On the well-posedness of a nonlinear diffusive SIR epidemic model

TL;DR

This paper proves the well-posedness of a spatially extended nonlinear diffusive SIR epidemic model, called the Kermack-McKendrick equations, using methods from fluid dynamics and PDE analysis.

Contribution

It extends the classical SIR model to include spatial diffusion and establishes mathematical well-posedness in Sobolev spaces, a novel theoretical result.

Findings

Proves well-posedness of the diffusive SIR model in Sobolev spaces

Adapts fluid dynamics methods to epidemiological PDEs

Provides a rigorous mathematical foundation for spatial epidemic models

Abstract

This work considers an extension of the SIR equations from epidemiology that includes a spatial variable. This model, referred to as the Kermack-McKendrick equations (KM), is a pair of diffusive partial differential equations, and methods developed for the Navier-Stokes equations and models of fluid dynamics are adapted to prove that KM is well-posed in the homogenous Sobolev spaces with exponent $0 \le s <2$.