Mathematical Models in Healthcare

Abstract

In the recent years, healthcare applications of mathematical models have been increasingly developed although the field of healthcare models is not a new area. Current trends could be explained with growing rate of data and computing skills, rising healthcare costs, decreasing resources as well as more complex health problems due to extended life expectancy. In this paper, we survey the mathematical models applied to healthcare problems with a focus on disease applications. Infectious and chronic disease modelling which has been studied for several diseases such as measles, influenza is an important research area. Furthermore, effectiveness and cost-effectiveness of prevention, screening and treatment interventions could be assessed with the help of these models. In this study, we present the definition of mathematical modeling, advantages and disadvantages of modelling and introduce an extensive summary of published literature. We mainly focus on three modeling methodology: Markov models, compartmental models and agent-based simulation.

Keywords

• Agent-based simulation
• compartmental models
• disease modeling
• markov models
• mathematical modeling

Sağlık Araştırmalarında Matematik Model Kullanımı

Öz

Sağlık araştırmalarında matematik modellerin uygulanması yeni olmamakla beraber son yıllarda oldukça yaygınlaşmıştır. Bu artışın nedeni olarak veriyle hesaplama gücündeki artış kadar sağlık maliyetlerinin artması, kaynakların azalması bununla beraber artan yaşam süresi nedeniyle rastlanan kompleks sağlık sorunları da gösterilebilir. Bu çalışma, matematik modellerin sağlık alanındaki uygulamalarını incelemeyi amaçlamakta olup özellikle klinik uygulamaları ve hastalık modellerine önem vermiştir. Bulaşıcı hastalıklar ve kronik hastalıkların modellenmesi bunlara bağlı olarak tedavi ve korunma yöntemlerinin arasından en etkin ve maliyet etkili olanların belirlenmesi önemli bir alandır. Kızamık, grip, kanser ve HIV gibi birçok hastalık ve halk sağlığı sorunu matematik modeller yardımıyla incelenip var olan kaynakların etkin kullanımını sağlayacak karar destek çalışmaları mevcuttur. Bu çalışmada, bu çalışmaların geniş bir özeti kullanılan matematik modelleme yöntemlerinin sınıflandırılmasıyla verilmiştir. Hastalık model yöntemleri olarak Markov modeller, kompartıman modelleri ve ajan temelli benzetim modelleri metot olarak özetlenmiş ve yapılan önemli çalışmalardan bazıları ve Türkiye’de yapılan uygulamalar incelenmiştir.

Anahtar Kelimeler

• Ajan temelli simülasyon
• Hastalık modelleri
• Kompartıman modelleri
• Markov modeller
• Matematik modelleme

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