Spatial Aspects of HIV Infection - Mathematical Methods and Models in Biomedicine - page 7

This finding may explain why HIV replicates more efficiently in areas densely
populated with appropriate target cells in close contact to each other such as in
lymphoid tissue [ 42 , 94 , 114 ].
The mode of transmission within a host also has an influence on the evolutionary
development of the infecting viral strain. Cell-to-cell transmission could allow the
virus to avoid the selective pressure mediated by the humoral immune response
[ 22 ], possibly leading to foci of infected cells dominated by one viral mutant [ 23 ].
However, recent experimental observations showed that cell-to-cell transmission
and free viral spread are equivalently sensitive to entry inhibitors [ 70 ]. The local
clustering of infected cells dominated by one viral mutant also has implications for
the effectiveness of the local immune response and therapeutic interventions.
In the same way as spatial effects play a role in the establishment and mainte-
nance of HIV infection, space also plays a role in the immune response against the
infection. To kill infected cells, antigen-specific CD8 + T cells need to make direct
physical contact with these cells. The absence of specific immune effector cells
at certain spatial locations, e.g., mucosal tissue, could help explain the success of
initial infection [ 26 , 55 , 108 ]. Similar to the immune response, therapeutic drugs
are influenced by spatiality as they have to reach their targets in order to act
efficiently. Due to this, drug concentration heterogeneity among different tissue
compartments can facilitate the evolution of drug-resistant viral strains [ 60 ].
Overall, due to its importance for the infection and evolutionary dynamics of HIV
within a host, spatial aspects should be considered while modeling and analyzing
HIV infection.

3 Analyzing HIV Viral Dynamics: The Contribution

of ODE Models

3.1 ODE Models of HIV Infection

The analysis of infection processes by HIV requires the consideration of virus
particles, i.e., virions, and cells susceptible to infection, i.e., target cells, in which
the virus can replicate and produce new virions. In mathematical terms, these
interactions that occur during infection can be described by a system of ODE as
formulated in Eq. ( 1 ):

d T
d t = λ −

dT − β VT ,

d I
d t = β

VT − δ I ,

d V
d t =

pI − cV . (1)