On the effectiveness of imposing restrictive measures in a graded Self-Organized Criticality epidemic spread model The case of COVID-19.

The scope of this work is to serve as a guiding tool against subjective estimations on real pandemic situations (mainly due to the inability to acquire objective real data over whole populations). The previously introduced model of closed self-organized criticality (SOC), is adapted in the case of a virus-induced epidemic. In this version this physical model can distinguish the virus spread according to the virus aggressiveness. The study presented, highlights the critical value of virus density over a population. For low values of the initial virus density (lower than the critical value) it is proved that the virus-diffusion behavior is safe and quantitatively similar to usual real epidemical data. However, it is revealed that very close to the critical point, the critical slowing-down (CSD) phenomenon, introduced by the theory of critical phenomena, emerges, leading to a tremendous increase of both the percentage of active carriers and the duration of the epidemic. A behavior of the epidemic obeying to a second order phase transition, also occurs. For virus density values higher than the critical value, the epidemic duration becomes extremely prolonged. Additionally, the effect of the closed system population size revealed interesting properties. All these results, together with an investigation of the effectiveness of applying physical contact restriction measures, document scientifically their worthiness, while they also demonstrate the limits for which herd immunity holds safely. Finally, the model has been compared against real epidemic data in the case of Greece, which imposed restrictive measures consistently and in time.