  Recently, research that focuses on the rigorous understanding of the relation
between simulation and/or exact models on graphs and approximate counterparts
has gained lots of momentum. This includes revisiting the performance of
classic pairwise models with closures at the level of pairs and/or triples as
well as effective-degree-type models and those based on the probability
generating function formalism. In this paper, for a fully connected graph and
the simple $SIS$ (susceptible-infected-susceptible) epidemic model, a novel
closure is introduced. This is done via using the equations for the moments of
the distribution describing the number of infecteds at all times combined with
the empirical observations that this is well described/approximated by a
binomial distribution with time dependent parameters. This assumption allows us
to express higher order moments in terms of lower order ones and this leads to
a new closure. The significant feature of the new closure is that the
difference of the exact system, given by the Kolmogorov equations, from the
solution of the newly defined approximate system is of order $1/N^2$. This is
in contrast with the $\mathcal{O}(1/N)$ difference corresponding to the
approximate system obtained via the classic triple closure.
