SIR MODELİ İLE SOSYAL İLETİŞİM AĞLARINDA SALGIN YAYILIM ANALİZİ

Epidemiyoloji alanında kompartıman tipi matematiksel modellerden sıklıkla yararlanılmaktadır. Bu tip modellerin birçoğu, gerçek hayattaki olayları matematiksel olarak modelleyebilmek amacıyla, toplumun homojen yapıda olduğu ve her bireyin temas oranının eşit olduğu gibi bazı varsayımlar üzerine kurulur. Gerçek hayatta ise toplumu oluşturan sosyal ağın heterojen yapıda olması nedeniyle bireylerin temas oranları ve temas süreleri farklılık göstermektedir. Ani ve yeni tip salgınlarda aşı gibi salgınları yavaşlatacak yada sonlandıracak çözümler sınırlı olabilmektedir. Bu tip durumlarda sınırlı kaynakları maksimum verim ile kullanmak daha önemli hale gelmektedir. Yapılan çalışmada, SIR kompartıman modeli kullanılarak, homojen ve heterojen toplum yapısındaki hastalık yayılımı tahmin sonuçları karşılaştırılmıştır. Gerçek hayattaki heterojen toplum yapısını örneklemek amacıyla 2009 yılında Dublin’deki bilim galerisini ziyaret eden ve yüz yüze temaslarda bulunan sergi ziyaretçilerine ait veri seti kullanılarak, ağdaki farklı merkeziyet derecelerine sahip bireylerin bağışıklık kazanması durumunda hastalık yayılımı simüle edilmiştir. Elde edilen sonuçlar karşılaştırıldığında, arasındalık merkezilik değeri yüksek olan bireylerin aşılanması durumunda enfeksiyon yayılımı SIR modellerinde kabul edilen homojen ağ yapısına göre % 14,39 daha az gerçekleşmektedir.

Anahtar Kelimeler:

graph, epidemiology, closeness, betweenness, sir model

EPIDEMIC SPREAD ANALYSIS IN SOCIAL COMMUNICATION NETWORKS WITH SIR MODEL

Compartmental mathematical models are frequently used in epidemiology. These types of models rely on some assumptions, such as the homogeneity of the society and the equal contact ratio of everyone, to model real-life events mathematically. In real life, due to the heterogeneous nature of the social network that constitutes society, the contact rates and contact times of individuals vary. In sudden and new types of epidemics, solutions such as vaccines to slow down or end epidemics may be limited. In such cases, it becomes more important to use limited resources with maximum efficiency. In this study, the estimation results of disease spread in homogeneous and heterogeneous population structures were compared using the SIR compartment model. The dataset obtained from the science gallery in Dublin in 2009 was used to illustrate the heterogeneous community structure in real life. In the exhibition, the spread of the disease was simulated when individuals with different degrees of centrality in the network formed by the visitors who made face-to-face contacts were immunized. When the results obtained are compared, in the case of vaccination of individuals with high betweenness centrality, the spread of infection occurs 14,39% less than the homogeneous network structure accepted in SIR models.

Keywords:

graph, epidemiology, closeness, betweenness, sir model,

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