Epidemic Spreading in Dynamic Small World Networks
  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 probability of a small world network has a profound effect on the velocity for the spread of an infection. The quantitative results show that the characteristic time $\tau$ of infection at initial stage decreases exponentially with $p_{move}$. 
Sheng Li, Meng Meng and Hongru Ma