# Rejection-Based Simulation of Stochastic Spreading Processes on Complex Networks

## TL;DR

This paper introduces a rejection-based simulation method for stochastic spreading processes on complex networks, significantly improving efficiency and scalability while maintaining statistical accuracy.

## Contribution

A novel simulation approach combining event-based simulation and rejection sampling, outperforming existing methods in speed and scalability for large networks.

## Key findings

- Method reduces simulation run-time compared to state-of-the-art techniques.
- Scales efficiently to large, realistic network sizes.
- Maintains statistical equivalence with traditional simulation methods.

## Abstract

Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest. In this work we consider the wide-spread compartment model where each node is in one of several states (or compartments). Nodes change their state randomly after an exponentially distributed waiting time and according to a given set of rules. For networks of realistic size, even the generation of only a single stochastic trajectory of a spreading process is computationally very expensive. Here, we propose a novel simulation approach, which combines the advantages of event-based simulation and rejection sampling. Our method outperforms state-of-the-art methods in terms of absolute run-time and scales significantly better, while being statistically equivalent.