The impact of effective participation in stopping misinformation: an approach based on branching processes

The emergence of research focused to understand the spreading and impact of disinformation is increasing year over year. Most times, the purpose of those who start the spreading of information intentionally false and designed to cause harm is in catalyzing its fast transformation into misinformation, which is the false content shared by people who do not realize it is false or misleading. Our interest is in discussing the role of people who decide to adopt an active role in stopping the propagation of an information when they realize that it is false. For this, we formulate two simple probabilistic models to compare misinformation spreading in the possible scenarios for which there is a passive or an active environment of aware individuals. With aware individuals we mean those individuals who realize that a given information is false or misleading. In the passive environment we assume that if one of an aware individual is exposed to the misinformation then he/she will not spread it. In the active environment we assume that if one of an aware individual is exposed to the misinformation then he/she will not spread it but also he/she will stop the propagation to other individuals from the individual who contacted him/her. We appeal to the theory of branching processes to analyse propagation in both scenarios and we discuss the role and the impact of effective participation in stopping misinformation. We show that the propagation reduces drastically provided we assume an active environment, and we obtain theoretical and computational results to measure such a reduction, which in turns depends on the proportion of aware individuals and the number of potential contacts of each individual which is assumed to be random.