Fractional Order Mathematical Modeling of COVID-19 Dynamics with Mutant and Quarantined Strategy

Yıl 2024, Cilt: 1 Sayı: 1, 19 - 27, 27.05.2024

İlknur Koca

Öz

Mathematical models provide a common language for communicating ideas, theories, and findings across disciplines. They allow researchers to represent complex concepts in a concise and precise manner, facilitating collaboration and interdisciplinary research. Additionally, visual representations of models help in conveying insights and understanding complex relationships. Mathematical modeling finds applications in various areas across science, engineering, economics, and other fields. Recently disease models have helped us understand how infectious diseases spread within populations. By studying the interactions between susceptible, infected, and recovered individuals, we can identify key factors influencing transmission, such as contact patterns, population density, and intervention strategies. The incorporation of fractional order modeling in studying disease models such as COVID-19 dynamics holds significant importance, offering a more accurate and efficient portrayal of system behavior compared to conventional integer-order derivatives. So in this study, we adopt a fractional operator-based approach to model COVID-19 dynamics. The existence and uniqueness of solutions are crucial properties of mathematical models that ensure their reliability, stability, and relevance for real-world applications. These properties underpin the validity of predictions, the interpretability of results, and the effectiveness of models in informing decision-making processes. Our investigation focuses on positivity of solutions, the existence and uniqueness of solutions within the model equation system, thereby contributing to a deeper understanding of the pandemic's dynamics. Finally, we present a numerical scheme for our model.

Anahtar Kelimeler

Fractional differential equation, Covid-19 model, existence and uniquness

Kaynakça

• Alkahtani, B. S. T., and Koca, I. (2021). Fractional stochastic sır model. Results in Physics, 24, 104124.
• Anderson, R. M., and May, R. M. (1991). Infectious diseases of humans: dynamics and control. Oxford University Press.
• Atangana, A., and Baleanu, D. (2016). New fractional derivative with nonlocal and non-singular kernel, theory and application to heat transfer model. Thermal Science, 20(2), 763–769.
• Atangana, A. (2021). Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?. Advances in Difference Equations, 2021(1), 403.
• Caputo, M., and Fabrizio, M. (2016). Applications of new time and spatial fractional derivatives with exponential kernels. Progress in Fractional Differentiation and Applications, 2(1), 1-11.
• Dokuyucu, M. A., and Çelik, E. (2021). Analyzing a novel coronavirus model (COVID-19) in the sense of Caputo- Fabrizio fractional operator. Applied and Computational Mathematics, 20(1), 49-69.
• Kermack, W. O., and McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 115(772), 700-721.
• Kilbas, A. A., Srivastava, H. M., and Trujillo, J. J. (2006). Theory and applications of fractional differential equations. Amsterdam, Elsevier.
• Koca, I., and Ozalp, N. (2013). Analysis of a fractional-order couple model with acceleration in feelings. The Scientific World Journal, 2013, 730736.
• Koca, I. (2018). Efficient numerical approach for solving fractional partial differential equations with non-singular kernel derivatives. Chaos, Solitons and Fractals, 116, 278–286.
• Podlubny, I. (1999). Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Academic Press, New York.
• Toufik, M., and Atangana, A. (2017). New numerical approximation of fractional derivative with non-local and non-singular kernel: application to chaotic models. The European Physical Journal Plus, 132(10), 444.
• Yu, Z., Zhang, J., Zhang, Y., Cong, X., Li, X., and Mostafa, A. M. (2024). Mathematical modeling and simulation for COVID-19 with mutant and quarantined strategy. Chaos, Solitons and Fractals, 181, 114656.