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

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.Comment: 24 pages, 12 figure

Dynamic message-passing equations for models with unidirectional dynamics

Understanding and quantifying the dynamics of disordered out-of-equilibrium models is an important problem in many branches of science. Using the dynamic cavity method on time trajectories, we construct a general procedure for deriving the dynamic message-passing equations for a large class of models with unidirectional dynamics, which includes the zero-temperature random field Ising model, the susceptible-infected-recovered model, and rumor spreading models. We show that unidirectionality of the dynamics is the key ingredient that makes the problem solvable. These equations are applicable to single instances of the corresponding problems with arbitrary initial conditions, and are asymptotically exact for problems defined on locally tree-like graphs. When applied to real-world networks, they generically provide a good analytic approximation of the real dynamics.Comment: Final versio

A dynamic model for rumors spread with communication costs

In this article we start by reviewing some mathematical models for the spreadof rumors. We mention some studies carried out using graphs, stochastic andprobabilistic models and also some epidemic like and evolutionary models.We analyze a repeated game with the replicator dynamics for the spread ofa rumor in a society conformed by an informed population about a rumorthat communicates the rumor to another population. The rumor can becommunicated in its original form or with the opposite content. We comparethe results obtained when only social costs are involved with the case whenalso communication costs are present.Fil: Accinelli , Elvio. Universidad Autónoma de San Luis Potosí; MéxicoFil: Quintas, Luis Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaFil: Muñiz, Humberto. Universidad Autónoma de San Luis Potosí; MéxicoFil: Rosenstock, Nicole. Universidad Autónoma de San Luis Potosí; Méxic