Stability Analysis of a Variable Meme Transmission Model

Memes propagation is a usual form of social interaction. Understanding the dynamics of memes transmission enables one to find the conditions that leads to persistence or disappearance of memes. In this paper we analyze qualitatively a mathematical model of variable meme transmission. Two equilibrium points of the model are examined: meme free equilibrium and meme existence equilibrium. The reproduction number R? that generates new memes is found. Local and global stability of the equilibrium points are explored. Finally, we support our results using numerical simulations. Keywords: Basic reproduction number, Global stability, Local stability, Liapunov function, Variable memes transmission model.