Spatial Aspects of HIV Infection - Mathematical Methods and Models in Biomedicine - page 16

Burks [ 123 ]. Since then, the mathematical properties of cellular automata have been
intensively studied and are well described, e.g., [ 126 ]. Several studies have applied
the concept of cellular automata to questions in the field of viral dynamics and
immunity [ 9 , 16 , 18 , 37 , 75 , 96 , 97 , 120 , 130 ]. In the following we discuss some of
them.

Cellular Automata and the Study of HIV Viral Dynamics

Cellular automata have been used to study HIV infection dynamics using either two-
dimensional [ 12 , 19 , 120 , 130 ] or three-dimensional representations of the modeled
environment [ 96 , 97 ]. In the following, we will present and discuss two studies in
detail that applied two-dimensional cellular automata to the case of HIV infection.
Zorzenon dos Santos and Coutinho [ 130 ] studied the dynamics of HIV infection
in a lymph node using a two-dimensional lattice. Each site on the lattice represented
aCD4 + T cell or a monocyte, both of which are target cells for HIV. Each cell
could be in one of four different stages: (1) uninfected, (2) productively infected,
(3) infected but in a final stage before the cell dies due to the action of the immune
system, and (4) dead. Uninfected cells become infected dependent on the number
of infected cells in the neighborhood and can be killed by an immune response
after a certain number of time steps represents the time the

immune system needs to generate a target-specific immune response. With a certain
probability, dead cells are replaced by uninfected cells, representing new targets
which can then become infected. By starting the infection with a few infected cells,
the authors found a parameter regime that recapitulates the three-phase dynamics
observed in HIV infection ( acute-chronic-AIDS ) without varying the underlying
parameters during the simulation. The model also showed that the infection spread
in a wave form pattern through the simulated layer of cells as expected from the cell-
to-cell transmission of the virus implemented in the model. Zorzenon dos Santos and
Coutinho [ 130 ] also assumed that each newly infected cell carries a different lineage
of the virus. Using this assumption, the authors incorporate the high mutation rate
of HIV [ 102 ] into their model. Because each infected cell is assumed to carry a
different viral genome the time the immune system needs to generate an immune
response against an infected cell is assumed to be the same for each newly infected
cell. However, this assumption might not be true. It might be also likely that due
to cell-to-cell transmission clusters of infected cells are dominated by one infecting
viral strain. If that is the case, then the effect of CD8 + T cells, which are the immune
cells responsible for recognizing and killing infected cells, might be faster in some
local environments, possibly terminating the spread of the disease in this location.
In the second study, Strain et al. [ 120 ] also used a two-dimensional cellular
automaton to study HIV infection dynamics in a layer of cells and compared the
outcome to the results of a model formulated by ordinary differential equations [see
Eq. ( 1 )]. Similar to Zorzenon dos Santos and Coutinho [ 130 ], each site in the cellular
automaton represented a T cell. Based on the diffusion rate of virions and their
rate of encounter and attachment to T cells, the authors calculate the probability of

τ . The parameter τ