Nodal infection in Markovian susceptible-infected-susceptible and susceptible-infected-removed epidemics on networks are non-negatively correlated

By invoking the famous Fortuin, Kasteleyn, and Ginibre (FKG) inequality, we prove the conjecture that the correlation of infection at the same time between any pair of nodes in a network cannot be negative for (exact) Markovian susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemics on networks. The truth of the...

Second-order mean-field susceptible-infected-susceptible epidemic threshold