TY  - JOUR
T1  - Optimal Control of an Infectious Disease Model in Case of Imperfect Testing
TT  - Kusurlu Test Durumunda Bulaşıcı Hastalık Modellerinin Optimal Kontrolü
AU  - Yılmaz, Fikriye
AU  - Akman, Tuğba
AU  - Esen, Rana
PY  - 2025
DA  - June
Y2  - 2025
DO  - 10.33484/sinopfbd.1637257
JF  - Sinop Üniversitesi Fen Bilimleri Dergisi
JO  - Sinop Uni J Nat Sci
PB  - Sinop University
WT  - DergiPark
SN  - 2536-4383
SP  - 244
EP  - 258
VL  - 10
IS  - 1
LA  - en
AB  - In this work, we study the spread of a communicable disease using an SIR model that includes the effect of imperfect testing. The model is extended by adding birth and natural death rates, and it uses a standard incidence rate to describe disease dynamics over a long period, rather than just during an outbreak. We find the disease-free equilibrium and the basic reproduction number to analyze the system’s stability. To control transmission and testing rates, we set up an optimal control problem to find the best values. To do this, we simulate three different control problems: one with only isolation, one with only testing, and one with both. We see that reducing contact between susceptible and infected people is very important, along with having an effective testing strategy.
KW  - Mathematical modeling
KW  - optimal control problem
KW  - reproduction number
KW  - stability analysis
KW  - testing
N2  - Bu çalışmada, bulaşıcı bir hastalığın yayılımını kusurlu testlerin etkisini içeren bir SIR modeli kullanarak inceliyoruz. Model, doğum ve doğal ölüm oranları eklenerek genişletilmiş ve sadece bir salgın dönemi içindeğil, uzun bir zaman aralığında hastalık dinamiklerini tanımlamak amacıyla standart bulaşma oranı kullanılmıştır. Hastalığın olmadığı denge noktasını ve temel üreme sayısını sistemin kararlılığını analiz etmek için buluyoruz. Bulaşma ve test oranlarını kontrol etmek için en uygun değerleri bulmaya yönelik bir optimal kontrol problemi kurduk. Bunu yapmak için üç farklı kontrol problemi simülasyonu yapıyoruz: yalnızca izolasyon uygulanan, yalnızca test oranının optimize edildiği ve her iki müdahalenin birlikte uygulandığı durumlar. Duyarlı ve enfekte bireyler arasındaki temasın azaltılmasının, etkili bir test stratejisiyle birlikte, oldukça önemli olduğunu gözlemledik.
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UR  - https://doi.org/10.33484/sinopfbd.1637257
L1  - https://dergipark.org.tr/en/download/article-file/4598052
ER  -