Dynamic behaviour of competing memes' spread with alert influence in multiplex social-networks

This study elucidates the dynamic behaviour of the two competing mutually exclusive epidemic (meme) spreading model with the alert of memes over multiplex social networks. Each meme spreads over a distinct contact networks (CN1,CN2) of an undirected multiplex social network. The behavioural responses of agents (alerts) to the spread of competing memes is disseminated through information dissemination network (IDN). Here, IDN has the same nodes but different links with respect to the respective CNi(i=1,2). The analytical treatment of this model is analysed through the mean field approximation of the epidemic process. Also, it has been shown through numerical illustrations that a node in the alert state is less probable to become infected than a node in the susceptible state. Moreover, co-existence of both the memes, the survival threshold, the absolute dominance threshold of the two competitive memes and the alert threshold for minimizing the severity of meme spread are analytically explored and numerically illustrated.