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 $μ_n(A)$ is the incidence -density of infectives individuals- in the set $A$, at time $n$ and $$μ_{n+1}(A)(ω)=\int_S{π_{n+1}(A;s)(ω)μ_n(ds)(ω)}, {for any Borel set} A, $$ with random transition kernels of the form $$π_n(.;.)(ω)=Π(.;.)(ξ_n(ω),Y_n(ω)),$$ where $ξ$, $Y$ satisfy some ergodic conditions. The support of $μ_n$ is called $S_n$. We also assume that $S_0$ is compact with regular border and that for any $x,y$ the kernel $Π(.;.)(x,y)$ has compact support. A random set $K_{n+1}$ is a safety area of level $α$ if: [{$i$)}] $K_{n+1}$ {\rm is a function of} $S_0, S_1, ...,S_n.$ [{$ii$)}] $P(K_{n+1} \cap S_{n+1} \neq \emptyset)\leq α.$ We present a method to find these safety areas and some related results.