Information diffusion in sub-communities

We develop dynamic equations that describe the dissemination of knowledge in sub-communities, which represent various groups in a community. Knowledge is represented by a set of concepts. With respect to each concept, the community is divided into two parties: the cognoscenti, who have already produced references to the concept, and the dilettanti, who have not yet produced a reference to the concept. The obtained equations take into account the birth-death processes, and determine the dynamic distribution of ages in the sub-communities. In the case of natural community, such equations with the values in the scales of human life, specify real distribution of the ages; however, in the case of social networks and corresponding communities and groups, the birth-death processes stand for the processes of joining the communities, active communication, and leaving the communities or interrupting communication in them. We study the mutual impact of the dynamics of the concepts and groups of concepts on one hand, and the dynamics of the sub-communities on the other hand. We show that the long-term dynamics of the concepts and sub-communities depend on communication resources of the community, capabilities of concepts' comprehension, and distribution of ages. Higher values of these three parameters allow more flexibility in choosing a policy of allocating the communication resource over the set of concepts. Given the three parameters, the community may develop a policy formulated in terms of the informational measure of the set of concepts, as illustrated in the presentation.