Control of information dissemination in online environments: optimal feedback control

Abstract

In this article, we consider a discrete-time model describing the dissemination of information between members of any kind of online structure, it can be shared word-to-mouth via video calls and/ or chat or shares in online environments such as Facebook, WhatsApp and Twitter. The impact of information sharing is becoming more and more noticeable in the world, its potential has become clearer through controlling people’s behavior and influencing their opinions. Thus, depending on the speed of the latter’s spread and its impact, the reaction and measures taken by the state or authorities concerned varies.

In this direction, we chose to use a feedback control function depending on the number of convinced people who share the information at any time. Therefore, the reaction of the control depends on the relevance of this information. We provide sufficient conditions of the existence of such control. And based on a discrete version of Pontryagin’s Maximum Principle we characterize the optimal control. Numerical simulations are carried out to study this scenario before and after the use of our control strategy, accompanied by discussions of results.