Phase transitions in a model for the formation of herpes simplex ulcers - art. no. 041903

The critical properties of a cellular automaton model describing the spread ing of infection of the herpes simplex virus in corneal tissue are investig ated through the dynamic Monte Carlo method. The model takes into account d ifferent cell susceptibilities to the viral infection, as suggested by expe rimental findings. In a two-dimensional square lattice the sites are associ ated with two distinct types of cells. namely, permissive and resistant to the infection. While a permissive cell becomes infected in the presence of a single infected cell in its neighborhood, a resistant cell needs to be su rrounded by at least R>1 infected or dead cells in order to become infected . The infection is followed by the death of the cells resulting in ulcers w hose forms may be dendritic (self-limited clusters) or amoeboid (percolatin g clusters) depending on the degree of resistance R of the resistant cells as well as on the density of permissive cells in the healthy tissue. We sho w that a phase transition between these two regimes occurs only for R great er than or equal to5 and, in addition, that the phase transition is in the universality class of the ordinary percolation.