A New Fixed Point Iterative Scheme Applied to the Dynamics of an Ebola Delayed Epidemic Model

Godwin Amechi Okeke (), Rubayyi T. Alqahtani and Ebube Henry Anozie
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Godwin Amechi Okeke: Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526 Owerri, Imo State, Nigeria
Rubayyi T. Alqahtani: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh P.O. Box 90950, Saudi Arabia
Ebube Henry Anozie: Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526 Owerri, Imo State, Nigeria

Mathematics, 2025, vol. 13, issue 11, 1-19

Abstract: In this paper, we introduce a fast iterative scheme and establish its convergence under a contractive condition. This new scheme can be viewed as an extension and generalization of existing iterative schemes such as Picard–Noor and UO iterative schemes for solving nonlinear equations. We demonstrate theoretically and numerically that the new scheme converges faster than several existing iterative schemes with the fastest known convergence rates for contractive mappings. We also analyze the stability of the new scheme and provide numerical computations to validate the analytic results. Finally, we implement the new scheme in MATLAB R2023b to simulate the dynamics of the Ebola virus disease.

Keywords: fixed point iterative scheme; rate of convergence; fixed point approximation; stability; data dependence; Ebola epidemic model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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