The persistence of information communicated between humans is difficult to measure as it is affected by many features. This paper presents an approach to computationally model the cognitive processes of information sharing to describe persistence or extinction of communication in Twitter over time. The adaptive mental network model explains, for example, how an individual can experience information overflow on a topic, and how this affects the sharing of information. Parameter tuning by Simulated Annealing is used to identify characteristics of the network model that fit to empirical data from Twitter. The data collected is related to the independentism in Catalunya, Spain, which is considered a global issue with repercussion in Europe.