Spatial Aspects of HIV Infection - Mathematical Methods and Models in Biomedicine - page 21

who had the “ideal” therapy was 1.14 times more efficient than those receiving the
optimal therapy with interruptions. However, the optimal strategy they found with
their genetic algorithm uses approximately 40% less drug than the full therapy.
The application of agent-based models to problems in infection and immunity is
still in its infancy. The appropriateness of each model and simulation environment
can only be validated given appropriate experimental observations. Unfortunately,
some models and especially those that follow a large number of different cell
populations [ 16 , 66 ] require a large number of parameters, many of which have not
been estimated from experimental data so far. As more interest develops in building
quantitative models and with the development of new experimental techniques ( see
Sect. 6 ) this gap hopefully will be filled. This will allow the implementation of
enhanced simulation tools and even the aims of the ImmunoGrid -project might
be reached.

6 Conclusion and Discussion

Mathematical models based on ordinary differential equations have taught us much
about the HIV infection dynamics (reviewed in [ 101 ]). These kinds of models
helped to quantify rates at which HIV replicates, rates at which target cells, such
as CD4 + T cells, proliferate, and HIV virions or infected cells are cleared from the
system. Variation in parameter estimates obtained using different models as well
as advances in experimental techniques suggest that the simplistic view provided
by ODE models, although sometimes useful, may need to be reconsidered in other
situations. For example, the well-mixed assumption of interacting cell populations
as assumed in the basic ODE models for virus dynamics [ 89 , 91 , 101 , 104 ]hastobe
revised in order to model infection in tissues.
In Sect. 2 of this chapter, we outlined the importance of spatial factors throughout
the different stages of the HIV infection process. Novel experiments broadened our
view of the first steps of HIV infection [ 43 ]. However, there is a growing interest
in obtaining a better understanding of the way in which HIV establishes infection,
particularly with regard to its interplay with the different immune responses and
the local tissue structure [ 43 ]. The mucosal barrier of the genital tract, the main
portal of HIV entry, shows heterogeneous vulnerability to infection [ 43 ]. Proximity
and constant supply of susceptible target cells close to the site of viral entry is
another important factor determining the successful establishment of an infection
[ 43 , 47 ]. But what is the success rate of viral entry? How many target cells are
needed to establish an infection at the site of entry? How do they have to be
distributed? And in the end, the ultimate goal is, how the establishment of HIV
infection can be prevented. While it is generally possible to formulate the different
factors mentioned above in terms of stochastic events incorporated into an ODE
model, determining the corresponding rate distributions provides a heavy challenge
for the modeler given the current experimental data. Advances in experimental
techniques, such as two-photon microscopy, have made it possible to visualize the