Modelling Influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates

Year 2023, Volume: 3 Issue: 1, 58 - 73, 31.03.2023

Fırat Evirgen , Esmehan Uçar Sümeyra Uçar Necati Özdemir

https://doi.org/10.53391/mmnsa.1274004

Cited By: 16

Abstract

The objective of this manuscript is to present a novel approach to modeling influenza A disease dynamics by incorporating the Caputo-Fabrizio (CF) fractional derivative operator into the model. Particularly distinct contact rates between exposed and infected individuals are taken into account in the model under study, and the fractional derivative concept is explored with respect to this component. We demonstrate the existence and uniqueness of the solution and obtain the series solution for all compartments using the Laplace transform method. The reproduction number of the Influenza A model, which was created to show the effectiveness of different contact rates, was obtained and examined in detail in this sense. To validate our approach, we applied the predictor-corrector method in the sense of the Caputo-Fabrizio fractional derivative and demonstrate the effectiveness of the fractional derivative in accurately predicting disease dynamics. Our findings suggest that the use of the Caputo-Fabrizio fractional derivative can provide valuable insights into the mechanisms underlying influenza A disease and enhance the accuracy of disease models.

Keywords

Fractional differential equations, fixed point theory, Caputo-Fabrizio derivative, influenza

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