Described is a system for predicting temporal evolution of contagions on multilayer networks. The system determines a functional epidemic threshold for disappearance of a contagion on a multilayer network model according to a score value s=λβ/δ, where λ corresponds to an adjacency matrix of the first layer of the multilayer network model, β represents a spread rate of the contagion, and δ represents a recovery rate. A prediction of future behavior of the contagion on the multilayer network model using the functional epidemic threshold is output and utilized to inform decisions regarding connectivity within a multilayer network in order to prevent spread of the contagion on a multilayer network.