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Cator and Van Mieghem [Cator E, Van Mieghem P., Phys. Rev. E 89, 052802(2014)] stated that the correlation of infection at the same time between anypair of nodes in a network is non-negative for the Markovian SIS and SIRepidemic models. The arguments used to obtain this result rely strongly on thegraphical construction of the stochastic process, as well as the FKGinequality. In this note we show that although the approach used by the authorsapplies to the SIS model, it cannot be used for the SIR model as stated intheir work. In particular, we observe that monotonicity in the process iscrucial for invoking the FKG inequality. Moreover, we provide an example ofsimple graph for which the nodal infection in the SIR Markovian model isnegatively correlated.

physical review. e

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