  We study the contact process running in the one-dimensional lattice
undergoing dynamical percolation, where edges open at rate $vp$ and close at
rate $v(1-p)$. Our goal is to explore how the speed of the environment, $v$,
affects the behavior of the process. We show in particular that for small
enough $v$ the process dies out, while for large $v$ the process behaves like a
contact process on $\mathbb{Z}$ with rate $\lambda p$, so it survives if
$\lambda$ is large. We also show that if $v$ and $p$ are small then the network
becomes immune, in the sense that the process dies out for any infection rate
$\lambda$, while if $p$ is sufficiently close to $1$ then for all $v>0$
survival is possible for large enough $\lambda$.
