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In this paper, we use a series of small world networks to simulate the epidemic spreading in the real world. To make our model more similar to the real world, we employ a parameter p_move to denote its moving probability, which corresponds with the general mobility of individuals in realistic social network. The networks keep the same small world properties when they are varying. And the SIRS model is used to simulate the disease propagation. From these simulations we see the moving probabilityarXiv:nlin/0411017v1 fatcat:e6p6zoxmmzdh3ecnqqhggoa2pu