738736867904663},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.44948041439056396},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.44346484541893005},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.43422842025756836},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4223308265209198},{"id":"https://openalex.org/keywords/mathematical-model","display_name":"Mathematical model","score":0.4148993194103241},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3737691342830658},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36706000566482544},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3331940174102783},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1505829095840454},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09579572081565857},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07403638958930969}],"concepts":[{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6251518726348877},{"id":"https://openalex.org/C3013748606","wikidata":"https://www.wikidata.org/wiki/Q15787","display_name":"Human immunodeficiency virus (HIV)","level":2,"score":0.6110533475875854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5148293375968933},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4891107678413391},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.47738736867904663},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.44948041439056396},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.44346484541893005},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.43422842025756836},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4223308265209198},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.4148993194103241},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3737691342830658},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36706000566482544},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3331940174102783},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1505829095840454},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09579572081565857},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07403638958930969},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C512399662","wikidata":"https://www.wikidata.org/wiki/Q3505712","display_name":"Family medicine","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/amcs-2013-0027","is_oa":true,"landing_page_url":"https://doi.org/10.2478/amcs-2013-0027","pdf_url":"https://sciendo.com/pdf/10.2478/amcs-2013-0027","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:repository.uwc.ac.za:10566/2550","is_oa":true,"landing_page_url":"http://hdl.handle.net/10566/2550","pdf_url":null,"source":{"id":"https://openalex.org/S4306400180","display_name":"UWC Research Repository (University of the Western Cape)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I869660684","host_organization_name":"University of the Western Cape","host_organization_lineage":["https://openalex.org/I869660684"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:zbc.uz.zgora.pl:78832","is_oa":false,"landing_page_url":"https://zbc.uz.zgora.pl/dlibra/docmetadata?showContent=true&id=78832","pdf_url":null,"source":{"id":"https://openalex.org/S4306400400","display_name":"Digital library of Zielona Gora (University of Zielona G\u00f3ra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I46305939","host_organization_name":"University of Zielona G\u00f3ra","host_organization_lineage":["https://openalex.org/I46305939"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.amcs.uz.zgora.pl/?action=papers&issue=53","raw_type":"artyku\u0142"}],"best_oa_location":{"id":"doi:10.2478/amcs-2013-0027","is_oa":true,"landing_page_url":"https://doi.org/10.2478/amcs-2013-0027","pdf_url":"https://sciendo.com/pdf/10.2478/amcs-2013-0027","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8500000238418579,"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2083969438.pdf","grobid_xml":"https://content.openalex.org/works/W2083969438.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W245940479","https://openalex.org/W370471672","https://openalex.org/W1480781224","https://openalex.org/W1592337542","https://openalex.org/W1968845093","https://openalex.org/W1971651546","https://openalex.org/W1974133499","https://openalex.org/W1983268101","https://openalex.org/W1988315351","https://openalex.org/W1990852726","https://openalex.org/W2002944058","https://openalex.org/W2007692324","https://openalex.org/W2010898275","https://openalex.org/W2019823335","https://openalex.org/W2022690777","https://openalex.org/W2024125882","https://openalex.org/W2024474624","https://openalex.org/W2038276476","https://openalex.org/W2049679050","https://openalex.org/W2051695941","https://openalex.org/W2059344753","https://openalex.org/W2063513094","https://openalex.org/W2076346435","https://openalex.org/W2082823632","https://openalex.org/W2101687492","https://openalex.org/W2111467186","https://openalex.org/W2162279400","https://openalex.org/W2249505760","https://openalex.org/W2284953690","https://openalex.org/W2327115700","https://openalex.org/W4285719527","https://openalex.org/W4297938501"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W1965041963","https://openalex.org/W2766044013","https://openalex.org/W2007426143","https://openalex.org/W56705272","https://openalex.org/W2384221708","https://openalex.org/W2171402820","https://openalex.org/W2044635454"],"abstract_inverted_index":{"We":[0],"formulate":[1],"and":[2],"analyze":[3],"an":[4],"unconditionally":[5],"stable":[6],"nonstandard":[7],"finite":[8],"difference":[9],"method":[10,45,53],"for":[11,93],"a":[12],"mathematical":[13],"model":[14,23,39],"of":[15,21,30,36,58,64],"HIV":[16],"transmission":[17],"dynamics.":[18],"The":[19],"dynamics":[20],"this":[22,50],"are":[24,40,78,81,90],"studied":[25],"using":[26],"the":[27,37,43,56,59,65,85],"qualitative":[28,34],"theory":[29],"dynamical":[31],"systems.":[32],"These":[33],"features":[35],"continuous":[38],"preserved":[41],"by":[42],"numerical":[44,73],"that":[46,89],"we":[47],"propose":[48],"in":[49],"paper.":[51],"This":[52],"also":[54,82],"preserves":[55],"positivity":[57],"solution,":[60],"which":[61],"is":[62],"one":[63],"essential":[66],"requirements":[67],"when":[68],"modeling":[69],"epidemic":[70],"diseases.":[71],"Robust":[72],"results":[74],"confirming":[75],"theoretical":[76],"investigations":[77],"provided.":[79],"Comparisons":[80],"made":[83],"with":[84],"other":[86],"conventional":[87],"approaches":[88],"routinely":[91],"used":[92],"such":[94],"problems.":[95]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}