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