{"id":"https://openalex.org/W7204999653","doi":"https://doi.org/10.55730/1300-0098.3781","title":"A delayed SIAMR prostate cancer model with vertical transmission and treatment: stability analysis and numerical simulation","display_name":"A delayed SIAMR prostate cancer model with vertical transmission and treatment: stability analysis and numerical simulation","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7204999653","doi":"https://doi.org/10.55730/1300-0098.3781"},"language":"en","primary_location":{"id":"doi:10.55730/1300-0098.3781","doi":"https://doi.org/10.55730/1300-0098.3781","is_oa":true,"landing_page_url":"https://doi.org/10.55730/1300-0098.3781","pdf_url":"https://journals.tubitak.gov.tr/cgi/viewcontent.cgi?article=3781&context=math","source":{"id":"https://openalex.org/S145882832","display_name":"TURKISH JOURNAL OF MATHEMATICS","issn_l":"1300-0098","issn":["1300-0098","1303-6149"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-b","jufo-1","poland-40","russia-white-list-2","tr-dizin","vabb-shw"],"host_organization":"https://openalex.org/P4310318422","host_organization_name":"Scientific and Technological Research Council of Turkey (TUBITAK)","host_organization_lineage":["https://openalex.org/P4310318422"],"host_organization_lineage_names":["Scientific and Technological Research Council of Turkey (TUBITAK)"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Turkish Journal of Mathematics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W7204999653"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://journals.tubitak.gov.tr/cgi/viewcontent.cgi?article=3781&context=math","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029189700","display_name":"H\u00fcseyin Demir","orcid":"https://orcid.org/0000-0003-3606-878X","observed_orcids":["https://orcid.org/0000-0003-3606-878X"]},"institutions":[{"id":"https://openalex.org/I4210115931","display_name":"Samsun University","ror":"https://ror.org/02brte405","country_code":"TR","type":"education","lineage":["https://openalex.org/I4210115931"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"H\u00dcSEY\u0130N DEMIR","raw_affiliation_strings":["Department of Software Engineering , Faculty of Engineering and Natural Sciences , Samsun University , Samsun , Turkiye"],"raw_orcid":"https://orcid.org/0000-0003-3606-878X","affiliations":[{"raw_affiliation_string":"Department of Software Engineering , Faculty of Engineering and Natural Sciences , Samsun University , Samsun , Turkiye","institution_ids":["https://openalex.org/I4210115931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008240652","display_name":"\u0130nci \u00c7ilingir S\u00fcng\u00fc","orcid":"https://orcid.org/0000-0001-7788-181X","observed_orcids":["https://orcid.org/0000-0001-7788-181X"]},"institutions":[{"id":"https://openalex.org/I227306068","display_name":"Ondokuz May\u0131s University","ror":"https://ror.org/028k5qw24","country_code":"TR","type":"education","lineage":["https://openalex.org/I227306068"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"\u0130NC\u0130 \u00c7\u0130L\u0130NG\u0130R S\u00dcNG\u00dc","raw_affiliation_strings":["Department of Education of Mathematics and Sciences , Faculty of Education , Ondokuz May\u0131s University , Samsun , Turkiye"],"raw_orcid":"https://orcid.org/0000-0001-7788-181X","affiliations":[{"raw_affiliation_string":"Department of Education of Mathematics and Sciences , Faculty of Education , Ondokuz May\u0131s University , Samsun , Turkiye","institution_ids":["https://openalex.org/I227306068"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080277622","display_name":"\u0130brahim Kele\u015f","orcid":"https://orcid.org/0000-0001-8252-2635","observed_orcids":["https://orcid.org/0000-0001-8252-2635"]},"institutions":[{"id":"https://openalex.org/I4210115931","display_name":"Samsun University","ror":"https://ror.org/02brte405","country_code":"TR","type":"education","lineage":["https://openalex.org/I4210115931"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"\u0130BRAH\u0130M KELES","raw_affiliation_strings":["Department of Mechanical Engineering , Faculty of Engineering and Natural Sciences , Samsun University , Samsun , Turkiye"],"raw_orcid":"https://orcid.org/0000-0001-8252-2635","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering , Faculty of Engineering and Natural Sciences , Samsun University , Samsun , Turkiye","institution_ids":["https://openalex.org/I4210115931"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"50","issue":"5","first_page":"1053","last_page":"1066"},"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":0.9477999806404114,"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":0.9477999806404114,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.05220000073313713,"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/T10410","display_name":"COVID-19 epidemiological studies","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/prostate-cancer","display_name":"prostate cancer","score":0.9610000252723694},{"id":"https://openalex.org/keywords/vertical-transmission","display_name":"vertical transmission","score":0.8460000157356262},{"id":"https://openalex.org/keywords/time-delay","display_name":"time delay","score":0.6520000100135803},{"id":"https://openalex.org/keywords/force-of-infection","display_name":"force of infection","score":0.6759999990463257},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"basic reproduction number","score":0.9070000052452087},{"id":"https://openalex.org/keywords/disease-free-equilibrium","display_name":"disease-free equilibrium","score":0.949999988079071},{"id":"https://openalex.org/keywords/endemic-equilibrium","display_name":"endemic equilibrium","score":0.9869999885559082},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.9739999771118164},{"id":"https://openalex.org/keywords/limit-cycles","display_name":"limit cycles","score":0.7300000190734863},{"id":"https://openalex.org/keywords/well-posedness","display_name":"well-posedness","score":0.8619999885559082},{"id":"https://openalex.org/keywords/positive-invariance","display_name":"positive invariance","score":0.777999997138977},{"id":"https://openalex.org/keywords/viral-etiology","display_name":"viral etiology","score":0.5699999928474426},{"id":"https://openalex.org/keywords/age-related-susceptibility","display_name":"age-related susceptibility","score":0.5799999833106995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7407000064849854},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6428999900817871},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5221999883651733},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5055000185966492},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4562999904155731},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4449000060558319},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.4212000072002411},{"id":"https://openalex.org/C2777910003","wikidata":"https://www.wikidata.org/wiki/Q1707292","display_name":"Asymptomatic","level":2,"score":0.41280001401901245},{"id":"https://openalex.org/C52079815","wikidata":"https://www.wikidata.org/wiki/Q7229808","display_name":"Population model","level":3,"score":0.39640000462532043},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.3659000098705292},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.3531000018119812},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.32839998602867126},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.31859999895095825},{"id":"https://openalex.org/C2780192828","wikidata":"https://www.wikidata.org/wiki/Q181257","display_name":"Prostate cancer","level":3,"score":0.31859999895095825},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.31029999256134033},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.29319998621940613},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29179999232292175},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.257099986076355},{"id":"https://openalex.org/C2776235491","wikidata":"https://www.wikidata.org/wiki/Q9625","display_name":"Prostate","level":3,"score":0.2551000118255615},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.2524999976158142}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.55730/1300-0098.3781","doi":"https://doi.org/10.55730/1300-0098.3781","is_oa":true,"landing_page_url":"https://doi.org/10.55730/1300-0098.3781","pdf_url":"https://journals.tubitak.gov.tr/cgi/viewcontent.cgi?article=3781&context=math","source":{"id":"https://openalex.org/S145882832","display_name":"TURKISH JOURNAL OF MATHEMATICS","issn_l":"1300-0098","issn":["1300-0098","1303-6149"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-b","jufo-1","poland-40","russia-white-list-2","tr-dizin","vabb-shw"],"host_organization":"https://openalex.org/P4310318422","host_organization_name":"Scientific and Technological Research Council of Turkey (TUBITAK)","host_organization_lineage":["https://openalex.org/P4310318422"],"host_organization_lineage_names":["Scientific and Technological Research Council of Turkey (TUBITAK)"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Turkish Journal of Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.55730/1300-0098.3781","doi":"https://doi.org/10.55730/1300-0098.3781","is_oa":true,"landing_page_url":"https://doi.org/10.55730/1300-0098.3781","pdf_url":"https://journals.tubitak.gov.tr/cgi/viewcontent.cgi?article=3781&context=math","source":{"id":"https://openalex.org/S145882832","display_name":"TURKISH JOURNAL OF MATHEMATICS","issn_l":"1300-0098","issn":["1300-0098","1303-6149"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-b","jufo-1","poland-40","russia-white-list-2","tr-dizin","vabb-shw"],"host_organization":"https://openalex.org/P4310318422","host_organization_name":"Scientific and Technological Research Council of Turkey (TUBITAK)","host_organization_lineage":["https://openalex.org/P4310318422"],"host_organization_lineage_names":["Scientific and Technological Research Council of Turkey (TUBITAK)"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Turkish Journal of Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.9537000060081482,"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204999653.pdf","grobid_xml":"https://content.openalex.org/works/W7204999653.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W795615427","https://openalex.org/W2071510289","https://openalex.org/W2217868517","https://openalex.org/W2889598458","https://openalex.org/W2895523961","https://openalex.org/W3039445551","https://openalex.org/W3154621758","https://openalex.org/W3165400087","https://openalex.org/W3200519920","https://openalex.org/W3205006112","https://openalex.org/W3209061903","https://openalex.org/W4200466048","https://openalex.org/W4210896203","https://openalex.org/W4214940089","https://openalex.org/W4366380119","https://openalex.org/W4390233968","https://openalex.org/W4391443514","https://openalex.org/W4392377079","https://openalex.org/W4399906872","https://openalex.org/W4410756063"],"related_works":["https://openalex.org/W4406056349","https://openalex.org/W7170150911","https://openalex.org/W2026899212","https://openalex.org/W2557271382","https://openalex.org/W7095666576","https://openalex.org/W2390587193","https://openalex.org/W6889724429","https://openalex.org/W3027817760","https://openalex.org/W2087597220","https://openalex.org/W2091107174"],"abstract_inverted_index":{"\u200bIn":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"and":[5,19,42,105,121,149,179],"analyse":[6],"a":[7,75,80,137,153,160,171],"delayed-compartmental":[8],"mathematical":[9],"model":[10,59],"of":[11,63,71,82,94,108,125,136,152],"prostate":[12],"cancer":[13],"dynamics":[14],"that":[15,79,142],"incorporates":[16],"vertical":[17],"transmission":[18,70],"therapeutic":[20],"intervention.":[21],"The":[22],"population":[23],"is":[24,52],"stratified":[25],"into":[26],"five":[27],"compartments:":[28],"susceptible":[29],"(S),":[30],"infected/virally":[31],"activated":[32],"(I),":[33],"asymptomatic":[34],"infectious":[35],"under":[36],"treatment":[37],"(A),":[38],"malignant":[39],"untreated":[40],"(M),":[41],"recovered":[43],"(R).":[44],"A":[45],"discrete":[46],"time":[47],"delay":[48,155],"\u03c4":[49],">":[50,147],"0":[51],"introduced":[53],"in":[54,65],"the":[55,60,85,90,95,111,126],"force-of-infection":[56],"term":[57],"to":[58],"age-dependent":[61],"onset":[62],"susceptibility":[64],"middle-aged":[66],"adult":[67],"males.":[68],"Vertical":[69],"viral":[72],"etiology":[73],"at":[74],"rate":[76],"q\u039b":[77],"ensures":[78],"fraction":[81],"newborns":[83],"enter":[84],"infected":[86],"compartment":[87],"directly,":[88],"rendering":[89],"disease":[91],"persistent":[92],"regardless":[93],"basic":[96],"reproduction":[97],"number":[98],"R\u2080.":[99],"We":[100],"rigorously":[101],"establish:":[102],"(i)":[103],"well-posedness":[104],"positive":[106],"invariance":[107],"solutions;":[109],"(ii)":[110],"explicit":[112],"formula":[113],"R\u2080":[114,131],"=":[115],"\u03b2(1\u2212q)\u039b":[116],"/":[117],"[\u03bc(\u03b1+\u03bc)];":[118],"(iii)":[119],"local":[120],"global":[122],"asymptotic":[123],"stability":[124],"disease-free":[127],"equilibrium":[128,140],"E\u2080":[129],"when":[130],"<":[132],"1;":[133],"(iv)":[134],"existence":[135,151],"unique":[138],"endemic":[139],"E*":[141],"persists":[143],"for":[144],"all":[145,176],"q":[146],"0;":[148],"(v)":[150],"critical":[154],"threshold":[156],"\u03c4_c":[157],"beyond":[158],"which":[159],"Hopf":[161],"bifurcation":[162],"occurs,":[163],"generating":[164],"stable":[165],"limit":[166],"cycles.":[167],"Numerical":[168],"simulations":[169],"using":[170],"delayed":[172],"Euler":[173],"scheme":[174],"confirm":[175],"theoretical":[177],"findings":[178],"illustrate":[180],"distinct":[181],"qualitative":[182],"behaviours":[183],"across":[184],"parameter":[185],"regimes.":[186]},"counts_by_year":[],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2026-09-02T00:00:00"}