Continuum percolation and stochastic epidemic models on Poisson and Ginibre point processes

• Published in: Physica A Vol. 581; p. 126191
• Main Authors: Katori, Machiko, Katori, Makoto
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-11-2021
• Subjects: Continuum percolation model; Ginibre point process; Infection clusters; Poisson point process; SIR model; Social distancing; Infection clusters; Poisson point process; Social distancing; SIR model; Ginibre point process; Continuum percolation model
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2021.126191

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.
•New models of 2d continuum percolation and infection processes are proposed.•The models are based on the Poisson point process and the Ginibre point process (GPP).•First report of the critical filling factor for the continuum percolation on the GPP.•A new phenomenon of suppression of infection clusters found in the GPP-based models.