Salgın Hastalıkların Yayılmasında Yüksek Riskli Bireylerin Dikkate Alındığı Bir Matematiksel Modelin Analizi (Analysis of a Mathematical Model in which the High Risk Individuals is Considered in Spread of Epidemic Diseases)

ÇAKAN Ü.

Journal of Polytechnic, cilt.24, sa.3, ss.1205-1211, 2021 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.2339/politeknik.778167
  • Dergi Adı: Journal of Polytechnic
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1205-1211
  • Anahtar Kelimeler: Lyapunov function, local and global stability, mathematical model, epidemic model, reproduction number
  • İnönü Üniversitesi Adresli: Evet

Özet

In this study, in which the spread of epidemic diseases in a population has been examined as mathematically, a compartmental epidemic model is presented. In this model, which consists of a system of delay differential equation, the individuals who are susceptible to the disease are formed two separate groups: susceptible individuals with high risk and others susceptible individuals. Thus, the model obtained is considered to be more realistic than clasical SEIR models. In the first section of the study after the introduction, the model is introduced and then the disease-free equilibrium point is obtained. Then, using the next generation operator method, the threshold value R-0, which is very important for the spread of diseases, is calculated. Taking into consideration the value of R-0, existence of the endemic equilibrium point of the model is investigated. In the third section, the local and global stabilities of existing equilibrium points are analyzed.