Field theoretic formulation of an epidemic process with immunisation

The author describes a model of the spread of an epidemic on a lattice, in which sites may be infected by their neighbours, after which they recover and are subsequently immune. It corresponds to a modification of the directed percolation problem, and also to a growth model of clusters. The model is analysed using a continuum field theory, both within a self-consistent approximation and using an epsilon expansion below six transverse dimensions.