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

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 $r\to 0$, 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 $I_{\max }\propto r^{1/{\epsilon }_I}$.

arXiv comment19 pages, 6 figures, 3 tables

References in corpus (20)

• Catastrophic cascade of failures in interdependent networks
• Epidemic processes in complex networks
• Random graphs with arbitrary degree distributions and their applications
• The spread of epidemic disease on networks
• Evolution of networks
• Network robustness and fragility: Percolation on random graphs
• Robustness of a Network of Networks
• Percolation Critical Exponents in Scale-Free Networks
• Edge-Based Compartmental Modeling for Infectious Disease Spread Part I: An Overview
• Second look at the spread of epidemics on networks
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• Epidemics in partially overlapped multiplex networks
• Percolation of a general network of networks
• Resilience of networks with community structure behaves as if under an external field
• Quarantine generated phase transition in epidemic spreading
• Epidemics, the Ising-model and percolation theory: a comprehensive review focussed on Covid-19
• Shortest-Path Fractal Dimension for Percolation in Two and Three Dimensions
• How does bond percolation happen in coloured networks?
• Dynamic vaccination in partially overlapped multiplex network
• Role of bridge nodes in epidemic spreading: Different regimes and crossovers

Cited by in corpus (1)

• Scale-Free Networks beyond Power-Law Degree Distribution