Generalized model of information spreading in continuous time

Abstract

The diffusion of information or spreading of rumours is a social phenomenon and plays a significant role in a daily life. Rumours play a very important role in social life and have existed as a social fact since ancient times. The rumour model explains the spread of rumours and serves as a tool for understanding this social phenomenon. Rumours in economics have become more intensively discussed and investigated in recent decades. There are examples of rumour dynamics based on communication and exchange at auctions, in the stock markets and during trading. These backgrounds and motivations give the basis for a mathematical model of the diffusion of information or the spreading of rumours. We give a model that is a generalization of the classical Maki—Thompson model and the stochastic Daley—Kendall model of rumour spreading using the probability approach. A new parameter is suggested for the probability of rumour spreading. The generalized model is formulated and is considered in continuous time. The process of spreading rumours is described by a system of linear differential equations. The general solution for dynamics of spreading of rumours is constructed. Refs 13. Figs 2. Tables 2.