A study of the influence of the mobility on the phase transitions of the synchronous SIR model

TL;DR

This study investigates how mobility and dilution influence the critical immunization rate in a synchronous SIR epidemic model, revealing that increased mobility raises the immunization threshold while dilution decreases it logarithmically.

Contribution

It introduces a detailed analysis of the combined effects of dilution and mobility on epidemic thresholds using time-dependent Monte Carlo simulations.

Findings

Critical immunization rate decreases with dilution logarithmically.

Mobility increases the critical immunization rate.

Mobility mitigates the effects of dilution on epidemic thresholds.

Abstract

By using an appropriate version of the synchronous SIR model, we studied the effects of dilution and mobility on the critical immunization rate. We showed that, by applying time-dependent Monte Carlo (MC) simulations at criticality, and taking into account the optimization of the power law for the density of infected individuals, the critical immunization necessary to block the epidemic in two-dimensional lattices decreases as dilution increases with a logarithmic dependence. On the other hand, the mobility minimizes such effects and the critical immunizations is greater when the probability of movement of the individuals increases.