Dynamical Model for Virus Spread

Abstract

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 in this model to mimic cells regeneration (with probability {\it p}) and to consider infection processes by other means than contiguity (with probability {\it f}). Simulations are carried on a $L \times L$ square lattice considering the eigth first neighbors. The mean density population of infected cells ($D_i$) is measured as function of the regeneration probability {\it p}, and analized for small values of the ratio {\it f/p } and for distinct degrees of the cell resistance. The results obtained by a mean field like approach recovers the simulations results. The role of the resistant parameter $R$ ($R \geq 2)$ on the steady state properties is investigated and discussed in comparision with the $R=1$ monocell case which corresponds to the {\em self organized critical} forest fire model. The fractal dimension of the dead cells ulcers contours were also estimated and analised as function of the model parameters.