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

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.