Impact of Singular and Non-Singular Kernels on Crossover Monkeypox Mathematical Model

This study presents three crossover models describing monkeypox disease that includes Caputo, MittagLeffler, and Caputo Fabrizio definitions. To represent a monkeypox disease, three models of variable-order fractional, fractal-fractional, and stochastic, as well as their piecewise derivatives are provided at three different time periods. To approximate these models, we use the nonstandard Grunwald ¨ −Letnikov finite difference method to approximate the deterministic model with a singular kernel and a nonsingular Mittag-Leffler kernel to approximate the deterministic model using the Toufik-Atangana approach. Moreover, we use the approximation of the integral Caputo-Fabrizio and Lagrange polynomial of two steps to approximate the deterministic model with a nonsingular exponential decay kernel. We implemented the Milstein method to approximate the stochastic differential equation. An analysis of the suggested model’s stability is conducted. The effectiveness of the procedures was confirmed, and the theoretical results were supported, through numerical testing and comparisons with actual data.