A non-absorbing SIR stochastic lattice gas model on hybrid lattices

TL;DR

This study introduces a stochastic lattice gas SIR model on hybrid lattices, using Monte Carlo simulations and percolation theory to analyze critical thresholds and universality classes of disease spread.

Contribution

It presents a novel hybrid lattice approach for the SIR model, combining percolation theory and finite-size scaling to estimate critical parameters.

Findings

Estimated critical thresholds for disease spread on hybrid lattices.

Determined the universality class of the non-absorbing SIR model.

Analyzed cluster size distributions to understand epidemic dynamics.

Abstract

In this paper, we perform Monte Carlo calculations to study the critical behavior of the spread of infectious diseases through a novel approach to the SIR epidemiological model. A stochastic lattice gas version of the model was applied on hybrid lattices which, in turn, are generated from typical square lattices when inserting a connection probability $p$ that a given lattice site has both first- and second-nearest neighbor interactions. By combining percolation theory and finite-size scaling analysis, we estimate both the critical threshold and leading critical exponent ratios of the non-absorbing SIR model in different cases of hybrid lattices. An analysis of the average size of the percolating cluster and the size distribution of non-percolating clusters of recovered individuals was carried out to determine the universality class of the model.