Phase transitions in a model for the formation of herpes simplex ulcers.

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 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 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.

Dynamics of HIV infection: a cellular automata approach.

We use a cellular automata model to study the evolution of human immunodeficiency virus (HIV) infection and the onset of acquired immunodeficiency syndrome (AIDS). The model takes into account the global features of the immune response to any pathogen, the fast mutation rate of the HIV, and a fair amount of spatial localization, which may occur in the lymph nodes. Our results reproduce the three-phase pattern observed in T cell and virus counts of infected patients, namely, the primary response, the clinical latency period, and the onset of AIDS. The dynamics of real experimental data is related to the transient behavior of our model and not to its steady state. We have also found that the infected cells organize themselves into spatial structures, which are responsible for the decrease on the concentration of uninfected cells, leading to AIDS.