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

Year 2024, Volume: 1 Issue: 1, 19 - 27, 27.05.2024

İlknur Koca

Abstract

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.

Keywords

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

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