# Asynchronous SIR model on Two-Dimensional Quasiperiodic Lattices

## TL;DR

This paper investigates the critical behavior of the asynchronous SIR epidemic model on quasiperiodic lattices using a novel algorithm, revealing that it belongs to the 2D percolation universality class and quasiperiodic order is irrelevant.

## Contribution

It introduces a Newman-Ziff based algorithm for simulating SIR on non-periodic lattices and analyzes its critical properties.

## Key findings

- System exhibits 2D percolation universality class.
- Quasiperiodic order does not affect critical behavior.
- Identifies epidemic threshold and cluster properties.

## Abstract

We considered the Asynchronous SIR (susceptible-infected-removed) model on Penrose and Ammann-Beenker quasiperiodic lattices, and obtained its critical behavior by using Newman-Ziff algorithm to track cluster propagation by making a tree structure of clusters grown at the dynamics, allowing to simulate SIR model on non-periodic lattices and measure any observable related to percolation. We numerically calculated the order parameter, defined in a geographical fashion by distinguish between an epidemic state, characterized by a spanning cluster formed by the removed nodes and the endemic state, where there is no spanning cluster. We obtained the averaged mean cluster size which plays the role of a susceptibility, and a cumulant ratio defined for percolation to estimate the epidemic threshold. Our numerical results suggest that the system falls into two-dimensional dynamic percolation universality class and the quasiperiodic order is irrelevant, in according to results for classical percolation.