# Epidemic Spreading on Activity-Driven Networks with Attractiveness

## TL;DR

This paper analyzes how the interplay of activity and attractiveness in time-varying networks influences epidemic spreading, deriving thresholds and confirming findings through simulations, revealing the impact of heterogeneity and correlations.

## Contribution

It introduces a generalized activity-driven network model incorporating attractiveness, deriving epidemic thresholds analytically for various distributions and correlations.

## Key findings

- Heterogeneous attractiveness affects contagion dynamics.
- Positive correlations facilitate spreading, negative correlations hinder it.
- Analytical results are validated by numerical simulations.

## Abstract

We study SIS epidemic spreading processes unfolding on a recent generalisation of the activity-driven modelling framework. In this model of time-varying networks each node is described by two variables: activity and attractiveness. The first, describes the propensity to form connections. The second, defines the propensity to attract them. We derive analytically the epidemic threshold considering the timescale driving the evolution of contacts and the contagion as comparable. The solutions are general and hold for any joint distribution of activity and attractiveness. The theoretical picture is confirmed via large-scale numerical simulations performed considering heterogeneous distributions and different correlations between the two variables. We find that heterogeneous distributions of attractiveness alter the contagion process. In particular, in case of uncorrelated and positive correlations between the two variables, heterogeneous attractiveness facilitates the spreading. On the contrary, negative correlations between activity and attractiveness hamper the spreading. The results presented contribute to the understanding of the dynamical properties of time-varying networks and their effects on contagion phenomena unfolding on their fabric.