Biomedical Engineering Reference
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rate,
λ
death rate
d
death rate
δ
infection rate,
β
T
target cells
I
infected cells
V
virions
clearance rate,
c
viral production rate,
p
Fig. 3
Basic model of viral dynamics: target cells,
T
, are infected by virions,
V
, with a rate
constant
. Infected cells,
I
, produce new virions at rate
p
. Virions and infected cells are lost
with clearance rate
c
and death rate
β
δ
, respectively. New target cells are generated at a rate
λ
and
target cells have an average lifetime of 1
/
d
. Typical values of the model parameters are given in
Tabl e 1
Equation (
1
) represents the basic model of viral dynamics as described by Nowak
and Bangham [
89
],NowakandMay[
91
], Perelson [
101
], and Perelson et al.
[
104
]. Here,
T
denotes the concentration of target cells,
I
the concentration of
infected cells, and
V
the viral load. Target cells are created at a constant rate
λ
and have an average lifetime of 1
/
d
. Target cells can become infected by virions
at a transmission rate
per cell.
Productively infected cells produce new virions, which have an average lifetime of
1
β
, and the resulting infected cells die with rate
δ
c
,atrate
p
per cell (see Fig.
3
for a sketch of the model).
The model presented in Eq. (
1
) has been extended by including (1) the incorpo-
ration of an immune response, humoral as well as cell-based [
91
], (2) the separation
between long- and short-lived infected cells [
105
], and (3) the consideration of an
incubation period before an infected cell starts the production and release of new
virions [
86
,
103
].
The application of models based on ODEs, such as the one in Eq. (
1
), to
experimental and clinical data has improved our knowledge about the dynamics
of viral infections in several ways. The estimation of viral production and clearance
rates has shown that chronic infections in which the viral load attains a set-point,
such as HIV, hepatitis C virus, and human cytomegalovirus (CMV) [
31
,
87
,
98
], are
maintained by high rates of viral replication and equally high rates of viral clearance
[
51
,
89
,
93
,
109
]. However, the estimates for the clearance rate constants vary quite
substantially depending on the experimental or clinical data that are analyzed. It has
been estimated that HIV virions have a very short half-life and are cleared from
the circulation with an average clearance rate of
c
/
23 day
−
1
[
109
]. In contrast,
the clearance rate of SIV, the monkey equivalent of HIV, was estimated to be
c
=
300 day
−
1
in the blood [
128
]. Partly
influenced by those estimates, the estimated number of virions produced by one
infected cell per day varies quite substantially as well, ranging from 100 [
29
,
44
]to
650-3400 [
110
] and up to the order of 2
5day
−
1
in lymphoid tissue [
110
]and
c
=
5
.
=
10
4
[
21
] viral particles per infected
cell per day. A lower bound for the total viral production in an infected patient was
estimated to be around 10
10
virions per day [
104
].
−
5
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