Peak fraction of infected in epidemic spreading for multi-community networks

TL;DR

This paper analyzes how the peak infected fraction in multi-community epidemic models depends on bridge nodes, providing analytical insights into the effectiveness of targeted intervention strategies.

Contribution

It introduces an analytical framework for understanding the asymptotic behavior of peak infection in two-community networks with bridge nodes under the SIR model.

Findings

Peak infected fraction follows different power-law relations as bridge node fraction approaches zero.

Crossovers occur between different power-law regimes of peak infection.

The power-law exponent predicts the effectiveness of strategies targeting bridge nodes.

Abstract

One of the most effective strategies to mitigate the global spreading of a pandemic (e.g., COVID-19) is to shut down international airports. From a network theory perspective, this is since international airports and flights, essentially playing the roles of bridge nodes and bridge links between countries as individual communities, dominate the epidemic spreading characteristics in the whole multi-community system. Among all epidemic characteristics, the peak fraction of infected, $I_{\max}$, is a decisive factor in evaluating an epidemic strategy given limited capacity of medical resources, but is seldom considered in multi-community models. In this paper, we study a general two-community system interconnected by a fraction $r$ of bridge nodes and its dynamic properties, especially $I_{\max}$, under the evolution of the Susceptible-Infected-Recovered (SIR) model. Comparing the characteristic time scales of different parts of the system allows us to analytically derive the asymptotic behavior of $I_{\max}$ with $r$, as $r\rightarrow 0$, which follows different power-law relations in each regime of the phase diagram. We also detect crossovers when $I_{\max}$ changes from one power law to another, crossing different power-law regimes as driven by $r$. Our results enable a better prediction of the effectiveness of strategies acting on bridge nodes, denoted by the power-law exponent $\epsilon_I$ as in $I_{\max}\propto r^{1/\epsilon_I}$.