Abstract
We investigate an extended version of the probabilistic Forest-Fire model conceived as a model of disease spreading. We show that the model self-organizes spatially and temporally from random initial conditions into a well-defined state with a characteristic length and time scale. The time scale τ has a power-law dependence on the correlation length ξ, i.e., τ ≈ ξ z with a non-trivial exponent of ≈ 0.83 in d = 2. We show that stochastic input of susceptible individuals is essential for this behaviour. A mean field approximation is presented, predicting an exponent of z = 1 2 .
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