Dynamical model for virus spread

The steady state properties of the mean density population of infected cells in a viral spread is simulated by a general forest fire like cellular automaton model with two distinct populations of cells (permissive and resistant ones) and studied in the framework of the mean field approximation. Stochastic dynamical ingredients are introduced into this model to mimic cells regeneration (with probability p) and to consider infection processes by other means than contiguity (with probability f). Simulations are carried out on a L x L square lattice taking into consideration the eighth first neighbors. The mean density population of infected cells (D-i) is measured as a function of the regeneration probability p, and analyzed for small values of the ratio f/p and for distinct degrees of cell resistance. The results obtained by a mean field like approach recovers the simulations results. The role of the resistant parameter R (R greater than or equal to 2) on the steady state properties, is investigated and discussed in comparison with the R = 1 monocell case which corresponds to the self organized critical forest fire model. The fractal dimension of the dead cells ulcers contours was also estimated and analyzed as a function of the model parameters.