Optimal Control of an Infectious Disease Model in Case of Imperfect Testing

Year 2025, Volume: 10 Issue: 1, 244 - 258, 29.06.2025

Tuğba Akman , Rana Esen , Fikriye Yılmaz

https://doi.org/10.33484/sinopfbd.1637257

Abstract

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.

Keywords

Mathematical modeling , optimal control problem , reproduction number , stability analysis , testing

Thanks

This paper is produced from Master Thesis of Rana Esen during he studies at Gazi University Thesis number (Council of Higher Education, Thesis Center): 727862

Kusurlu Test Durumunda Bulaşıcı Hastalık Modellerinin Optimal Kontrolü

Abstract

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 için
değil, 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.

Keywords

Matematiksel modelleme , optimal kontrol problemi , temel üreme sayısı , kararlılık analizi , test

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