In this talk I will introduce the contact process for general infection matrices (which is slightly more general than graphs) as a model for the spread of disease or information. Since in general the contact process is hard to analyse, many ways of approximating the process have been studied. An important example of such an approximation is a type of mean field approach. I will show that this corresponds to approximating the infection matrix with a rank 1 matrix. We will extend this to higher finite rank approximations, and we will give an exact description of the behaviour of the contact process on such a finite rank matrix, as the number of nodes goes to infinity. In particular, we will be able to describe the meta-stable state of the contact process as a Gaussian process with known covariance structure.