Traveling waves for SIR model on two-dimensional lattice
Ran Zhang, Shunchang Su, Xue Ren
TL;DR
This paper proves the existence of traveling wave solutions for a two-dimensional lattice SIR epidemic model using fixed-point theorems and constructs a Lyapunov functional to study their long-term behavior.
Contribution
It introduces a novel approach to analyze traveling waves in a 2D lattice SIR model, combining fixed-point methods with Lyapunov functionals.
Findings
Existence of traveling wave solutions established
Lyapunov functional constructed for asymptotic analysis
Method applicable to complex lattice epidemic models
Abstract
In this study, we investigate the existence of traveling wave solutions for a SIR model on two-dimensional lattice. The existence of traveling waves is established within the framework of upper and lower solutions and the Schauder fixed-point theorem. Moreover, we construct a Lyapunov functional to analyze the asymptotic behavior of the traveling wave solutions. This is a challenging task due to the two-dimensional lattice structure.
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Taxonomy
TopicsNonlinear Photonic Systems · Mathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Waves and Solitons