Comparison of Fractional-Order Monkeypox Model with Singular and Non-Singular Kernels

Raqqasyi Rahmatullah Musafir; Agus Suryanto; Isnani Darti; Trisilowati Trisilowati

doi:10.37905/jjbm.v5i1.24920

Comparison of Fractional-Order Monkeypox Model with Singular and Non-Singular Kernels

Raqqasyi Rahmatullah Musafir, Agus Suryanto, Isnani Darti, Trisilowati Trisilowati

Abstract

The singularity of the kernel of the Caputo fractional derivative has become an issue, leading many researchers to consider the Atangana-Baleanu-Caputo (ABC) fractional derivative in epidemic models where the kernel is non-singular. In this context, the objective of this study is to compare the calibration and forecasting performance of fractional-order monkeypox models with singular and nonsingular kernels, represented by the model with respect to the Caputo operator and the ABC operator, respectively. We have proposed a monkeypox epidemic model with respect to the ABC operator (MPXABC), where the model with respect to the Caputo derivative (MPXC) has been proposed in previous research. We have analyzed the existence and uniqueness of the solution. Three equilibrium points of the model are endemic, human endemic, and monkeypox-free, and their global stability has been investigated. The global dynamics of the MPXABC are the same as those of the MPXC. In evaluating the performance, we collected secondary data on weekly monkeypox cases from June 1 to November 23, 2022, in the USA. Parameter estimation has been performed using the least squares method, while the solutions of the model have been determined numerically using a predictor-corrector scheme. The benchmark for performance has been determined based on the root mean square error. Data calibration and forecasting indicate that the MPXC generally has the best performance for each value of the derivative order. For certain values of derivative order, the MPXABC performs better than the corresponding firstorder model. However, generally, the corresponding first-order model performs better than the MPXABC. Depending on the data trends and the specified orders, the MPXC outperforms the MPXABC. Thus, the singularity issue of the Caputo derivative does not always have a negative impact on model fitting to data.

Keywords

Monkeypox model; Fractional-order model; Caputo derivative; Atangana-Baleanu-Caputo derivative; Parameter estimation

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DOI: https://doi.org/10.37905/jjbm.v5i1.24920

Copyright (c) 2024 Raqqasyi Rahmatullah Musafir, Agus Suryanto, Isnani Darti, Trisilowati

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