A Comprehensive Evaluation of the Impact of Mask-Wearing on COVID-19 Transmission Dynamics: A Fractional Calculus Approach to Understanding Public Health Dynamics

Year 2025, Volume: 13 Issue: 3, 126 - 143, 06.09.2025

Elif Demir , Canan Vural

https://doi.org/10.36753/mathenot.1695610

Abstract

The COVID-19 pandemic exposed vulnerabilities in global public health systems, emphasizing the urgent need for effective interventions. Among these, mask-wearing has proven to be a critical measure in reducing viral transmission by limiting respiratory droplet spread. To quantitatively evaluate the impact of mask usage, this study develops a fractional SIR model incorporating mask protection efficiency and mask-wearing rates for both susceptible and infected populations. The model utilizes the Caputo fractional derivative to better capture memory effects in disease transmission dynamics. Stability analysis is conducted, and the basic reproduction number is derived to assess the model's behavior under varying conditions.
The fractional forward Euler method is applied to approximate the system's solutions, and numerical simulations are performed using MATLAB. Real COVID-19 data from Türkiye, spanning April 21–30, 2021, is employed to estimate mask-wearing rates, combined with actual demographic statistics and average mask efficacy values. The results highlight the significant role of mask efficiency and adherence in reducing disease spread, with visualizations providing insights into the effects of parameter variations. This study underscores the critical importance of mask-wearing as a non-pharmaceutical intervention and demonstrates the applicability of fractional calculus in epidemiological modeling.

Keywords

Caputo type fractional derivative , Fractional SIR model , Mask protection efficiency , Transmission of COVID-19

Thanks

The authors are grateful to the Scientific and Technological Research Council of Türkiye (TUBITAK) for their financial support within the scope of "2211-E (2024/2) Direct Domestic PhD Scholarship Programme" .

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