  In this work we study safety areas in epidemic spred. The aim of this work
is, given the evolution of epidemic at time $t$, find a safety set at time
$t+h$. This is, a random set $K_{t+h}$ such that the probability that infection
reaches $K_{t+h}$ at time $t+h$ is small.
  More precisely, inspired on the study of epidemic spread, we consider a model
in which the measure $\mu_n(A)$ is the incidence -density of infectives
individuals- in the set $A$, at time $n$ and
$$\mu_{n+1}(A)(\omega)=\int_S{\pi_{n+1}(A;s)(\omega)\mu_n(ds)(\omega)}, {for
any Borel set} A, $$ with random transition kernels of the form
$$\pi_n(.;.)(\omega)=\Pi(.;.)(\xi_n(\omega),Y_n(\omega)),$$ where $\xi$, $Y$
satisfy some ergodic conditions. The support of $\mu_n$ is called $S_n$. We
also assume that $S_0$ is compact with regular border and that for any $x,y$
the kernel $\Pi(.;.)(x,y)$ has compact support. A random set $K_{n+1}$ is a
safety area of level $\alpha$ if: [{$i$)}] $K_{n+1}$ {\rm is a function of}
$S_0, S_1, ...,S_n.$
  [{$ii$)}] $P(K_{n+1} \cap S_{n+1} \neq \emptyset)\leq \alpha.$ We present a
method to find these safety areas and some related results.
