  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 any
pair of nodes in a network is non-negative for the Markovian SIS and SIR
epidemic models. The arguments used to obtain this result rely strongly on the
graphical construction of the stochastic process, as well as the FKG
inequality. In this note we show that although the approach used by the authors
applies to the SIS model, it cannot be used for the SIR model as stated in
their work. In particular, we observe that monotonicity in the process is
crucial for invoking the FKG inequality. Moreover, we provide an example of
simple graph for which the nodal infection in the SIR Markovian model is
negatively correlated.
