  In this paper, we define a class of random growth models whose growth is at
least and at most linear and prove an asymptotic shape theorem for these
models. This proof generalizes already known proofs for the classical contact
process or some of its variants and allows us to obtain conjectured asymptotic
shape theorems for several models: the contact process in a randomly evolving
environment, the oriented percolation with hostile immigration, the bounded
modified contact process, Richardson's model with stirring and the contact
process with stirring
