The dynamics of the dissemination of information in society during hype

The process of dissemination of information in society consisting of possible adepts (individuals who perceive this information) in the presence of distrust, which means a decrease in the level of interest in assimilating the proposed information, is considered. It is assumed that the degree of influence of distrust is determined by the excitement, i.e. the rate of change in the number of adepts over time. A mathematical model of this process is considered, which is the Cauchy problem for a nonlinear ordinary differential equation depending on several numerical parameters. As a result of the study, conditions are formulated that must be satisfied by the parameters of the problem for its correct solvability. The obtained conditions, in addition, can be used in forecasting, as well as modeling the described modes of the studied process.