Worlds. Both lattice networks and small world networks begin with the same formulation: individuals are regularly spaced on a grid (usually in just one or two dimensions), and each individual is connected to their k nearest neighbours-these connections define a lattice. The advantage of such networks is that they retain many elements of the initial spatial arrangement of points, and hence contain both many short loops as well as the property that infection tends to spread locally. There is a clear link between such lattice-based networks and the field of probabilistic cellular automata [72, 73] . The fundamental difficulty with such lattice models is that the presence of short loops and localised spread means that is it difficult (if not impossible) to prove exact results, and hence large-scale multiple simulations are required.