ANALYZING A NOVEL CORONAVIRUS MODEL (COVID-19) IN THE SENSE OF CAPUTO-FABRIZIO FRACTIONAL OPERATOR

Dokuyucu M. A., ÇELİK E.

APPLIED AND COMPUTATIONAL MATHEMATICS, cilt.20, sa.1, ss.49-69, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 1
  • Basım Tarihi: 2021
  • Dergi Adı: APPLIED AND COMPUTATIONAL MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.49-69
  • Anahtar Kelimeler: Novel Coronavirus (COVID-19), Caputo-Fabrizio (CF) Fractional Derivative, Fixed-Point Theorem, Hyers-Ulam Stability
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, a new model has been proposed to analyze the infection due to the coronavirus (COVID-19). The model emphasizes the importance of environmental reservoir in spreading the infection and infecting others. It also keeps control measures regarding infection at the highest level by using non-constant transmission rates in the model. The analysis of the coronavirus model has been done via Caputo-Fabrizio fractional derivative operator. The existence of solutions of the model has been examined by using a fixed-point approach and the uniqueness of the solution has also been obtained. Further, the stability analysis of the model has been performed in the sense of Hyers-Ulam stability. Finally, the numerical solution has been obtained by using the Adam-Basford numerical approach, and also simulations for different fractional derivative values have been carried out. As a result, the mathematical modeling of the new type of coronavirus (COVID-19) has been applied to fractional-order derivatives and integral operators and its simulations with the real data have been shown.