# The Impact of Past Epidemics on Future Disease Dynamics

## TL;DR

This paper develops mathematical models to understand how contact network structures influence long-term dynamics of seasonal diseases with partial immunity, revealing potential impacts on disease persistence and evolution.

## Contribution

It introduces two novel mathematical approaches using percolation theory to model consecutive seasonal outbreaks with different immunity types in contact-heterogeneous populations.

## Key findings

- Contact network structure significantly affects long-term disease dynamics.
- Partially immune populations can limit future outbreaks.
- Disease evolution may be driven by these network-mediated dynamics.

## Abstract

Many pathogens spread primarily via direct contact between infected and susceptible hosts. Thus, the patterns of contacts or contact network of a population fundamentally shapes the course of epidemics. While there is a robust and growing theory for the dynamics of single epidemics in networks, we know little about the impacts of network structure on long term epidemic or endemic transmission. For seasonal diseases like influenza, pathogens repeatedly return to populations with complex and changing patterns of susceptibility and immunity acquired through prior infection. Here, we develop two mathematical approaches for modeling consecutive seasonal outbreaks of a partially-immunizing infection in a population with contact heterogeneity. Using methods from percolation theory we consider both leaky immunity, where all previously infected individuals gain partial immunity, and perfect immunity, where a fraction of previously infected individuals are fully immune. By restructuring the epidemiologically active portion of their host population, such diseases limit the potential of future outbreaks. We speculate that these dynamics can result in evolutionary pressure to increase infectiousness.