{"id":"https://openalex.org/W3045857308","doi":"https://doi.org/10.22146/jmt.51490","title":"ANALISIS KESTABILAN MODEL PENYEBARAN PENYAKIT TUBERKULOSIS DENGAN LAJU INFEKSI TERSATURASI (STABILITY ANALYSIS OF TUBERCOLOSIS SPREAD DISEASES MODEL CONSIDERING SATURATED INFECTION RATE)","display_name":"ANALISIS KESTABILAN MODEL PENYEBARAN PENYAKIT TUBERKULOSIS DENGAN LAJU INFEKSI TERSATURASI (STABILITY ANALYSIS OF TUBERCOLOSIS SPREAD DISEASES MODEL CONSIDERING SATURATED INFECTION RATE)","publication_year":2020,"publication_date":"2020-07-28","ids":{"openalex":"https://openalex.org/W3045857308","doi":"https://doi.org/10.22146/jmt.51490","mag":"3045857308"},"language":"en","primary_location":{"id":"doi:10.22146/jmt.51490","doi":"https://doi.org/10.22146/jmt.51490","is_oa":true,"landing_page_url":"https://doi.org/10.22146/jmt.51490","pdf_url":"https://jurnal.ugm.ac.id/jmt/article/download/51490/28253","source":{"id":"https://openalex.org/S4210210980","display_name":"Jurnal Matematika Thales","issn_l":"2715-1891","issn":["2715-1891"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310314959","host_organization_name":"Gadjah Mada University","host_organization_lineage":["https://openalex.org/P4310314959"],"host_organization_lineage_names":["Gadjah Mada University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Jurnal Matematika Thales","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://jurnal.ugm.ac.id/jmt/article/download/51490/28253","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035521611","display_name":"Handika Lintang Saputra","orcid":"https://orcid.org/0000-0003-0304-7157","observed_orcids":["https://orcid.org/0000-0003-0304-7157"]},"institutions":[{"id":"https://openalex.org/I11855966","display_name":"Diponegoro University","ror":"https://ror.org/056bjta22","country_code":"ID","type":"education","lineage":["https://openalex.org/I11855966"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Handika Lintang Saputra","raw_affiliation_strings":["Departemen Matematika, Universitas Diponegoro"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departemen Matematika, Universitas Diponegoro","institution_ids":["https://openalex.org/I11855966"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044922225","display_name":"Sutimin Sutimin","orcid":"https://orcid.org/0000-0003-0337-7383","observed_orcids":["https://orcid.org/0000-0003-0337-7383"]},"institutions":[{"id":"https://openalex.org/I11855966","display_name":"Diponegoro University","ror":"https://ror.org/056bjta22","country_code":"ID","type":"education","lineage":["https://openalex.org/I11855966"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Sutimin Sutimin","raw_affiliation_strings":["Departemen Matematika, Universitas Diponegoro"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departemen Matematika, Universitas Diponegoro","institution_ids":["https://openalex.org/I11855966"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100343026","display_name":"Sutrisno Sutrisno","orcid":"https://orcid.org/0000-0003-1130-0044","observed_orcids":["https://orcid.org/0000-0003-1130-0044"]},"institutions":[{"id":"https://openalex.org/I11855966","display_name":"Diponegoro University","ror":"https://ror.org/056bjta22","country_code":"ID","type":"education","lineage":["https://openalex.org/I11855966"]}],"countries":["ID"],"is_corresponding":true,"raw_author_name":"Sutrisno Sutrisno","raw_affiliation_strings":["Departemen Matematika, Universitas Diponegoro"],"raw_orcid":"https://orcid.org/0000-0003-1130-0044","affiliations":[{"raw_affiliation_string":"Departemen Matematika, Universitas Diponegoro","institution_ids":["https://openalex.org/I11855966"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100343026"],"corresponding_institution_ids":["https://openalex.org/I11855966"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10702721,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"2","issue":"1","first_page":null,"last_page":null},"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":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10410","display_name":"COVID-19 epidemiological studies","score":9.999999747378752e-05,"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":0.0,"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/tuberculosis","display_name":"tuberculosis","score":0.8109999895095825},{"id":"https://openalex.org/keywords/disease-transmission-modeling","display_name":"disease transmission modeling","score":0.8100000023841858},{"id":"https://openalex.org/keywords/local-stability","display_name":"local stability","score":0.7170000076293945},{"id":"https://openalex.org/keywords/equilibrium-points","display_name":"equilibrium points","score":0.6190000176429749},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"basic reproduction number","score":0.8190000057220459},{"id":"https://openalex.org/keywords/next-generation-matrix","display_name":"next generation matrix","score":0.9319999814033508},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"transcritical bifurcation","score":0.9300000071525574},{"id":"https://openalex.org/keywords/treatment-effectiveness","display_name":"treatment effectiveness","score":0.8259999752044678},{"id":"https://openalex.org/keywords/latent-tuberculosis-infection","display_name":"latent tuberculosis infection","score":0.6240000128746033},{"id":"https://openalex.org/keywords/endemic-equilibrium","display_name":"endemic equilibrium","score":0.7570000290870667}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6106055974960327},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.6025600433349609},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.57612144947052},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.5657798051834106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48552608489990234},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.43919551372528076},{"id":"https://openalex.org/C3019203654","wikidata":"https://www.wikidata.org/wiki/Q506680","display_name":"Endemic disease","level":3,"score":0.4164939224720001},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.3930639624595642},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3536596894264221},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34016960859298706},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18119710683822632},{"id":"https://openalex.org/C2779134260","wikidata":"https://www.wikidata.org/wiki/Q12136","display_name":"Disease","level":2,"score":0.1685931384563446},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1642947793006897},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13748767971992493},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.09582680463790894},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.09062272310256958},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07756578922271729},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"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/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22146/jmt.51490","doi":"https://doi.org/10.22146/jmt.51490","is_oa":true,"landing_page_url":"https://doi.org/10.22146/jmt.51490","pdf_url":"https://jurnal.ugm.ac.id/jmt/article/download/51490/28253","source":{"id":"https://openalex.org/S4210210980","display_name":"Jurnal Matematika Thales","issn_l":"2715-1891","issn":["2715-1891"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310314959","host_organization_name":"Gadjah Mada University","host_organization_lineage":["https://openalex.org/P4310314959"],"host_organization_lineage_names":["Gadjah Mada University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Jurnal Matematika Thales","raw_type":"journal-article"},{"id":"pmh:oai:journal.ugm.ac.id:article/51490","doi":null,"is_oa":true,"landing_page_url":"https://journal.ugm.ac.id/jmt/article/view/51490","pdf_url":"https://journal.ugm.ac.id/jmt/article/download/51490/28253","source":{"id":"https://openalex.org/S4210210980","display_name":"Jurnal Matematika Thales","issn_l":"2715-1891","issn":["2715-1891"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310314959","host_organization_name":"Gadjah Mada University","host_organization_lineage":["https://openalex.org/P4310314959"],"host_organization_lineage_names":["Gadjah Mada University"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2715-1891","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.22146/jmt.51490","doi":"https://doi.org/10.22146/jmt.51490","is_oa":true,"landing_page_url":"https://doi.org/10.22146/jmt.51490","pdf_url":"https://jurnal.ugm.ac.id/jmt/article/download/51490/28253","source":{"id":"https://openalex.org/S4210210980","display_name":"Jurnal Matematika Thales","issn_l":"2715-1891","issn":["2715-1891"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310314959","host_organization_name":"Gadjah Mada University","host_organization_lineage":["https://openalex.org/P4310314959"],"host_organization_lineage_names":["Gadjah Mada University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Jurnal Matematika Thales","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.9391000270843506,"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3045857308.pdf","grobid_xml":"https://content.openalex.org/works/W3045857308.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1985601696","https://openalex.org/W1994821982","https://openalex.org/W2018455423","https://openalex.org/W2040280016","https://openalex.org/W2078190445","https://openalex.org/W2112680994","https://openalex.org/W2475038746","https://openalex.org/W2754639867","https://openalex.org/W2793890249","https://openalex.org/W2971460053"],"related_works":["https://openalex.org/W7045293238","https://openalex.org/W4399192098","https://openalex.org/W4210661131","https://openalex.org/W2955812325","https://openalex.org/W4389889327","https://openalex.org/W3085826100","https://openalex.org/W3207272213","https://openalex.org/W7213721293","https://openalex.org/W4417311727","https://openalex.org/W4244974615"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,11],"the":[4,16,21,25,29,33,44,49,62,67,75,80,86,93,99,107,123,138,141,147,151,155,158,165,168,176],"analysis":[5],"of":[6,24,32,48,66,79,140,154],"tuberculosis":[7,152],"disease":[8,51,109,153],"spread":[9],"model":[10,26],"saturated":[12],"infection":[13],"rate":[14],"and":[15,116,144],"treatment":[17,148,166],"effect.":[18],"We":[19],"analyze":[20,43,61],"dynamical":[22,142],"behavior":[23,143],"to":[27,42,60,136,145],"observe":[28],"stability":[30,46,64,77],"peroperty":[31,47],"model\u2019s":[34],"equilibrium":[35,52,69,81,110,125],"points.":[36],"The":[37,71],"Routh-Hurwitz":[38],"Theorem":[39],"is":[40,58,83,103,112,119,127],"used":[41,59],"local":[45,63,76],"free":[50,108],"point":[53,111,126],"whereas":[54],"Transcritical":[55],"Bifurcation":[56],"principle":[57],"property":[65,78],"endemic":[68,124],"pont.":[70],"result":[72,174],"show":[73],"that":[74,164],"points":[82],"depending":[84],"on":[85],"basic":[87,100],"reproduction":[88,101],"number":[89,102],"value":[90],"calculated":[91],"by":[92],"next":[94],"generation":[95],"matrix":[96],"(NGM).":[97],"When":[98],"less":[104],"than":[105,121,175],"1,":[106,122],"locally":[113,128],"asymptotically":[114,129],"stable,":[115],"when":[117],"it":[118,161],"greater":[120],"stable.":[130],"Numeric":[131],"simulation":[132,159],"results":[133],"were":[134],"presented":[135],"describe":[137],"evolution":[139],"understand":[146],"effectiveness":[149],"for":[150],"population.":[156],"From":[157],"results,":[160],"was":[162],"derived":[163],"in":[167,178],"infected":[169],"subpopulation":[170],"had":[171],"a":[172],"better":[173],"one":[177],"latent.":[179]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2020-08-03T00:00:00"}