A stochastic evolutionary model for capturing human dynamics

TL;DR

This paper introduces a stochastic generative model for human dynamics that captures survival analysis behavior, validated with real-world search engine query data and capable of modeling various survival distributions.

Contribution

It presents a novel stochastic model for human dynamics based on survival analysis, with a continuous approximation and empirical validation using search query data.

Findings

Model accurately fits search query survival data

Power-law mortality effectively describes query survival

Provides a flexible framework for diverse survival distributions

Abstract

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.