Traveling Wave for a diffusive SIR model with delay in diffusion term

Traveling Wave for a diffusive SIR model with delay in diffusion term

This paper is concerned with traveling waves to an diffusive SIR model with delay placed in the diffusion terms as well as nonlinear incidence rate with delay. Using a cross iteration scheme and partial monotone conditions it will be shown that the existence of quasi upper and lower solutions is a s...

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Veröffentlicht in:arXiv.org 2023-10
1. Verfasser: Barker, William Kyle
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Sprache:eng
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Delay
Diffusion rate
Fixed points (mathematics)
Iterative methods
Steady state
Traveling waves
Wave fronts
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description This paper is concerned with traveling waves to an diffusive SIR model with delay placed in the diffusion terms as well as nonlinear incidence rate with delay. Using a cross iteration scheme and partial monotone conditions it will be shown that the existence of quasi upper and lower solutions is a sufficient condition for the existence of a traveling wave front. This will be shown via Schauder's fixed point theorem. Given an appropriate basic reproduction number the traveling wave front will flow from a disease-free steady state to endemic steady state. The construction of quasi upper and lower solutions will be carried out for a specific model.
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subjects Delay
Diffusion rate
Fixed points (mathematics)
Iterative methods
Steady state
Traveling waves
Wave fronts
title Traveling Wave for a diffusive SIR model with delay in diffusion term
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