  The most studied continuum percolation model in two dimensions is the Boolean
model consisting of disks with the same radius whose centers are randomly
distributed on the Poisson point process (PPP). We also consider the Boolean
percolation model on the Ginibre point process (GPP), which is a typical
repelling point process realizing hyperuniformity. We think that the PPP
approximates a disordered configuration of individuals, while the GPP does a
configuration of citizens adopting a strategy to keep social distancing in a
city in order to avoid contagion. We consider the SIR models with contagious
infection on supercritical percolation clusters formed on the PPP and the GPP.
By numerical simulations, we studied dependence of the percolation phenomena
and the infection processes on the PPP- and the GPP-underlying graphs. We show
that in a subcritical regime of infection rate the PPP-based models show
emergence of infection clusters on clumping of points which is formed by
fluctuation of uncorrelated Poissonian statistics. On the other hand, the
cumulative numbers of infected individuals in processes are suppressed in the
GPP-based models.
