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Human behaviors are assumed as randomly distribution in current models for human dynamics. But more and more evidence proves that the intervals of human actions follows the power-law distributions with heavy tails. A model considering habit of humans is introduced to explain bursts and heavy tails in human dynamics more exactly, and the simulation results are consistent with the real data from a university emails record and an online movie order web site. Normal distribution is used to simulate intervals of succession of events, and random parameters are set as unexpected events disturbing habit behaviors. Furthermore, a worm propagation model based on the habit model and SI model is presented to investigate the impact of human behavior on virus propagation. The model shows that the consuming time of infecting all nodes in a network increases significantly with the extending of network scale based on the proposed habit model, while the time increases very slowly based on Poisson model.

Impact of habitual behaviors on human dynamics and spreading process