Analysis of the Ebola with a fractional-order model involving the Caputo-Fabrizio derivative

Abstract

This paper uses a fractional-order epidemic model to describe the transmission dynamics of the Ebola virus. The proposed model uses the fractional-order derivative in Caputo-Fabrizio’s sense. It calculates the time-independent solutions of the proposed model, and the next-generation matrix method is used to calculate the basic reproduction number. It provides the conditions for the existence and uniqueness of solutions to the model. Further, the conditions for generalized Ulam-Hyers-Rassias stability of the proposed model are obtained. Numerical simulations show how the proposed model’s approximate solution varies for integer and fractional orders. They also show the behavior of the Ebola in terms of infections, deceased, and susceptible counts, for various contact rates. To demonstrate efficiency while using less time, CPU times are given in tabular form.

Keywords

• ebola
• caputo-fabrizio derivative
• stability
• basic reproduction number
• simulations