Document Type
Article
Source of Publication
Alexandria Engineering Journal
Publication Date
8-1-2024
Abstract
In this paper, we propose a novel methodology for studying the dynamics of epidemic spread, focusing on the utilization of fundamental mathematical concepts related to piecewise differential and integral operators. These mathematical tools play a crucial role in the process of modeling epidemic phenomena, enabling us to investigate the behavior of infectious diseases within defined time intervals. Our primary objective is to enhance our understanding of epidemic dynamics and the underlying influencing factors. We introduce the Susceptible–Infectious–Recovered (SIR) model as the foundational framework, which is formulated as a system of differential equations. Our approach involves discretizing time and employing interpolation techniques for integrals, specifically utilizing the collocation method with Bernoulli wavelets. By incorporating piecewise derivatives, we are able to conduct comprehensive simulations and analyses of epidemic spread under various intervention strategies, including social distancing measures. The outcomes of our numerical simulations serve to validate the efficacy of our proposed methodology, offering valuable insights into the intricate dynamics of real-world epidemic scenarios. This contribution significantly advances the field of epidemic control optimization, providing an integrated framework that seamlessly integrates fractional calculus, piecewise differential derivatives, and the capabilities of wavelets. Our findings provide crucial guidance for policymakers and healthcare leaders, offering a deeper understanding of the effectiveness of different control strategies. By considering our innovative approach, we can better inform and shape epidemic control measures, ultimately enhancing public health and fortifying our defenses against infectious diseases.
DOI Link
ISSN
Publisher
Elsevier BV
Volume
101
First Page
245
Last Page
253
Disciplines
Life Sciences
Keywords
Bernoulli wavelets, Collocation techniques, Epidemiological modeling, Fractional derivatives, Numerical simulations, Piecewise differentiation
Scopus ID
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Mohammad, Mutaz; Sweidan, Mohyeedden; and Trounev, Alexander, "Piecewise fractional derivatives and wavelets in epidemic modeling" (2024). All Works. 6627.
https://zuscholars.zu.ac.ae/works/6627
Indexed in Scopus
yes
Open Access
yes
Open Access Type
Gold: This publication is openly available in an open access journal/series