Spatial Aspects of HIV Infection - Mathematical Methods and Models in Biomedicine - page 2

Spatial Aspects of HIV Infection

Frederik Graw and Alan S. Perelson

1 Introduction

Human immunodeficiency virus type 1 (HIV-1) is one of the most and intensely
studied viral pathogens in the history of science. However, despite the huge scientific
effort, many aspects of HIV infection dynamics and disease pathogenesis within a
host are still not understood. Mathematical modeling has helped to improve our
understanding of the infection as well as the dynamics of the immune response.
Fitting models to clinical data has provided estimates for the turnover rate of target
cells [ 82 , 83 , 111 ], the lifetime of infected cells and viral particles [ 104 , 109 ],
as well as for the rate of viral production by infected cells [ 21 , 44 ]. Most
mathematical models applied to experimental data on viral infections have been
formulated as systems of ordinary differential equations (ODE) [ 91 , 101 , 104 ].
While helpful and appropriate in many situations, ODE models simplify the
actual biological processes and have some limitations. One limitation is the
assumption that the interacting viral and cell populations are well mixed and
homogeneously distributed. This assumption, which may be realistic for populations
in blood, is not realistic for populations interacting in tissues [ 36 ]. Within a tissue
virus may not be distributed homogeneously and an infected cell will interact
preferentially with neighboring cells. As HIV mainly infects CD4 + T cells [ 42 ]
which are most abundant and densely packed in secondary lymphoid organs, such
as lymph nodes and the spleen, the spatial arrangement of cells might influence the
infection dynamics. Furthermore, during the establishment of infection, stochastic
effects influenced by spatial conditions, such as the local availability of appro-

F. Graw ￿ A.S. Perelson ( )
Theoretical Biology and Biophysics, Los Alamos National Laboratory,
Los Alamos, NM 87545, USA
e-mail: [e-mail] ; [e-mail]