In this article, we introduce the model describing the interaction and mutual influence of agents in a social network. The interactions in the model are represented by the spreading of two opposite types of activity. Agents have beliefs of different strength and two activation thresholds of different heights. Depending on beliefs agents choose the type of activity which they consider as their own and excite only by their own type, whichever of two activation thresholds is exceeded. Agents may have different sensitivities to the two types of external influence. The main properties of agents and principles of activity spreading are defined. The classification of agents according to their parameters is represented. The results of computational experiments are demonstrated.