Yıl: 2021 Cilt: 33 Sayı: 2 Sayfa Aralığı: 265 - 276 Metin Dili: Türkçe DOI: 10.7240/jeps.796442

Epidemiyolojideki Kompartman Modellerinin Eşlenmiş Hamilton Analizi

Öz:
Epidemiyolojideki SIR, SEIR, 2-SIR ve 2-SEIR modellerinin Hamilton formülasyonu verildi. Eşlenmiş Lie-Poisson sistemleriyazıldı. SIR ve SEIR modellerinin eşlenmiş Lie-Poisson sistemi oldukları gösterildi. Bir Lie cebiri için bükülmüş eşçevrimgenişlemesi çalışıldı. Bu genişlemenin dual uzayı üzerinde eşlenmiş Lie-Poisson denklemleri elde edildi. SIR ve SEIRkompartman modellerinin iki popülasyon karşılığı olan 2-SIR ve 2-SEIR modellerinin bükülmüş eşçevrim genişlemesiyle eldeedilmiş Lie-Poisson sistemi olarak ifade edilebilecekleri gösterildi.
Anahtar Kelime: Eşlenmiş Lie-Poisson sistemleri Bükülmüş eşçevrim genişlemesi Eşlenmiş Lie cebirleri Epidemiyolojik Kompartman Modelleri

Matched Pair Hamiltonian Analysis of the Compartmental Models in Epidemiology

Öz:
Hamiltonian formulations of SIR, SEIR, 2-SIR and 2-SEIR epidemiological models are presented. Matched Lie-Poisson dynamics is exhibited. SIR and SEIR models are expressed as matched pair Lie-Poisson systems. A twisted cocycle extension of a Lie algebra is studied. Lie-Poisson equations are written on the dual of a twisted cocycle extension. It is shown that two population 2-SIR and 2-SEIR models admit this Lie-Poisson formulation.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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APA ATEŞLİ B, ESEN O, SÜTLÜ S (2021). Epidemiyolojideki Kompartman Modellerinin Eşlenmiş Hamilton Analizi. International journal of advances in engineering and pure sciences (Online), 33(2), 265 - 276. 10.7240/jeps.796442
Chicago ATEŞLİ Begüm,ESEN Oğul,SÜTLÜ Serkan Epidemiyolojideki Kompartman Modellerinin Eşlenmiş Hamilton Analizi. International journal of advances in engineering and pure sciences (Online) 33, no.2 (2021): 265 - 276. 10.7240/jeps.796442
MLA ATEŞLİ Begüm,ESEN Oğul,SÜTLÜ Serkan Epidemiyolojideki Kompartman Modellerinin Eşlenmiş Hamilton Analizi. International journal of advances in engineering and pure sciences (Online), vol.33, no.2, 2021, ss.265 - 276. 10.7240/jeps.796442
AMA ATEŞLİ B,ESEN O,SÜTLÜ S Epidemiyolojideki Kompartman Modellerinin Eşlenmiş Hamilton Analizi. International journal of advances in engineering and pure sciences (Online). 2021; 33(2): 265 - 276. 10.7240/jeps.796442
Vancouver ATEŞLİ B,ESEN O,SÜTLÜ S Epidemiyolojideki Kompartman Modellerinin Eşlenmiş Hamilton Analizi. International journal of advances in engineering and pure sciences (Online). 2021; 33(2): 265 - 276. 10.7240/jeps.796442
IEEE ATEŞLİ B,ESEN O,SÜTLÜ S "Epidemiyolojideki Kompartman Modellerinin Eşlenmiş Hamilton Analizi." International journal of advances in engineering and pure sciences (Online), 33, ss.265 - 276, 2021. 10.7240/jeps.796442
ISNAD ATEŞLİ, Begüm vd. "Epidemiyolojideki Kompartman Modellerinin Eşlenmiş Hamilton Analizi". International journal of advances in engineering and pure sciences (Online) 33/2 (2021), 265-276. https://doi.org/10.7240/jeps.796442