International Journal of Nonlinear Analysis and Applications

Analysis of SIRC model for influenza A with Caputo-Fabrizio derivative

Document Type : Research Paper

Authors

1 Laboratory of Advanced Materials, Department of Mathematics, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box 12, 23000, Annaba, Algeria

2 Department of Mathematics, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box 12, 23000, Annaba, Algeria

3 Laboratory of Embedded Systems (LASE), Department of Computer Science, Badji Mokhtar-Annaba University, P.O. Box 12, 23000, Annaba, Algeria

Abstract

In this manuscript, we study the fractional-order SIRC epidemiological model for influenza A in the human population in the Caputo-Fabrizio sense. The existence and uniqueness of the solution of the proposed problem are established using fixed point theory. The local stability of both disease-free equilibrium and endemic equilibrium points is investigated. Using the three-step fractional Adams-Bashforth scheme, an iterative solution of our system is generated. In the numerical simulation, many plots are given for different values of the fractional order to check the stability of equilibrium points. Also, the effect of varying some parameters of the model was presented. Furthermore, we compared our numerical solutions with those using Caputo fractional derivative model via graphical representations. The obtained results show the efficiency and accuracy of our approach.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 1239-1259
  • Receive Date: 29 October 2021
  • Accept Date: 09 February 2022