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Binary-state dynamics (such as the susceptible-infected-susceptible (SIS)model of disease spread, or Glauber spin dynamics) on random networks areaccurately approximated using master equations. Standard mean-field andpairwise theories are shown to result from seeking approximate solutions of themaster equations. Applications to the calculation of SIS epidemic thresholdsand critical points of non-equilibrium spin models are also demonstrated.

High-accuracy approximation of binary-state dynamics on networks