Chaotic Behaviours and Chaos Control of a Conformable Fractional Order COVID-19 Model with Reel Data

Yıl 2022, Cilt: 22 Sayı: 6, 1299 - 1306, 28.12.2022

Güven Kaya

https://doi.org/10.35414/akufemubid.1125850

Cited By: 1

Öz

The aim of this study is to examine the complex behavior of the Conformable fractional order of a mathematical model that has been defined to make predictions about the spread of the Covid-19 virus. For this purpose, the model is transformed into a difference equation system. Then, the dynamic behavior of this new system is examined and it is shown that Neimark-Sacker bifurcation occurred in the system. In addition, two different chaos control strategies have been applied to the system to control the chaos and bifurcation that occur in the system. Finally, the accuracy of all these analytical results are shown with numerical simulations by taking the parameter values from real data.

Anahtar Kelimeler

Covid-19, Conformable Fractional Derivative, Stability, Bifurcation, Chaos Control.

Conformable Kesirli Mertebeden COVID-19 Modelinin Reel Veriye Bağlı Kaotik Davranışları ve Kaos Kontrolü

Öz

Bu çalışmanın amacı, Covid-19 virüsünün yayılımı hakkında tahminde bulunabilmek için tanımlanmış olan bir matematiksel modelin Conformable kesirsel mertebeli halinin kompleks davranışlarını incelemektir. Bunu yaparken model tam değer sabitlerinin kullanılmasına dayalı bir süreçten geçirilerek fark denklem sistemine dönüştürülmüştür. Daha sonra bu yeni sistemin dinamik davranışları incelenmiş, sistemde Neimark-Sacker çatallanması oluştuğu gösterilmiştir. Ayrıca sistemde ortaya çıkan kaosun ve çatallanmanın kontrolü için sisteme iki farklı kaos kontrol stratejisi uygulanmıştır. Son olarak bulunan bütün bu analitik sonuçların doğruluğu parametre değerleri reel verilerden alınarak nümerik simülasyonlar ile gösterilmiştir.

Anahtar Kelimeler

Covid-19, Conformable Kesirli Mertebeden Türev, Kararlılık, Çatallanma, Kaos Kontrol.

Kaynakça

• Andraus, M., Thorpe, J., Tai, X. Y., et al. 2021. Impact of the COVID-19 pandemic on people with epilepsy: Findings from the Brazilian arm of the COV-E study. Epilepsy & Behavior, 123, 108261.
• Mogensen, I., Hallberg, J., Björkander, et al. and BAMSE COVID-19 Study Group. 2022. Lung function before and after COVID-19 in young adults: A population-based study. Journal of Allergy and Clinical Immunology: Global.
• Apergis, N. 2021. COVID-19 and cryptocurrency volatility: Evidence from asymmetric modelling. Finance Research Letters, 102659.
• Omame, A., Abbas, M., Onyenegecha, C. P. 2021. A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana–Baleanu derivative. Chaos, Solitons & Fractals, 153, 111486.
• Inc, M., Acay, B., Berhe, H. W., Yusuf, A., Khan, A., Yao, S. W. 2021. Analysis of novel fractional COVID-19 model with real-life data application. Results in Physics, 23, 103968.
• Ayris, D., Imtiaz, M., Horbury, K., Williams, B., Blackney, M., See, C. S. H., Shah, S. A. A. 2022. Novel deep learning approach to model and predict the spread of COVID-19. Intelligent Systems with Applications, 14, 200068.
• Lee, H., Jang, G., Cho, G. 2022. Forecasting COVID-19 cases by assessing control-intervention effects in Republic of Korea: a statistical modeling approach. Alexandria Engineering Journal, 61(11), 9203-9217.
• Mohammed, W. W., Aly, E. S., Matouk, A. E., Albosaily, S., & Elabbasy, E. M. 2021. An analytical study of the dynamic behavior of Lotka-Volterra based models of COVID-19. Results in physics, 26, 104432.
• Elaydi, S. N. 2007. Discrete chaos: with applications in science and engineering. Chapman and Hall/CRC.
• Kartal, Ş., Gurcan, F. 2019. Discretization of conformable fractional differential equations by a piecewise constant approximation. International Journal of Computer Mathematics, 96(9), 1849-1860.
• Ott, E., Grebogi, C., Yorke, J. A. 1990. Erratum:''Controlling chaos''[Phys. Rev. Lett. 64, 1196 (1990)]. Physical Review Letters, 64(23), 2837.
• Din, Q. 2018. A novel chaos control strategy for discrete-time Brusselator models. J. Math. Chem. 56(10), 3045–3075.
• Pérez, J. E. S., Gómez-Aguilar, J. F., Baleanu, D., Tchier, F. 2018. Chaotic attractors with fractional conformable derivatives in the Liouville–Caputo sense and its dynamical behaviors. Entropy, 20(5), 384 . Balcı, E., Öztürk, İ., Kartal, S. 2019. Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative. Chaos, Solitons & Fractals, 123, 43-51.
• Kaya, G., Kartal, S., Gurcan, F. 2020. Dynamical analysis of a discrete conformable fractional order bacteria population model in a microcosm. Physica A: Statistical Mechanics and Its Applications, 547, 123864.
• Kaya, G., Kartal, S. 2020. Conformable Kesirsel Mertebeden Tam Deger Fonksiyonlu Lojistik Modelin Kararlilik ve Catallanma Analizi, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 9 (3), 1080-1090.