A PROBABILISTIC ANALYSIS FOR MENTAL HEALTH PROBLEMS: EVALUATION OF POLICIES FOR MANAGING DISTRACTED INDIVIDUALS

Year 2024, Volume: 12 Issue: 4, 643 - 652, 25.12.2024

Yasin Göçgün

https://doi.org/10.21923/jesd.1418675

Abstract

Mental health problems are among the problems that negatively affect people's daily lives. Depression, post-traumatic stress disorder and anxiety disorder can be given as examples of these problems. The mind of a person exposed to such problems cannot efficiently perform basic functions such as interpreting, synthesizing and understanding what is read. Such problems are addressed with scientific analysis and mathematical models are developed for them. In this paper, we define a class of mental health problems where the goal is to effectively manage distracted individuals that are required to complete specific tasks. The problem has the property that individuals are classified based on the level of distraction and face distraction with certain probability. We perform probabilistic analysis to evaluate different policies that can be implemented by the respective authority to which distracted individuals are responsible for. Numerical experiments reveal that the policy imposing task-related assignments to individuals and offering them the recompense of high-reward and low-penalty significantly outperforms other policies in all the scenarios we examined. This study will pioneer the mathematical modelling of mental health problems.

Keywords

Mental Health, Probability Models, Policy Evaluation

ZİHİNSEL SAĞLIK PROBLEMLERİ İÇİN OLASILIKSAL ANALİZ: DİKKATİ DAĞILMIŞ BİREYLERİ YÖNETMEYE YÖNELİK POLİTİKALARIN DEĞERLENDİRİLMESİ

Abstract

Zihinsel sağlık problemleri insanın gündelik hayatını olumsuz etkileyen problemler arasında yer almaktadır. Bu problemlere depresyon, travma sonrasi stress bozukluğu ve anksiyete bozukluğu örnek gösterilebilir. Bu tür problemere maruz kalan insanın zihni yorumlama, sentezleme, okuduğunu anlama gibi temel işlevleri verimli bir şekilde gerçekleştiremez. Bu tür problemler bilimsel analizle ele alınır ve bunlar için matematiksel modeller geliştirilmektedir. Bu makalede amacın belirli görevleri tamamlaması gereken dikkati dağılmış bireyleri etkin bir şekilde yönetmek olduğu bir zihinsel sağlık problemleri sınıfını tanımlamaktayız. Problem, bireylerin dikkat dağınıklığı düzeyine göre sınıflandırılması ve belirli bir olasılıkla dikkat dağınıklığı ile karşı karşıya kalma özelliğine sahiptir. Dikkati dağılmış bireylerin sorumlu olduğu ilgili otorite tarafından uygulanabilecek farklı politikaları değerlendirmek için olasılıksal analiz yapmaktayız. Sayısal deneyler, bireylere görevleriyle ilgili atamaları empoze eden ve onlara yüksek ödül ve düşük ceza karşılığı sunan politikanın, incelediğimiz tüm senaryolarda diğer politikalardan önemli ölçüde daha iyi performans gösterdiğini ortaya koymaktadır. Bu çalışma zihinsel sağlık problemlerinin matematiksel olarak modellemesine öncülük edecek niteliktedir.

Keywords

Zihinsel Sağlık, Olasılık Modelleri, Politika Değerlendirmesi

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