  Models of epidemic spreading on complex networks have attracted great
attention among researchers in physics, mathematics, and epidemiology due to
their success in predicting and controlling scenarios of epidemic spreading in
real-world scenarios. To understand the interplay between epidemic spreading
and the topology of a contact network, several outstanding theoretical
approaches have been developed. An accurate theoretical approach describing the
spreading dynamics must take both the network topology and dynamical
correlations into consideration at the expense of increasing the complexity of
the equations. In this short survey we unify the most widely used theoretical
approaches for epidemic spreading on complex networks in terms of increasing
complexity, including the mean-field, the heterogeneous mean-field, the quench
mean-field, dynamical message-passing, link percolation, and pairwise
approximation. We build connections among these approaches to provide new
insights into developing an accurate theoretical approach to spreading dynamics
on complex networks.
