On the control of information and their objectives: multi-information model

Abstract

In this article, we propose a new multi-information discrete-time model describing the dissemination of several pieces of information from one person to another, it can be shared word-to-mouth or in certain types of online environments such as Facebook, WhatsApp, and Twitter. First, we present the model and the different possible interactions between its compartments. Based on the fact that there is always an objective behind the dissemination of information, in the modeling process we distinguish between information that shares the same purpose and information that shares an opposite objective to study their mutual effect. To do this, we divide the entire target population into three groups for each piece of information and consider the possible transition between these groups. We suggest an optimal control strategy that helps to eliminate target information. We use a discrete version of Pontryagin’s Maximum Principle to characterize optimal controls. Numerical simulations are carried out to illustrate the different effects and to show the efficiency of the proposed approach.