Estimating epidemic arrival times using linear spreading theory

TL;DR

This paper develops a mathematical framework to predict the arrival times of epidemics in different cities using linear spreading theory and tests it on real airline network data.

Contribution

It introduces a novel method combining linearized epidemic models with network analysis to estimate disease spread timings.

Findings

Predictions closely match actual epidemic arrival times on airline networks.

Heat kernel expansion provides accurate estimates of spreading speeds.

Simplified models like lattice or tree approximations yield useful uniform predictions.

Abstract

We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is comprised of a system of ordinary differential equations describing a meta-population SIR compartmental model defined on a network where each node represents a city and edges represent flight paths connecting cities. Making use of the linear determinacy of the system, we consider spreading speeds and arrival times in the system linearized about the unstable disease free state and compare these to arrival times in the nonlinear system. Two predictions are presented. The first is based upon expansion of the heat kernel for the linearized system. The second assumes that the dominant transmission pathway between any two cities can be approximated by a one dimensional lattice or homogeneous tree and gives a uniform prediction for arrival times independent of specific network features. We test these predictions on a real network describing worldwide airline traffic.