English

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

Analysis of PDEs 2025-07-28 v1

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.

Keywords

Cite

@article{arxiv.2507.19252,
  title  = {A Wave-type Model for Age- and Space-structured Epidemics},
  author = {Nicolas Schlosser},
  journal= {arXiv preprint arXiv:2507.19252},
  year   = {2025}
}
R2 v1 2026-07-01T04:18:50.110Z