Convergence of a finite volume scheme for nonlocal reaction-diffusion systems modelling an epidemic disease

TL;DR

This paper proves that a finite volume numerical scheme for a nonlocal SIR epidemic model converges to a weak solution, ensuring reliable simulations of disease spread with nonlocal interactions.

Contribution

It establishes the existence and convergence of a finite volume scheme for a nonlocal reaction-diffusion epidemic model, providing theoretical validation for numerical methods.

Findings

Finite volume scheme converges to a weak solution.

Existence of solutions to the scheme is proven.

A priori estimates and $L^p$ compactness are used in the proof.

Abstract

We analyze a finite volume scheme for nonlocal SIR model, which is a nonlocal reaction-diffusion system modeling an epidemic disease. We establish existence solutions to the finite volume scheme, and show that it converges to a weak solution. The convergence proof is based on deriving series of a priori estimates and using a general $L^p$ compactness criterion.