| Summary: | Understanding epidemic propagation patterns and assessing disease control measures require the use of mathematical and computational methodologies. In recent years, complexity science, management science, sociology, and computer science have all been progressively merged with epidemiology. The interdisciplinary collaboration has sped up the development of computational and mathematical methods for simulating epidemics. The model with the classical time derivative in the influenza disease model is formulated with the Caputo (power-law kernel), Caputo–Fabrizio (exponential kernel), and the novel Atangana–Baleanu fractional derivatives which combined both nonlocal and non-singular properties. Also this article presents the boundness and positiveness Solutions for the influenza model. The analysis of the equilibrium point is also given. Various published articles have utilized the reproductive number notion to investigate disease-spread stability. There were certain conditions proposed to predict whether there would be stability or instability. It was also advised that an analysis be conducted to discover the conditions under which infectious classes will grow or die out. Some authors pointed out that the reproductive number is limited, including its inability to fairly aid in understanding distribution patterns. The concept of strength number and analysis of derivatives of mathematical models were presented to help in understanding the disease model. Further, the stability of disease-free and endemic equilibrium is presented. Finally, a numerical solution with simulation is given. We hope to use these extra studies in a basic model to forecast the future of this research.
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