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

Fırat Evirgen; Esmehan Uçar; Sümeyra Uçar; Necati Özdemir

doi:10.53391/mmnsa.1274004

EN

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

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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Details

Primary Language

English

Subjects

Bioinformatics and Computational Biology, Applied Mathematics

Journal Section

Research Article

Authors

Fırat Evirgen ^*
0000-0002-0798-5004
Türkiye

Esmehan Uçar This is me
0000-0003-0870-6270
Türkiye

Sümeyra Uçar This is me
0000-0002-6628-526X
Türkiye

Necati Özdemir
0000-0002-6339-1868
Türkiye

Publication Date

March 31, 2023

Submission Date

February 14, 2023

Acceptance Date

March 27, 2023

Published in Issue

Year 2023 Volume: 3 Number: 1

DOI

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

IZ

https://izlik.org/JA52CY99TT

APA

Evirgen, F., Uçar, E., Uçar, S., & Özdemir, N. (2023). Modelling Influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates. Mathematical Modelling and Numerical Simulation With Applications, 3(1), 58-73. https://doi.org/10.53391/mmnsa.1274004

AMA

1.Evirgen F, Uçar E, Uçar S, Özdemir N. Modelling Influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates. MMNSA. 2023;3(1):58-73. doi:10.53391/mmnsa.1274004

Chicago

Evirgen, Fırat, Esmehan Uçar, Sümeyra Uçar, and Necati Özdemir. 2023. “Modelling Influenza A Disease Dynamics under Caputo-Fabrizio Fractional Derivative With Distinct Contact Rates”. Mathematical Modelling and Numerical Simulation With Applications 3 (1): 58-73. https://doi.org/10.53391/mmnsa.1274004.

EndNote

Evirgen F, Uçar E, Uçar S, Özdemir N (March 1, 2023) Modelling Influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates. Mathematical Modelling and Numerical Simulation with Applications 3 1 58–73.

IEEE

[1]F. Evirgen, E. Uçar, S. Uçar, and N. Özdemir, “Modelling Influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates”, MMNSA, vol. 3, no. 1, pp. 58–73, Mar. 2023, doi: 10.53391/mmnsa.1274004.

ISNAD

Evirgen, Fırat - Uçar, Esmehan - Uçar, Sümeyra - Özdemir, Necati. “Modelling Influenza A Disease Dynamics under Caputo-Fabrizio Fractional Derivative With Distinct Contact Rates”. Mathematical Modelling and Numerical Simulation with Applications 3/1 (March 1, 2023): 58-73. https://doi.org/10.53391/mmnsa.1274004.

JAMA

1.Evirgen F, Uçar E, Uçar S, Özdemir N. Modelling Influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates. MMNSA. 2023;3:58–73.

MLA

Evirgen, Fırat, et al. “Modelling Influenza A Disease Dynamics under Caputo-Fabrizio Fractional Derivative With Distinct Contact Rates”. Mathematical Modelling and Numerical Simulation With Applications, vol. 3, no. 1, Mar. 2023, pp. 58-73, doi:10.53391/mmnsa.1274004.

Vancouver

1.Fırat Evirgen, Esmehan Uçar, Sümeyra Uçar, Necati Özdemir. Modelling Influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates. MMNSA. 2023 Mar. 1;3(1):58-73. doi:10.53391/mmnsa.1274004