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

TL;DR

This paper introduces a new epidemic model combining age structure with wave equations, transforming reaction-diffusion models into hyperbolic systems, and demonstrates convergence to classical models with numerical support.

Contribution

The paper presents a novel wave-type epidemic model integrating age structure, providing a hyperbolic PDE framework and establishing convergence to traditional reaction-diffusion models.

Findings

Existence of weak solutions established

Model solutions converge to reaction-diffusion solutions as wave parameter diminishes

Numerical example illustrates the model's behavior

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.