A model for diffusion of mulucomponent information

Abstract

The epidemic model of diffusion of news (or disease) is generalized to describe the diffusion of a multi‐component information. The multivaluedness of information in our model arises due to the large number (k) of constituent components or items of the information in question. When the different components of information are assumed to bear no hierarchy, the master equation of the model contains an intractably large number of variables (2 ^k ). The dynamics of the model, however, displays some simplifying features, one of which is the conservation of homogeneity of distribution of population over the different information vectors (in the sense defined in the text). The homogenized version of the model is found to be numerically tractable. The growth curves for large k continue to display sigmoid shapes, but with large ‘saturation times’. The dependence of ‘saturation time’ (i.e. the time required for spread of all the information in almost the entire population) on various parameters of the model, for uniform initial distributions, is numerically investigated. The ‘saturation time’ is found to vary inversely with the intensity of interaction (ß) and the size of population (N), as expected. An important numerical feature that emerges is that the ‘saturation time’ seems to be in linear proportion to the number of information items (k).

Key words:

• Diffusion of multicomponent information
• homogeneous and non‐homogeneous initial conditions
• homogenized model
• growth curves
• saturation time