Time scales of epidemic spread and risk perception on adaptive networks

TL;DR

This study explores how dynamic social networks and delayed risk awareness influence infectious disease spread, revealing that epidemic thresholds decrease with increased risk perception time scales and memory length, affecting epidemic lifetime and network topology.

Contribution

It introduces a contagion model incorporating delayed awareness and network adaptation, analyzing how these factors influence epidemic thresholds and network properties.

Findings

Epidemic threshold decreases with higher risk perception time scales and memory length.

The degree distribution's standard deviation follows a power-law relation with epidemic lifetime.

Epidemic lifetime and network topology are significantly affected by social adaptation dynamics.

Abstract

Incorporating dynamic contact networks and delayed awareness into a contagion model with memory, we study the spreading patterns of infectious diseases in connected populations. It is found that the spread of an infectious disease is not only related to the past exposures of an individual to the infected but also to the time scales of risk perception reflected in the social network adaptation. The epidemic threshold $p_{c}$ is found to decrease with the rise of the time scale parameter s and the memory length T, they satisfy the equation $p_{c} =\frac{1}{T}+ \frac{\omega T}{<k>a^s(1-e^{-\omega T^2/a^s})}$. Both the lifetime of the epidemic and the topological property of the evolved network are considered. The standard deviation $\sigma_{d}$ of the degree distribution increases with the rise of the absorbing time $t_{c}$, a power-law relation $\sigma_{d}=mt_{c}^\gamma$ is found.