# The dynamics of two-stage contagion

## TL;DR

This paper investigates two-stage social contagion models, revealing complex nonlinear phenomena like bistability and oscillations, which could explain intricate social dynamics beyond classical epidemiological models.

## Contribution

It introduces and analyzes two-stage contagion models with demographic turnover, uncovering nonlinear behaviors absent in traditional models.

## Key findings

- Identification of bistability and critical transitions
- Discovery of endogenous oscillations and excitability
- Analysis of bifurcations through analytical and numerical methods

## Abstract

We explore simple models aimed at the study of social contagion, in which contagion proceeds through two stages. When coupled with demographic turnover, we show that two-stage contagion leads to nonlinear phenomena which are not present in the basic `classical' models of mathematical epidemiology. These include: bistability, critical transitions, endogenous oscillations, and excitability, suggesting that contagion models with stages could account for some aspects of the complex dynamics encountered in social life. These phenomena, and the bifurcations involved, are studied by a combination of analytical and numerical means.