A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative

Advances in Difference Equations

article

Rezapour, Shahram¹  Mohammadi, Hakimeh⁴ 

[1] Institute of Research and Development, Duy Tan University;Faculty of Natural Sciences, Duy Tan University;Department of Medical Research, China Medical University Hospital, China Medical University;Department of Mathematics, Miandoab Branch, Islamic Azad University

关键词: AH1N1 influenza;    Equilibrium point;    Numerical simulation;    SEIR model;   

DOI  :  10.1186/s13662-020-02945-x

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stability of the disease-free equilibrium point is investigated. We prove the existence of solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. In the numerical section, we present a simulation to examine the system, in which we calculate equilibrium points of the system and examine the behavior of the resulting functions at the equilibrium points. By calculating the results of the model for different fractional order, we examine the effect of the derivative order on the behavior of the resulting functions and obtained numerical values. We also calculate the results of the integer-order model and examine their differences with the results of the fractional-order model.

【 授权许可】

CC BY