Qualitative Behavior of Solutions to a Mathematical Model of Memes Transmission

Abstract

License, which perm its unrestricted use, distribution, and reproduction in any m edium , provided the original work is prop erly cited. AbstractResearchers have applied epidemiological models to study the 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 significant results in this paper is finding conditions that will lead to persistent of memes. Also numerical simulations are used to support the results.

Numerical simulations for stochastic meme epidemic model

“…On the other hand, Thompson explored the dynamics of rumor spread in a chat room [12]. Al-Amoudi et al quantitatively analyzed a meme propagation model of a constant meme [13]. Rumor is essential to forming public communication, and its transmission has important influence on the population or society.…”

“…As a result, higher authorities (policy makers) can scientifically implement or suggest safety measures. Lots of studies have presented various models of meme transmission dynamics [11][12][13].…”

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“…The number of passive active contacts on proportion to the product of ua S and ua I of these contacts, 1  fraction of individuals will develop active interest towards intellectual activity. Therefore, the rate of change in the susceptible under-aged population are given by…”