Stochastic processes with possible random binomial resetting to model the spread of fake news
In recent years, the interest in issues related to the spread of fake news and information security in general has increased significantly. Mainly, the researchers study the dynamics of online news diffusion to warn users against all those situations that can harm the security of their own data. In this work we define two time-inhomogeneous birth-death processes to model (i) the dynamic of a population divided into different compartments and (ii) the diffusion of a single fake rumor in the presence of random binomial resetting. In particular, we first consider a two-dimensional time-inhomogeneous birth-death process to model the time-evolution of fake news in social networks. The two components of the process represent (i) the number of individuals who know the rumor and intend to spread it, and (ii) the number of individuals who have forgotten the rumor previously received. We employ the probability generating function-based approach to obtain the moments and the covariance of the two-dimensional process. Some special cases are considered in which the expected number of individuals who possess the news is equal to suitable sigmoidal curves, which are often adopted in modelling growth phenomena. An application to real data related to the time-diffusion of fake news is also included. Taking into account that in reality the diffusion of fake news can be subject to random denials, we propose a one-dimensional time-inhomogeneous birth-death process representing the number of spreaders. Such process possesses a Richards-type mean and exhibits binomial-type resets at random times. At each reset instant, the process restarts from a state between 0 and the maximum level reached in the previous intertime. This state is randomly chosen through a binomial probability law with parameter p. The number of resets which occur in the time interval [0,t], t>0, is counted by a pure birth process with immigration. We study the probability law and the moments of the time-inhomogeneous birth-death process with random binomial resetting.
Area: CS32 - Stochastic processes with random resetting (Mario Abundo and Antonella Iuliano)
Keywords: Birth-death processes, probability generating function, random resetting, fake-news spreading.
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