Dinâmica da propagação de memes via sistemas com memória

Abstract

The word “meme” refers to anything that can be spread, such as an image, a video, a sound, an idea, a belief, a aesthetic or moral value, etc. Nowadays it is very useful to study the propagation of a meme because of its importance in social media and also its influence on society in general. Such a study is called "memetics", which is relevant because knowing the interest of the agents involved (in the case of this dissertation, the netizens), allows to understand what influences for a meme to be propagated over time, that is, for a meme to have wide reverberation or to be soon forgotten. In the same way that epidemiology concerns timing of infectious diseases occurrences to try to predict whether there will be a epidemic or a endemic and, in these cases, to seek ways to eradicate it, in memetic we study the meme behavior to predict whether its propagation will occur as planned. The difference is that one doesn’t necessarily desire that the meme die over time: in many cases like in marketing, for example, you want it to persist. Many authors use epidemiological models, usually of the SIR or SIRS type, to model the spread of memes, because it is possible to make an analogy between both areas. In the present work, this idea is adressed in detail. In addition, important concepts of the Fractional Calculus are presented to perform a process called “introduction of memory”, that can transform an epidemiological model composed by an Ordinary Differential Equations System into a Fractional Differential Equations System. The objective of this work was to introduce memory in an epidemiological model used in memetics and to evaluate if this new model describes with more precision the behavior of a meme popularity in relation to the real data, available in Google Trends tool. This new model was analyzed qualitatively and numerically, studying its effectiveness to describe the propagation of a meme from the comparison with its classic version. With this, we contribute with the memetics literature, proposing a new type of model to describe the propagation of memes, a model with memory effect, since, until the moment, the models used are classical epidemiological, without memory. Therefore, we show that the process of memory introduction is an option of improvement for the model and, consequently, for the study of the propagation of memes.