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arXiv · 2310.13799

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

William Kyle Barker
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Abstract

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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William Kyle Barker. 2023-10-20. Traveling Wave for a diffusive SIR model with delay in diffusion term. https://arxiv.org/abs/2310.13799

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