Mathematical Modeling and Optimal Control of Untrue Information : Dynamic SEIZ in Online Social Networks

TL;DR

This paper models rumor spread in online social networks using a specialized SEIR model and develops optimal control strategies to minimize rumor dissemination, supported by theoretical analysis and numerical simulations.

Contribution

It introduces a novel SEIR-based model for rumor spreading and derives optimal control strategies using Pontryagin's maximum principle.

Findings

Optimal controls effectively reduce rumor spread.

Theoretical existence and characterization of controls.

Numerical simulations validate the control strategies.

Abstract

We propose to model the phenomenon of the spread of a rumor in this paper. We manipulate a model that is based on SEIR model that specializes in spreading rumors. In the second part, we introduce a control strategy to fight against the diffusion of the rumor. Our main objective is to characterize the three optimal controls that minimize the number of spreaders, susceptibles who enter and spread the rumor, and skeptics. For that matter, using the maximum principle of Pontryagin, we prove the existence and give characterization of our controls. To illustrate the theoretical results obtained, numerical simulations are given to concretize our approach.