Dynamics of the Dissemination of Information in Society under the Conditions of Hype

The process of dissemination of information in society among its possible adherents (individuals who perceive this information) in the presence of mistrust, 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 hype, i.e., the rate of change in the number of adherents over time. A mathematical model of this process, which is the Cauchy problem for a nonlinear ordinary differential equation depending on several numerical parameters, is considered. As a result of the study, the 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 and modeling the described modes of the studied process.