Analysis of The Dynamics of The Classical Epidemic Model with Beta Distributed Random Components

Abstract

In this study, the classical epidemic model of Kermack and McKendrick is analyzed with beta distributed random components. A random analysis is done for the deterministic epidemic model by transforming the parameters and initial values of the system to random variables with beta distribution. The approximations for the expectations of the model variables are compared with the deterministic results to comment on the randomness of the cases with random parameters and random initial values. Results for some numerical characteristics of these two cases are also given to investigate the accuracy of the approximations for the expected values.

Keywords

• SIR Model
• Random Effect
• Beta Distribution
• Moment
• Random Differential Equation

Klasik Salgın Hastalik Modeli Dinamiklerinin Beta Dağılımına Sahip Rastgele Bileşenlerle İncelenmesi

Abstract

Bu çalışmada Kermack ve McKendrick’in klasik salgın hastalık modeli beta dağılımına sahip rastgele bileşenlerle incelenmektedir. Deterministik model için sistemin parametreleri ve başlangıç koşulları beta dağılımına sahip rastgele değişkenlere dönüştürülerek bir rastgele inceleme yapılmaktadır. Model değişkenlerinin beklenen değerleri için elde edilen yaklaşımlar deterministik sonuçlarla karşılaştırılarak rastgele başlangıç koşulları ve rastgele parametre içeren durumların rastgele yapıları hakkında yorum yapılmaktadır. Beklenen değerlerin yaklaşımlarının doğruluğunun incelenmesi için iki durumun bazı sayısal karakteristiklerinin sonuçları da verilmektedir.

Keywords

• Rastgele Etki
• SIR Modeli
• Beta Dağılımı
• Moment
• Rastgele Diferansiyel Denklem

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