The article discusses the SIHR  mathematical model, which describes the process of spreading misinformation (fake) on social networks. A distinctive feature of the study is the consideration of a group of “hibernating” users who temporarily stop exchanging information but can subsequently resume activity thanks to memory mechanisms. A series of numerical experiments was conducted to assess the impact of memory parameters and failure frequency on the dynamics of the process. For various model parameters, graphs of the dependence of group density on time were constructed. The results show that the most effective way to combat misinformation is to increase the dissemination failure rate. It was also found that the processes of spontaneous and forced information recovery significantly prolong the life of a rumor on the network, and the spontaneous recovery parameter determines the final state of the system.