# Synergistic Effects in Networked Epidemic Spreading Dynamics

## TL;DR

This paper introduces a rigorous method to analyze how synergistic interactions influence epidemic spreading in complex networks, providing bounds on growth rates and validating results with real social network data.

## Contribution

It develops a novel eigenvalue-based approach to quantify synergy effects in epidemic models on arbitrary networks, advancing beyond previous approximation methods.

## Key findings

- Derived an upper bound on epidemic growth rate considering synergy.
- Validated the theoretical bounds with simulations on real social networks.
- Showed that synergy significantly accelerates epidemic spreading.

## Abstract

In this brief, we study epidemic spreading dynamics taking place in complex networks. We specifically investigate the effect of synergy, where multiple interactions between nodes result in a combined effect larger than the simple sum of their separate effects. Although synergistic effects play key roles in various biological and social phenomena, their analyses have been often performed by means of approximation techniques and for limited types of networks. In order to address this limitation, this paper proposes a rigorous approach to quantitatively understand the effect of synergy in the Susceptible-Infected-Susceptible model taking place in an arbitrary complex network. We derive an upper bound on the growth rate of the synergistic Susceptible-Infected-Susceptible model in terms of the eigenvalues of a matrix whose size grows quadratically with the number of the nodes in the network. We confirm the effectiveness of our result by numerical simulations on empirically observed human and animal social networks.