Epidemic models on lattices

Lattice models, which were first explored in the context of cellular automata, act as good first approximations of more complex spatial configurations, although they do not reflect the heterogeneity of space (e.g. population density differences, urban geography and topographical differentiations).

[2] The mathematical modelling of epidemics was originally implemented in terms of differential equations, which effectively assumed that the various states of individuals were uniformly distributed throughout space.

Cardy and Grassberger [4] argued that this growth is similar to the growth of percolation clusters, which are governed by the "dynamical percolation" universality class (finished clusters are in the same class as static percolation, while growing clusters have additional dynamic exponents).

In asynchronous models, the individuals are considered one at a time, as in kinetic Monte Carlo or as a "Stochastic Lattice Gas.

For the synchronous model, all sites are updated simultaneously (using two copies of the lattice) as in a cellular automaton.