Epidemiyolojideki Kompartman Modellerinin Eşlenmiş Hamilton Analizi

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

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