Temporal percolation of a susceptible adaptive network

TL;DR

This paper investigates how adaptive social contacts influence disease spread by analyzing the temporal evolution of susceptible individuals in a network, revealing that adaptive behavior can slow down epidemics and preserve susceptible clusters.

Contribution

It introduces a novel edge-based compartmental model combined with percolation theory to study susceptible dynamics in adaptive networks, highlighting the impact of individual behavior on epidemic progression.

Findings

Adaptive contacts slow disease spread

Susceptible clusters are preserved longer

Critical time for network disintegration increases

Abstract

In the last decades, many authors have used the susceptible-infected-recovered model to study the impact of the disease spreading on the evolution of the infected individuals. However, few authors focused on the temporal unfolding of the susceptible individuals. In this paper, we study the dynamic of the susceptible-infected-recovered model in an adaptive network that mimics the transitory deactivation of permanent social contacts, such as friendship and work-ship ties. Using an edge-based compartmental model and percolation theory, we obtain the evolution equations for the fraction susceptible individuals in the susceptible biggest component. In particular, we focus on how the individual's behavior impacts on the dilution of the susceptible network. We show that, as a consequence, the spreading of the disease slows down, protecting the biggest susceptible cluster by increasing the critical time at which the giant susceptible component is destroyed. Our theoretical results are fully supported by extensive simulations.