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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 $$(CN_1,CN_2)$$ ( C N 1 , C N 2 ) of an undirected multiplex social network. The behavioural responses of agents (alerts) to the spread of competing memes is disseminated...