  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 $p_{move}$.
