Epidemiyolojideki Kompartman Modellerinin Eşlenmiş Hamilton Analizi

Yıl 2021, Cilt: 33 Sayı: 2, 265 - 276, 31.03.2021

Begüm Ateşli Oğul Esen Serkan Sütlü

https://doi.org/10.7240/jeps.796442

Öz

Epidemiyolojideki SIR, SEIR, 2-SIR ve 2-SEIR kompartman modellerinin Hamilton formülasyonuna yer verildi. Eşlenmiş Lie-Poisson sistemleri hatırlatıldı. SIR ve SEIR modellerinin eşlenmiş Lie-Poisson sistemi oldukları gösterildi. Bükülmüş eşçevrim genişlemesi kullanılarak eşlenmiş Lie-Poisson denklemlerinin bir genelleştirilmesi elde edildi. SIR ve SEIR kompartman modellerinin iki popülasyon karşılığı olan 2-SIR ve 2-SEIR modellerinin bükülmüş eşçevrim genişlemesiyle elde edilmiş Lie-Poisson sistemi olarak ifade edilebilecekleri gösterildi.

Anahtar Kelimeler

Eşlenmiş Lie cebirleri, Eşlenmiş Lie-Poisson sistemleri, Bükülmüş eşçevrim genişlemesi, Epidemiyolojik Kompartman Modelleri

Destekleyen Kurum

Tübitak

Proje Numarası

117F426

Teşekkür

Bu çalışma, TÜBITAK’ın 117F426 numaralı "Eşlenmis Lagrange ve Hamilton Sistemleri" isimli projesinin bir parçasıdır. Desteği için TÜBITAK’a teşekkür ederiz.

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