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Epidemic models on lattices
Classic epidemic models of disease transmission are described in Epidemic model and Compartmental models in epidemiology. Here we discuss the behavior when such models are simulated on a lattice.
==Introduction==
The mathematical modeling of epidemics was originally implemented in terms of differential equations, which effectively assumed that the various states of individuals were uniformly distributed throughout space. To take into account correlations and clustering, lattice-based models have been introduced. Grassberger
considered synchronous (cellular automaton) versions of models, and showed how the epidemic growth goes through a critical behavior such that transmission remains local when infection rates are below critical values, and spread throughout the system when they are above a critical value. Cardy and Grassberger
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."
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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