MO412

On an uncorrelated network with degree distribution P(k), the epidemic threshold for an SIR-type process depends not on the mean degree ⟨k⟩ alone but on the ratio ⟨k²⟩/⟨k⟩. For a large scale-free network with degree exponent 2 < α ≤ 3, what does this imply about the threshold transmissibility? a. The very large second moment ⟨k²⟩ drives the critical transmissibility toward very small values, so the network has effectively almost no epidemic threshold b. ⟨k²⟩/⟨k⟩ converges to ⟨k⟩, recovering the homogeneous threshold exactly c. The threshold rises with network size because hubs absorb infection d. The threshold equals 1/⟨k⟩ independently of the variance of the degree distribution e. None of the above Original idea by: João Pedro Carolino Morais