# Adaptive Susceptibility and Heterogeneity in Contagion Models on Networks

## TL;DR

This paper introduces a generalized network epidemic model, SIRI, accounting for adaptive susceptibility and heterogeneity, revealing complex dynamics like bistability and resurgent epidemics, with implications for control strategies.

## Contribution

It develops a novel SIRI model incorporating adaptive susceptibility and heterogeneity, providing necessary and sufficient conditions for various epidemic regimes, including bistability.

## Key findings

- Identification of four dynamic regimes: infection-free, epidemic, endemic, bistable.
- Bistable regime can cause rapid epidemic resurgence after apparent control.
- Model aids in designing effective containment strategies.

## Abstract

Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been used to understand and control both transient and steady-state behaviors. Typically it is assumed that after recovery from an infection, every agent will either return to its original susceptible state or acquire full immunity to reinfection. We study the network SIRI (Susceptible-Infected-Recovered-Infected) model, an epidemic model for the spread of contagious processes on a network of heterogeneous agents that can adapt their susceptibility to reinfection. The model generalizes existing models to accommodate realistic conditions in which agents acquire partial or compromised immunity after first exposure to an infection. We prove necessary and sufficient conditions on model parameters and network structure that distinguish four dynamic regimes: infection-free, epidemic, endemic, and bistable. For the bistable regime, which is not accounted for in traditional models, we show how there can be a rapid resurgent epidemic after what looks like convergence to an infection-free population. We use the model and its predictive capability to show how control strategies can be designed to mitigate problematic contagious behaviors.