Qualitative Behavior of Solutions to a Mathematical Model of Memes Transmission
Researchers have applied epidemiological models to studythe dynamics of social and behavioral processes, based on the fact that both biological diseases and social behavioral are a result from interactions between individuals. The main feature of the paper is to understand the dynamics of spreading a meme on a large scale in a short time through a chain of communications. In this paper we study a meme transmission model, which is an extension of the deterministic Daley-Kendall model and we analyze it by using stability theory of nonlinear differential equations. The model is based on dividing the population into three disjoint classes of individuals according to their reaction to the meme. We examine the existence of equilibria of the model and investigate their stability using linearization methods, Lyapunov method and Hopf bifurcation analysis. One of the significantresultsinthispaperisfinding conditions that will lead to persistent of memes. Also numerical simulations are used to support the results.
Keywords: Basic reproduction number, Global stability, Hopf bifurcation, Local stability, Lyapunov function, Memes transmission model.
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