Controlling information diffusion or propagation through social networks can be challenging when dealing with information related to a subject of highest interest for the public. The complexity level of control depends on subject importance, users’ dynamic, and network structure. When two published messages or pieces of information share the same interest for targeted readers, analyzing their propagation dynamic for control and prediction is of great interest. This article proposes to model, based on a modified interactive system with Holling type functional response, the dynamic of underlying relationship between two broadcasted messages traveling through social networks media. We showed in the qualitative analysis of the proposed model that system could be stable at certain conditions, and the model-system exhibited very rich dynamical behavior. Numerical simulation results validated theoretical analyses and suggested adapting resources harvesting and assimilation efficiency for an authoritative message to stabilize the system and control the dissemination of information in a closed environment.
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