Existence of Traveling Waves in a Spatially Diffusive SIR Model Considering Mask Wearing Behavior
Differential Equations and Dynamical Systems, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s12591-026-00790-0
- Dergi Adı: Differential Equations and Dynamical Systems
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: COVID-19, Diffusive SIR model, Mask efficacy, Traveling wave solutions
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
In this study, we develop a diffusive SIR model incorporating mask usage to investigate the spatial spread of COVID-19 and to quantify the effects of mask efficacy and heterogeneous mask-wearing rates among the susceptible and infected populations. The model further includes natural birth and death processes, mask-dependent transmission reduction, and spatial diffusion. By applying the Schauder fixed point theorem, we rigorously establish the existence of traveling wave solutions and identify the parameter conditions under which such solutions arise. To support the analytical results, numerical simulations are performed in MATLAB using a finite-difference discretization in space combined with the explicit forward Euler method for time integration. The computed wave profiles of the infected class confirm the presence of coherent traveling waves under biologically relevant parameter values. These findings demonstrate how mask efficacy and adherence influence the propagation dynamics of COVID-19 and provide a mathematical framework for evaluating non-pharmaceutical interventions.