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The authors are able to simulate the “three-phase” dynamics of the HIV infection.
However, their analysis is pretty qualitative and does not take into account at all the
complexity of the real immune system. For instance, there is no distinction between
immune cells targeted by HIV and other cells.
The spatial distribution of the virus infection and diffusion in the host's body
plays a major role in the work of Zorzenon dos Santos and Coutinho (2001). Their
model describes the immune system cells in the lymphoid tissues that can be a target
for HIV by means of a two-dimensional cellular automaton. Each lattice site contains
a single cell and each time step corresponds to one week of real life.
The values of the parameters required to tune the system have been determined
on the basis of experimental data. The results of the density of healthy and infected T
cells are in good qualitative agreement with those reported by Pantaleo et al. (1993).
However, this model does not describe how the immune system interacts with an
antigen like HIV that mutates at an extremely high rate. Many important entities like
the macrophages or the B cells are not included in the model.
8.3.1 A Detailed Model of the Immune Reaction
The model we use to study the immune response to HIV branched years ago from the
Celada-Seiden model
(Celada and Seiden 1992). In the original Celada-Seiden
model a single lymph node (or generically a small portion of a secondary lymphoid
organ) of a vertebrate animal is mapped onto a two-dimensional hexagonal lattice,
with full periodic boundary conditions. The primary lymphoid organs, thymus and
bone marrow, are modeled apart: the thymus is implicitly represented by the positive
and negative selection of immature thymocytes before they get into the lymphatic
system, whereas the bone marrow generates already mature B lymphocytes. Hence,
on the lattice there are only immunocompetent lymphocytes.
The
Celada-Seiden model belongs to the class of bit string models. Bit strings
represent the “binding site” of cells and molecules as, for example, lymphocyte re-
ceptors (T lymphocyte receptor, B lymphocyte receptor, Major histocompatibility
complex, antigen peptides and epitopes, immunocomplexes, etc.). The model in-
cludes the major classes of cells of the lymphoid lineage (T
H
, cytotoxic T lympho-
cytes or CTLs, B lymphocytes, and antibody-producing plasma cells) and some of
the myeloid lineage (macrophages and dendritic cells).
The interactions among these cells define their functional behavior. With respect
to other immune system models, the Celada-Seiden model has an additional level of
description, representing the intracellular processes of antigen digestion and presen-
tation. Both the cytosolic and endocytic pathways are implemented. Usually, each
time step of the simulation corresponds to 8 hours of “real life”.
8.4 Simulation of HIV-1 Infection
To account for the features of HIV-1, a number of additions are required to the origi-
nal Celada-Seiden model. First, the T
H
cells become, along with the dendritic cells
and the macrophages, a possible target of the antigen action. From our simulations, it
