Модель динаміки поведінки агентів соціальних мереж

Abstract

Побудова математичних моделей поширення інформації в соціальних мережах є досить складною, але перспективним завданням, оскільки математичні моделі взагалі й моделі соціальних мереж зокрема дозволяють не тільки глибше усвідомити взаємозв’язки між досліджуваними об’єктами, але й передбачати та певною мірою керувати поведінкою досліджуваного процесу. У цій роботі запропонована модель динаміки поведінки агентів соціальних мереж, яка поєднує елементи SIR-моделей та порогових моделей. Модель дає змогу охарактеризувати функції 𝑆𝑆(𝑡𝑡),𝐴𝐴(𝑡𝑡),𝑅𝑅(𝑡𝑡), які відповідно ілюструють динаміку поширення інформації в мережі та визначають частку сприйня-тливих, залучених та відновлених індивідів у момент часу 𝑡𝑡. Thanks to rapid development of Internet technologies, information dissemination in the modern world has undergone significant changes. Large groups of people have gained relatively easy access to any type of information and, in addition, can themselves disseminate significant volumes of information through social networks. Thus, today people have to interact in conditions of information overload. Timely access to reliable information can significantly contribute to the conscious adoption of certain decisions. On the other hand, rapid spread of erroneous or frankly false information can lead to social instability. Due to the above factors, the study of the spread of information in social networks, as well as the study of its impact on specific individuals and society as a whole, is currently extremely relevant. Building mathematical models of the spread of information in social networks is a rather difficult but promising task, since mathematical models in general and models of social networks in particular allow not only to more deeply understand the relationships between the objects under study, but also to predict and to some extent control the behavior of the process under study. This paper proposes a model of the dynamics of the behavior of social network agents, which combines elements of SIR models and threshold models. The model allows us to characterize functions S(t), A(t), R(t), which, respectively, illustrate the dynamics of information dissemination in the network and determine the proportion of susceptible, involved and recovered individuals at time t. The constructed model combines properties of susceptible-adopted-recovered and threshold models. When determining thresholds, it is assumed that all fragments of information that have reached an individual in a susceptible state are perceived by him as equivalent. However, in reality, most likely, fragments of information received from different actors will have different significance for the individual. Therefore, taking into account the characteristics of both the network and the individual in a susceptible state when constructing a threshold model may become the goal of further research.