# Burstiness in activity-driven networks and the epidemic threshold

## TL;DR

This paper analyzes how burstiness in activity-driven networks influences epidemic spreading, deriving an analytical epidemic threshold and revealing that burstiness lowers the threshold but has complex effects on prevalence depending on infectivity.

## Contribution

It provides a closed-form analytical expression for the epidemic threshold considering burstiness in activity-driven networks, clarifying its dual effects on epidemic prevalence.

## Key findings

- Burstiness lowers the epidemic threshold.
- In low-infectivity systems, burstiness increases infection probability.
- In high-infectivity systems, burstiness weakens epidemic spreading.

## Abstract

We study the effect of heterogeneous temporal activations on epidemic spreading in temporal networks. We focus on the susceptible-infected-susceptible (SIS) model on activity-driven networks with burstiness. By using an activity-based mean-field approach, we derive a closed analytical form for the epidemic threshold for arbitrary activity and inter-event time distributions. We show that, as expected, burstiness lowers the epidemic threshold while its effect on prevalence is twofold. In low-infective systems burstiness raises the average infection probability, while it weakens epidemic spreading for high infectivity. Our results can help clarify the conflicting effects of burstiness reported in the literature. We also discuss the scaling properties at the transition, showing that they are not affected by burstiness.