Propagation properties in a multi-species SIR reaction-diffusion system

TL;DR

This paper analyzes a multi-species reaction-diffusion model extending the classical SIR epidemiological model, revealing how multiple strains propagate, compete, and influence epidemic outcomes in spatial settings.

Contribution

It introduces a spatial multi-strain SIR model, studies long-term behavior, and identifies which strains propagate and invade, highlighting differences from classical single-strain models.

Findings

Only a subset of strains propagates and invades space with specific speeds.

Competition affects epidemic outcomes and cannot be characterized solely by the basic reproduction number.

The model exhibits a 'selection via propagation' phenomenon among strains.

Abstract

We consider a multi-species reaction-diffusion system that arises in epidemiology to describe the spread of several strains, or variants, of a disease in a population. Our model is a natural spatial, multi-species, extension of the classical SIR model of Kermack and McKendrick. First, we study the long-time behavior of the solutions and show that there is a "selection via propagation" phenomenon: starting with N strains, only a subset of them - that we identify - propagates and invades space, with some given speeds that we compute. Then, we obtain some qualitative properties concerning the effects of the competition between the different strains on the outcome of the epidemic. In particular, we prove that the dynamic of the model is not well characterized by the usual notion of basic reproduction number, which strongly differs from the classical case with one strain.