Extended optimal feedback control of information dissemination in online environments

Abstract

In this article, we consider a discrete-time model describing the dissemination of information from one person to another via word-to-mouth transmission or in certain types of online environments such as Facebook, WhatsApp and Twitter. The impact of information sharing is becoming more and more noticeable in the world with the increase of technologies, its potential has become clearer through controlling people’s behavior and opinions. In this paper, we consider control strategies depending on the rate of diffusion of the information, and its effect, by considering feedback controls of the populations’ numbers. We present the first scenario, where we consider the feedback control of the number of sharers and removed individuals, and the second scenario when we propose a feedback control of the three population functions. Based on a discrete version of Pontryagin’s Maximum principle we characterize optimal controls. We provide several numerical examples to compare and discuss the proposed scenarios.