Finite symmetries in agent-based epidemic models

TL;DR

This paper introduces an algorithm leveraging permutation symmetries to optimize the computation of agent-based epidemic models by reducing the transition matrix to a block diagonal form, thus improving efficiency.

Contribution

The paper presents a novel symmetry-based algorithm that significantly enhances the computational efficiency of agent-based epidemic simulations.

Findings

Transition matrix becomes block diagonal using permutation symmetries

Computational times are reduced by restricting to a single permutation eigenvalue sector

Algorithm improves scalability of epidemic modeling simulations

Abstract

We present an algorithm which explores permutation symmetries to describe the time evolution of agent-based epidemic models. The main idea to improve computation times relies on restricting the stochastic process to one sector of the vector space, labeled by a single permutation eigenvalue. In this scheme, the transition matrix reduces to block diagonal form, enhancing computational performance.