  The recent interest in human dynamics has led researchers to investigate the
stochastic processes that explain human behaviour in various contexts. Here we
propose a generative model to capture the dynamics of survival analysis,
traditionally employed in clinical trials and reliability analysis in
engineering. We derive a general solution for the model in the form of a
product, and then a continuous approximation to the solution via the renewal
equation describing age-structured population dynamics. This enables us to
model a wide range of survival distributions, according to the choice of the
mortality distribution. We provide empirical evidence for the validity of the
model from a longitudinal data set of popular search engine queries over 114
months, showing that the survival function of these queries is closely matched
by the solution for our model with power-law mortality.
