Year: 2026
Type: preprint
Abstract: We consider a reaction-diffusion system that arises in epidemiology to describe the spatial spread of a vector borne disease. Our model is a coupled version of the classical SIR model of Kermack and McKendrick. We study the long-time behavior of the solutions, giving optimal criteria on the propagation or extinction of the disease, and compute the asymptotic speed of spread of solutions, which is given by a Freidlin-G{ä}rtner type formula. We also give some qualitative properties of the model, which yield information on the influence of the parameters on the system's long-time behavior. In particular, we identify the limit of the spreading speed when the diffusions are very large, and we show that the system behaves in this case similarly to a homogenized system.
Source: arXiv (Cornell University)
Author: Wolff, Antoine
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W7223011382