Fluctuating epidemics on adaptive networks

TL;DR

This paper models epidemics on adaptive networks where nodes rewire connections to avoid infection, revealing how rewiring influences network structure, epidemic dynamics, and causes bistability and power-law fluctuations.

Contribution

It introduces a novel adaptive network model with rewiring based on infection status, analyzing its effects on epidemic behavior and network properties.

Findings

Rewiring alters degree distributions and increases average distance to infection.

The model exhibits bistability between endemic and disease-free states.

Fluctuations around endemic states follow power-law behavior.

Abstract

A model for epidemics on an adaptive network is considered. Nodes follow an SIRS (susceptible-infective-recovered-susceptible) pattern. Connections are rewired to break links from non-infected nodes to infected nodes and are reformed to connect to other non-infected nodes, as the nodes that are not infected try to avoid the infection. Monte Carlo simulation and numerical solution of a mean field model are employed. The introduction of rewiring affects both the network structure and the epidemic dynamics. Degree distributions are altered, and the average distance from a node to the nearest infective increases. The rewiring leads to regions of bistability where either an endemic or a disease-free steady state can exist. Fluctuations around the endemic state and the lifetime of the endemic state are considered. The fluctuations are found to exhibit power law behavior.