Spreading Rumors and External Actions.

In this paper, we consider a population of a social network in which a fake news propagates and divides it into four categories: ignorants, spreaders, stiflers who accept the rumor, and stiflers who oppose the rumor. Starting from a SIR type model describing the propagation of e-rumor, we modify it by adding some external actions and control them in order to reduce the spread of a bad information. To carry out this investigation, we use known facts from optimal control theory. Numerical simulations illustrate the efficiency of the obtained control strategy.