HARİCİ REENFEKSİYONLARA BAĞLI TÜBERKÜLOZUN UYARLAMALI KALMAN FİLTRE TEMELLİ OPTİMAL KONTROLÜ

Yıl 2020, Cilt: 8 Sayı: 4, 1260 - 1268, 25.12.2020

Meric Cetin Selami Beyhan

https://doi.org/10.21923/jesd.717130

Öz

Tüberküloz gibi epidemiyolojik hastalıkları matematiksel modeller üzerinden incelemek hastalığın gelecekteki dinamiklerini yorumlamak için faydalıdır. Bu modellerin varlığında, hastalığı ortadan kaldırabilecek stratejileri hesaplamak mümkün olmaktadır. Bu çalışmada, aktif tüberkülozlu, evde ya da hastanede tedavi edilen bireylerde ölçülemeyen tüberküloz dinamiklerini kontrol etmek için uyarlanabilir kokusuz bir Kalman filtre (UKKF) tabanlı optimal denetleyici tasarlanmıştır. Harici reenfeksiyona bağlı tüberküloz hastalarının evde ve hastanede tedavi görmeleri durumunun incelenmesi, optimal tedavi seçenekleri araştırılmasına olanak sağlamaktadır. Bu sayede küçük bir bulaşıcı insan grubu varlığında bile hastalığın uzun vadede kalıcı olmasının önüne geçileceği düşünülmektedir. Tüberküloz modelinden elde edilen tahmin ve kontrol sonuçlarına göre, tasarlanan uyarlanabilir optimal denetleyicinin, bulaşıcı virüs taşıyan kişilerin eve ya da hastaneye geçişi için doğru kararlar verebilecek nitelikte olduğu kanısına varılmıştır.

Anahtar Kelimeler

Optimal kontrol, Uyarlamalı kontrol, Kalman filtre, Tüberkuloz, Harici reenfeksiyon.

ADAPTIVE KALMAN FILTERING BASED OPTIMAL CONTROL OF TUBERCULOSIS DYNAMICS WITH EXOGENOUS REINFECTIONS

Öz

Examining epidemiological diseases such as tuberculosis through mathematical models is useful for interpreting the future dynamics of the disease. In the presence of these models, it is possible to calculate strategies that can exterminate the disease. In this study, an adaptive unscented Kalman filter (AUKF) -based optimal controller has been designed to control unknown tuberculosis dynamics in individuals treated with active tuberculosis, at home or in hospital. The investigation of the treatment of tuberculosis patients at home and in hospital due to exogenous reinfections helps to search for optimal treatment options. In this way, even in the presence of a small group of infectious people, the long-term persistence of the disease is thought to be prevented. According to the estimation and control results obtained from the tuberculosis model, it was concluded that the designed adaptive optimal controller was able to make the right decision about the transfer of infected persons to the home or to the hospital.

Anahtar Kelimeler

Optimal control, Adaptive control, Kalman filter, Tuberculosis, Exogenous reinfection

Kaynakça

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