Phase-Transitions in a model for the formation of herpes simplex ulcers

Abstract

The critical properties of a cellular automaton model describing the spreading of infection of the Herpes Simplex Virus in corneal tissue are investigated through the dynamic Monte Carlo method. The model takes into account different cell susceptibilities to the viral infection, as suggested by experimental findings. In a two-dimensional square lattice, the sites are associated to 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 surrounded 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 whose forms may be dendritic (self-limited clusters) or amoeboid (percolating 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 show that a phase transition between these two regimes occurs only for R>=5 and, in addition, that the phase-transition is in the universality class of the ordinary percolation.