Spreading and Suppression of Infection Clusters on the Ginibre Continuum Percolation Clusters

Abstract: Off-lattice SIR models are constructed on continuum percolation clusters defined on the Ginibre point process (GPP) and on the Poisson point process (PPP). The static percolation transitions in the continuum percolation models as well as the infection-spreading transitions in the SIR models, which are regarded as the dynamic percolation transitions, are enhanced in the GPP-based model compared with the PPP-based model. This enhancement is caused by hyperuniformity of the GPP. On the other hand, in the extinction phase of infection on the phase diagram, a wide parameter region is determined in which formation of infection clusters is suppressed in the GPP-based model compared with the PPP-based model. We think that the PPP approximates a disordered configuration of individuals and the GPP does a configuration of citizens adopting a strategy to keep social distancing in a city in order to avoid contagion. The suppression of infection clusters observed in the GPP-based model will prove that such a strategy is effective when the infectivity is relatively small.