Empirical study and modeling of human behaviour dynamics of comments on Blog posts

On-line communities offer a great opportunity to investigate human dynamics, because much information about individuals is registered in databases. In this paper, based on data statistics of online comments on Blog posts, we first present an empirical study of a comment arrival-time interval distribution. We find that people interested in some subjects gradually disappear and the interval distribution is a power law. According to this feature, we propose a model with gradually decaying interest. We give a rigorous analysis on the model by non-homogeneous Poisson processes and obtain an analytic expression of the interval distribution. Our analysis indicates that the time interval between two consecutive events follows the power-law distribution with a tunable exponent, which can be controlled by the model parameters and is in interval (1,+{\infty}). The analytical result agrees with the empirical results well, obeying an approximately power-law form. Our model provides a theoretical basis for human behaviour dynamics of comments on Blog posts.

💡 Research Summary

The paper investigates the temporal dynamics of user comments on blog posts, aiming to uncover the statistical regularities governing human online activity and to propose a theoretical model that captures these patterns. The authors begin by assembling a large dataset from several popular blogging platforms, extracting timestamps for millions of comments while filtering out spam, bot-generated entries, and non‑human interactions. After preprocessing, the remaining data represent genuine human responses to blog content.

Statistical analysis of the inter‑arrival times (the intervals between consecutive comments) reveals a heavy‑tailed distribution. Histograms and kernel density estimates show that short intervals are frequent, yet long intervals occur with a probability that decays much slower than an exponential law would predict. When plotted on log‑log axes, the distribution approximates a straight line, indicating a power‑law behavior. This observation contradicts the assumptions of a homogeneous Poisson process, which would imply an exponential inter‑arrival time distribution.

To explain the empirical findings, the authors introduce a non‑homogeneous Poisson process whose intensity function λ(t) decreases over time, reflecting the gradual loss of user interest in a given topic. Specifically, they define λ(t)=a/(b+t), where a>0 controls the initial activity level and b>0 determines how slowly the intensity decays. The cumulative intensity Λ(t) = a·ln(1+t/b) leads to an analytical expression for the probability density of inter‑arrival times:

 f(τ) = (a/(b+τ))·exp