Semptomatik ve Asemptomatik Bulaşmaların Etkisi ile COVID-19 Salgınının Matematiksel Modelinin Analizi

Yıl 2024, , 543 - 556, 31.12.2024

Özlem Ak Gümüş

https://doi.org/10.47112/neufmbd.2024.64

Öz

Bu çalışma, COVID-19 salgın sürecini ifade eden ayrık zamanlı bir SIR modelinin kararlılığını ve flip çatallanmasını ele almaktadır. Aşının etkisini dikkate alan model, hastalığın bulaşmasında semptomatik bireylerin yanı sıra asemptomatik bireylerin de etkisini içerir. Denge çözümleri belirli parametrik koşullar altında elde edilir. Daha sonra bu denge çözümlerinin lokal kararlılıkları araştırılır. Pozitif iç denge çözümü için çatallanmanın varlığı belirlenir.

Anahtar Kelimeler

COVID-19 Salgın Modeli, Flip Çatallanma, Lokal Asimptotik Kararlılık, SIR Modeli

Analyzing a Mathematical Model of the COVID-19 Pandemic with the Impact Symptomatic and Asymptomatic Transmissions

Öz

This study addresses the stability and flip bifurcation of a discrete-time SIR model expressing the COVID-19 pandemic. The model considers the effect of the vaccine, asymptomatic individuals, as well as symptomatic individuals in the transmission of the disease. Equilibrium solutions are obtained under certain parametric conditions. Then, the local stabilities of these equilibrium solutions are investigated. The existence of bifurcation is determined for the positive interior equilibrium solution.

Anahtar Kelimeler

COVID-19 Pandemic Model, Flip Bifurcation, Local Asymptotic Stability, SIR Model

Kaynakça

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