Epidemic processes on random graphs

Our goal is to  analyze epidemic processes   on random graphs. In particular, as first step, we have considered the Bootstrap percolation process on the Stochastic Block Model,  a natural extension of the Erdös–Rényi random graph that allows us to represent the “community structure” observed in many real systems. In the SBM the nodes are partitioned into subsets, which represent the different communities, and pairs of nodes are independently connected with a probability that depends on the communities they belong to. Under suitable assumptions on the system parameters, we prove the existence of a sharp phase transition for the final number of active nodes and characterize the sub-critical and the super-critical regimes in terms of the number of initially active nodes, which are selected uniformly at random in each community.

ERC Sector:

  • PE7_3 Simulation engineering and modelling

Keywords:

  • Stochastic Processes

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