The propagation of infection fronts in spatially distributed compartment models in epidemiology

TL;DR

This paper investigates reaction-diffusion models in epidemiology, focusing on infection front propagation, critical behaviors, and phase transition analogies, revealing universal dynamics and coexistence phenomena.

Contribution

It introduces spatially extended compartment models with reaction-diffusion dynamics, analyzing soliton-like infection fronts and phase transition analogies in epidemiological spread.

Findings

Identification of soliton-like infection fronts

Near-threshold critical behavior and universality

Possibility of static coexistence of different infection levels

Abstract

Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of reaction-diffusion systems, which allow familiar techniques to be applied. The focus is largely on the appearance of soliton-like moving fronts that spread infection to previously uninfected regions. Near threshold dynamical critical behavior and a degree of universality are revealed. Extending two of the models to include a simple nonlinearity in the strength of the binary interaction between a susceptible individual and an infected one, we find the possibility of static coexistence between spatial regions with different levels of infection and an analogy with first-order transitions in thermodynamics.