Rules for this example ("Dynamics of HIV Infection: A Cellular Automata Approach")

Rule 1: Update of a healthy cell: (a) If it has at least
one infected-A1 neighbor, it becomes infected-A1. (b) If it
has no infected-A1 neighbor but does have at least R (2 < R < 8) infected-A2 neighbors, it becomes infected-A1.
(c) Otherwise it stays healthy.—Rule 1a mimics the spread
of the HIV infection by contact, before the immune system
had developed its specific response against the virus.
Rule 1b represents the fact that infected-A2 cells may, before
dying, contaminate a healthy cell if their concentration
is above some threshold.

Rule 2: An infected-A1 cell becomes infected-A2 after t (t is 10 in this example)
time steps.—An infected-A2 cell is the one against which
the immune response has developed, and hence its ability
to spread the infection is reduced. Here t represents the
time required for the immune system to develop a specific
response to kill an infected cell. Such a time delay is required
for each infected cell since in our model we view
each new infected cell as carrying a different lineage
(strain) of the virus. This is the way we incorporate the
mutation rate of the virus in our model. When a healthy
cell is infected, the virus uses the cell’s DNA in order to
transcribe its RNA and replicate. During each transcription
an error may occur, producing, on the average, one mutation per generation and hence a new strain of the
virus is produced.

Rule 3: Infected-A2 cells become dead cells.—This rule
simulates the depletion of the infected cells by the immune
response.

Rule 4: (a) Dead cells can be replaced by healthy cells
with probability P_{repl} in the next time step (or remain dead
with probability 1 - P_{repl}). (b) Each new healthy cell introduced
may be replaced by an infected-A1 with probability
P_{infec}.—Rule 4a describes the replenishment of the
depleted cells, mimicking the high ability of the immune
system to recover from the immunosuppression generated
by infection. As a consequence, it will also mimic some
diffusion of the cells in the tissue. Rule 4b simulates the
introduction of new infected cells in the system, either
coming from other compartments of the immune system
or resulting from the activation of the latent infected cells,
as suggested in the literature.