# Multiple peaks patterns of epidemic spreading in multi-layer networks

## TL;DR

This paper demonstrates that multi-peak epidemic spreading patterns are characteristic of multi-layer networks, arising from delays and degree differences between layers, with an edge-based theory explaining the phenomena.

## Contribution

It reveals the origin of multiple epidemic peaks in multilayer networks due to delays and degree disparities, and develops a theoretical framework to explain these patterns.

## Key findings

- Multiple peaks are linked to delays in spreading between layers.
- Degree distribution differences influence epidemic peak patterns.
- Edge-based theory accurately predicts numerical results.

## Abstract

The study of epidemic spreading on populations of networked individuals has seen recently a great deal of significant progresses. A common point of all past studies is, however, that there is only one peak of infected density in each single epidemic spreading episode. At variance, real data from different cities over the world suggest that, besides a major single peak trait of infected density, a finite probability exists for a pattern made of two (or multiple) peaks. We show that such a latter feature is fully distinctive of a multilayered network of interactions, and reveal that actually a two peaks pattern emerges from different time delays at which the epidemic spreads in between the two layers. Further, we show that essential ingredients are different degree distributions in the two layers and a weak coupling condition between the layers themselves. Moreover, an edge-based theory is developed which fully explains all numerical results. Our findings may therefore be of significance for protecting secondary disasters of epidemics, which are definitely undesired in real life.