A Mathematical Model for the Dynamics of Information Spread under the Effect of Social Response

Abstract

Mark Granovetter promoted the threshold model of social behavior in which the acceptance value of an action is determined by the proportion of a population that already accepted it. The model is about an individual embracing an idea once a sufficient number of people embrace it. In this paper, we propose a mathematically accurate population dynamics model based on Granovetter's idea for the spread of information in a population. Individual threshold values with respect to the acceptance of a piece of information are distributed throughout the population ranging from low (easily accepts information) to high (hardly accepts). Results from the mathematical analysis on our model show that critical values exist for initial knower population size, mean and variance of threshold values. These critical values are about the drastic difference in the proportion of the population that end up knowing the information, depending on respective features of the population according to the information spread.