  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.
