Mean-Field Dynamics of Inter-Switching Memes Competing over Multiplex Social Networks

This letter characterizes the intertwined behavior of a susceptible-infected-susceptible epidemic model involving multiple mutually exclusive memes, each competing over distinct contact planes of an undirected multi-layer social network, with the possibility of inter-switching. Based on the mean-field theory, we contrast and derive closed-form analytical expressions for the steady-state thresholds that govern the transitions between extinction, co-existence, and absolute dominance of the inter-switchable memes. Moreover, a non-linear optimization formulation is presented to determine the optimal budget allocation for controlling the switching rates to a particular co-existing meme. Validated by simulations, the impact of switching on the tipping thresholds and their implications in reality are demonstrated using data extracted from online social networks.