Türkiye'de COVID-19'un ilk dalgası için bir matematiksel modelin tanımlanabilirlik analizi

Abstract

Bu çalışmada, Türkiye'de COVID-19'un birinci zirvesini ele alan yapısal olarak tanımlanabilir bir matematiksel model geliştirilmiştir. Pandemi İzleme Ekranı TURCOVID19'den elde edilen, ilk zirve dönemi boyunca COVID-19 vaka sayıları, ölümler, yoğun bakım ünitesindeki hasta sayısı ve solunum cihazına bağlı hasta sayısı, veri kullanılmıştır. Yapısal tanımlanabilirlik analizi, açık kaynak yazılımı Julia kullanılarak gerçekleştirilmiştir. Modeldeki bazı parametreler literatüre dayalı olarak sabitlenmiş olup, geri kalan parametreler ise Data2Dynamics yazılımı kullanılarak hesaplanmıştır. Sonuçlarımızın, kullanılan veri ile tutarlı olduğu görülmektedir. Parametre değerlerindeki belirsizlikleri incelemek için profil benzerliği yöntemiyle pratik tanımlanabilirlik analizi yapılmıştır. Bu analiz, model parametrelerinden üçünün, yani semptomatik enfekte bireylerin hastaneye yatış hızının, virüse maruz kalan bireylerin ve semptomatik enfekte bireylerin virüs bulaştırma hızlarının, pratik olarak tanımlanabilir olmadığını ortaya koymaktadır. Bu sonuçlar, oluşturulan model aracılığıyla müdahale stratejilerinin dikkatlice uygulanması gerektiği anlamına gelmektedir.

Keywords

• Yapısal tanımlanabilirlik
• pratik tanımlanabilirlik
• COVID-19
• matematiksel modelleme
• Türkiye

Identifiability Analysis of a Mathematical Model for the First Wave of COVID-19 in Türkiye

Abstract

In this work, a structurally identifiable mathematical model is developed to capture the first peak of COVID-19 in Türkiye. The daily numbers of COVID-19 cases, deaths, prevalence in the ICU, and prevalence on ventilation, obtained from the open-access TURCOVID-19 database, during the first peak, are used as observations. Structural identifiability analysis is performed using the open-source software Julia. For parameter estimation, some parameters are fixed based on the literature while the remaining parameters are estimated using the Data2Dynamics software. Our results align well with the observations. Then, a practical identifiability analysis based on the profile likelihood method is conducted to investigate uncertainties in the parameter values. It reveals that three of the model parameters, namely the progression rate of symptomatically infectious individuals to hospital and the transmission rates associated with exposed and symptomatically infectious individuals, are not practically identifiable. This means that the implementation of intervention strategies via this model must be performed carefully.

Keywords

• Structural identifiability
• practical identifiability
• COVID-19
• mathematical modeling
• Türkiye

Ethical Statement

The study is compiled with research and publication ethics.

Thanks

The author would like to thank the anonymous reviewers for the constructive feedback.

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