Qualitative properties of spatial epidemiological models

TL;DR

This paper analyzes a spatial SIR epidemiological model using PDEs, providing criteria for epidemic spread, exploring how individual movement affects propagation, and comparing spatial and temporal models.

Contribution

It introduces a criterion for epidemic propagation in spatial models and highlights how individual diffusivity influences disease spread, contrasting spatial and temporal SIR models.

Findings

Slowing down individuals can trigger an epidemic.

Spatial diffusion affects epidemic propagation criteria.

Differences between spatial and temporal SIR models are characterized.

Abstract

We study the qualitative properties of a spatial diffusive heterogeneous SIR model, that appears in mathematical epidemiology to describe the spread of an infectious disease in a population. The model we consider consists in a system of parabolic PDEs. In the first part of the paper, we give a criterion that ensures whether or not an epidemic propagates in a given population. We show how the features of the disease and of the population (rates of infection and of recovery, localisation and diffusivity of individuals) influence the propagation of the epidemic. In particular, we prove that there are situations where "slowing down" the individuals can trigger an epidemic that would not propagate otherwise. In the second part of the paper, we show how the spatial diffusive SIR model qualitatively differs from the usual, purely temporal, SIR model.