A Consideration of Information Diffusion on the Social Networking System Based on irSIR Model

Abstract

In the present work, we shall explore several fundamental properties of irSIR model for the information diffusion on SNS leading an implicit analytical solution of the state variables in similar manner with SIR model for the infectious disease. From the present simulation results, it will be elucidated that there may exist an analogy between the characteristics of the final size equations for SIR and irSIR models. Then the dependence of the final non-active users derived from the final size equation on the information diffusion rate and the maximum values of the active users will be examined in detail in connection with the existence of a peak behavior of the active users. Furthermore the effect of the time-dependent information diffusion rate will be investigated from viewpoints of the final values of the non-user population as well as the profiles of the active user population on SNS. Finally we shall present an example of comparison with the practical data for the active users on SNS.