Where to cut to delay a pandemic with minimum disruption? Mathematical analysis based on the SIS model

TL;DR

This paper develops a mathematical approach to identify network edges whose removal can significantly delay disease spread with minimal impact on network functionality, demonstrated on the UK airport network.

Contribution

It introduces an approximate solution to the SIS epidemic model linking network structure to disease dynamics, enabling strategic edge removal for epidemic control.

Findings

Removing specific airport connections delays disease spread by over 300%

The strategy minimizes disruption to transportation capacity

The method provides a practical tool for epidemic intervention planning.

Abstract

We consider the problem of modifying a network topology in such a way as to delay the propagation of a disease with minimal disruption of the network capacity to reroute goods/items/passengers. We find an approximate solution to the Susceptible-Infected-Susceptible (SIS) model, which constitutes a tight upper bound to its exact solution. This upper bound allows direct structure-epidemic dynamic relations via the total communicability function. Using this approach we propose a strategy to remove edges in a network that significantly delays the propagation of a disease across the network with minimal disruption of its capacity to deliver goods/items/passengers. We apply this strategy to the analysis of the U.K. airport transportation network weighted by the number of passengers transported in the year 2003. We find that the removal of all flights connecting four origin-destination pairs in the U.K. delays the propagation of a disease by more than 300\%, with a minimal deterioration of the transportation capacity of this network. These time delays in the propagation of a disease represent an important non-pharmaceutical intervention to confront an epidemics, allowing for better preparations of the health systems, while keeping the economy moving with minimal disruptions.