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The Contact process is a general stochastic model for spatial spread. Applications include the growth of bacterial colonies, human cities, tumors, etc.
The process works by spreading (infecting) discrete chunks of space, (sites, locations, hosts, etc) and transforming them from vacant to occupied (discrete state) in continuous time (rates of colonization/birth/infection and extinction/death/recovery). The lattice can also be seen as a population of replicating particles/sites which can die (go extinct locally) and/or, through birth process, colonize near-by vacant locations. It is a useful model to study the implications adjacency relationships (access, spatial structure) have in determining the long-term behavior of spatially-distributed birth-death (infection-recovery) process. Mathematically such stochastic process corresponds to an interacting particle system. For an introduction read,
Stochastic Spatial Models: A User's Guide to Ecological Applications by Durrett and Levin, 1998.
The code in this repository considers a two dimensional (2D) Lattice with periodic boundary conditions (a 2D torus of 256 x 256 sites). This represents a collection of spatial locations which can be in one of two discrete States; sites are either vacant (State 0) or occupied (State 1). Lattice sites which are occupied can locally go extinct (die at some rate/with some probability) and turn vacant or, if already vacant, can be colonized by adjacent occupied sites with a probability proportional to the local occupancy and the infection rate. Adjacency here, considers the four immediate neighbors of any given (focal) site in the Lattice. To implement continuous time, the algorithm uses a Monte Carlo method to update the Lattice state.