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Off-lattice SIR models are constructed on continuum percolation clustersdefined on the Ginibre point process (GPP) and on the Poisson point process(PPP). The static percolation transitions in the continuum percolation modelsas well as the infection-spreading transitions in the SIR models, which areregarded as the dynamic percolation transitions, are enhanced in the GPP-basedmodel compared with the PPP-based model. This enhancement is caused byhyperuniformity of the GPP. On the other hand, in the extinction phase ofinfection on the phase diagram, a wide parameter region is determined in whichformation of infection clusters is suppressed in the GPP-based model comparedwith the PPP-based model. We think that the PPP approximates a disorderedconfiguration of individuals and the GPP does a configuration of citizensadopting a strategy to keep social distancing in a city in order to avoidcontagion. The suppression of infection clusters observed in the GPP-basedmodel will prove that such a strategy is effective when the infectivity isrelatively small.

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