A Wave-type Model for Age- and Space-structured Epidemics

Nicolas Schlosser

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arXiv · 2507.19252

A Wave-type Model for Age- and Space-structured Epidemics

Nicolas Schlosser

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Abstract

We introduce a novel approach of epidemic modeling by combining age-structured models with damped wave equations. This transforms the parabolic-type reaction-diffusion model into a hyperbolic system that shares many properties with a wave or telegrapher's equation. After we establish the existence of a weak solution of the resulting partial differential equation by means of characteristics, we show that the solutions to the new model converge to a solution of the standard age-dependent reaction-diffusion equation when we let the wave parameter become arbitrarily small. We conclude with a numerical example to illustrate the behavior of the new model and to further support our findings.

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Nicolas Schlosser. 2025-07-25. A Wave-type Model for Age- and Space-structured Epidemics. https://arxiv.org/abs/2507.19252

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