An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus. (November 2020)

• Record Type: Journal Article
• Authors: Srivastava, H.M.; Saad, Khaled M.; Khader, M.M.
• Is Part Of: Chaos, solitons and fractals. Volume 140(2020)
• Publication Date: 2020-11
• Subjects: Fractional derivatives -- Ebola virus -- Epidemiological model -- Corona virus -- Chebyshev polynomials of the third-kind -- Chebyshev spectral collocation method -- Newton-Raphson method; 34A08 -- 35A22 -- 41A30 -- 65N22; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110174
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: This article investigates a family of approximate solutions for the fractional model (in the Liouville-Caputo sense) of the Ebola virus via an accurate numerical procedure (Chebyshev spectral collocation method). We reduce the proposed epidemiological model to a system of algebraic equations with the help of the properties of the Chebyshev polynomials of the third kind. Some theorems about the convergence analysis and the existence-uniqueness solution are stated. Finally, some numerical simulations are presented for different values of the fractional-order and the other parameters involved in the coefficients. We also note that we can apply the proposed method to solve other models.