Coupled lattice models are
specialized metapopulation models, where subpopulations are arranged on
a grid and coupling is generally to the nearest neighbors only.

For a disease with SIR-type dynamics and “commuter-like” interaction
terms,the governing equations become:

We stress that although these lattices are generally two-dimensional,
for simplicity of notation we use a single variable to identify each
subpopulation. In addition, given that this lattice formulation is
slightly abstract, we assume identical parameters for each
subpopulation (parameters are now scalars rather than vectors or
matrices).