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dc.contributor.authorBilge, Ayşe Hümeyra
dc.contributor.authorSamanlıoğlu, Funda
dc.contributor.authorErgönül, Önder
dc.date.accessioned2021-01-03T19:56:04Z
dc.date.available2021-01-03T19:56:04Z
dc.date.issued2015
dc.identifier.issn0303-6812en_US
dc.identifier.issn1432-1416en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12469/3710
dc.identifier.urihttps://doi.org/10.1007/s00285-014-0838-z
dc.description.abstractThe susceptible-infected-removed (SIR) and the susceptible-exposed-infected-removed (SEIR) epidemic models with constant parameters are adequate for describing the time evolution of seasonal diseases for which available data usually consist of fatality reports. The problems associated with the determination of system parameters starts with the inference of the number of removed individuals from fatality data, because the infection to death period may depend on health care factors. Then, one encounters numerical sensitivity problems for the determination of the system parameters from a correct but noisy representative of the number of removed individuals. Finally as the available data is necessarily a normalized one, the models fitting this data may not be unique. We prove that the parameters of the (SEIR) model cannot be determined from the knowledge of a normalized curve of "Removed" individuals and we show that the proportion of removed individuals, , is invariant under the interchange of the incubation and infection periods and corresponding scalings of the contact rate. On the other hand we prove that the SIR model fitting a normalized curve of removed individuals is unique and we give an implicit relation for the system parameters in terms of the values of and , where is the steady state value of and and are the values of and its derivative at the inflection point of . We use these implicit relations to provide a robust method for the estimation of the system parameters and we apply this procedure to the fatality data for the H1N1 epidemic in the Czech Republic during 2009. We finally discuss the inference of the number of removed individuals from observational data, using a clinical survey conducted at major hospitals in Istanbul, Turkey, during 2009 H1N1 epidemic.en_US
dc.language.isoengen_US
dc.publisherSpringer Heidelbergen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectEpidemic modelsen_US
dc.subjectDynamical systemsen_US
dc.subjectSIR modelen_US
dc.subjectSEIR modelen_US
dc.subjectInferenceen_US
dc.subjectFatality dataen_US
dc.titleOn the uniqueness of epidemic models fitting a normalized curve of removed individualsen_US
dc.typearticleen_US
dc.identifier.startpage767en_US
dc.identifier.endpage794en_US
dc.relation.journalJournal of Mathematical Biologyen_US
dc.identifier.issue4en_US
dc.identifier.volume71en_US
dc.departmentFakülteler, Mühendislik ve Doğa Bilimleri Fakültesi, Endüstri Mühendisliği Bölümüen_US
dc.identifier.wosWOS:000360851700001en_US
dc.identifier.doi10.1007/s00285-014-0838-zen_US
dc.identifier.scopus2-s2.0-84941336130en_US
dc.institutionauthorBilge, Ayşe Hümeyraen_US
dc.institutionauthorSamanlıoğlu, Fundaen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.pmid25312413en_US


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