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

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 $0\le s<2$.

References in corpus (2)

• A SIR model assumption for the spread of COVID-19 in different communities
• Qualitative properties of spatial epidemiological models