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HIV-1 Dynamics In Vivo: Virion
Clearance Rate, Infected Cell
Lifespan, and Viral Generation
Time
Alan S. Perelson
Avidan U. Neumann
Martin Markowitz
John M. Leonard
David D. Ho
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SANTA FE INSTITUTE
HIV-1 Dynamics In Vivo: Virion Clearance Rate,
Infected Cell Lifespan, and Viral Generation Time.
Alan S. Perelson, Avidan U. Neumann, Martin Markowitz
John M. Leonardy, and David D. Ho
Theoretical Division
Los Alamos National Laboratory, Los Alamos, NM 87545
Aaron Diamond AIDS Research Center
NYU School of Medicine
455 First Avenue, New York, NY 10016
yPharmaceutical Products Division
Abbott Laboratories, Abbott Park, IL 60064
Address all correspondence to DDH.
1
Abstract
Using a new mathematical model to analyze a detailed set of viral load data collected
from ve infected patients after the administration of a potent inhibitor of HIV-1 protease,
it was estimated that productively infected cells have, on average, a lifespan of 2.2 days
( 1=2 = 1 6 days) and that plasma virions have a mean lifespan of 0.3 days ( 1=2 = 0 24
t
:
t
:
days). The average total HIV-1 production was 10 3109 virions per day, which is substan:
tially higher than previous minimum estimates. Our results also suggest that the minimum
duration of the HIV-1 life cycle in vivo is 1.2 days on average, and that the average HIV-1
generation time, dened as the time from release of a virion until it infects another cell
and causes the release of a new generation of viral particles, is 2.6 days. These ndings
on viral dynamics provide not only a kinetic picture of HIV-1 pathogenesis, but also the
theoretical principles to guide treatment strategies.
2
Recent studies have shown that HIV-1 replication in vivo occurs continuously at high
levels 12. Ho et al 1 found that when a protease inhibitor was administered to infected
patients, plasma levels of HIV-1 decreased exponentially with a mean half-life ( 1=2 ) of
t
2 1 0 4 days. Wei et al 2 and Nowak et al 3 found essentially identical kinetics of viral
:
:
decay following the use of inhibitors of HIV-1 protease or reverse transcriptase. The viral
decay observed in these studies was a composite of two separate eects: clearance of
free virions from plasma and loss of virus-producing cells. To understand the kinetics of
these two viral compartments more precisely, we monitored the viral load closely in ve
HIV-1-infected subjects after the administration of a potent protease inhibitor. Using a
mathematical model for viral dynamics and nonlinear least-squares tting of the data,
separate estimates of the virion clearance rate, the infected cell lifespan, and the average
viral generation time in vivo were obtained.
Ritonavir 45 was administered orally (1200 mg/day) to ve infected patients, whose
baseline characteristics are shown in Table 1. Using an ultrasensitive modication 15 of the
branched DNA assay 67, HIV-1 RNA levels in plasma were measured after treatment at
frequent intervals (every 2 hours until the sixth hour, every 6 hours until day 2, and every
day until day 7). As shown in three examples in Figs. 1A and 1B, each patient responded
with a similar pattern of viral decay, with an initial lag followed by an approximately
exponential decline in plasma viral RNA.
After ritonavir was administered, a delay in its antiviral eect was expected due to
the time required for drug absorption, distribution, and penetration into the target cells.
This pharmacokinetic delay could be estimated by the time elapsed before the rst drop
3
in the titer of infectious HIV-1 in plasma (Table 1 Fig. 1B) However, even after the
pharmacokinetic delay was accounted for, a lag of 1 25 days was observed before the
:
plasma viral RNA fell (Fig. 1). This additional delay is consistent with the mechanism
of action of protease inhibitors, which render newly produced virions non-infectious but
inhibit neither the production of virions from already infected cells, nor the infection of
new cells by previously produced infectious virions 8.
In our previous study 1, measurements were only taken every three days, so the delay
in the fall of plasma RNA was missed. The results were tted to a single exponential,
which was sucient to provide minimum estimates of HIV-1 kinetics. In contrast, in the
present study, 15 data points were obtained during the rst seven days, allowing a careful
analysis of the results using a new mathematical model of viral kinetics.
We assume HIV-1 infects target cells, , with a rate constant
T
to become productively infected cells,
T
k
and causes them
. Before drug treatment, the dynamics of cell
infection and viral production are represented by
dT
dt
dV
dt
where
cells,
V
N
=
=
kV T
N T
;
(1)
cV (2)
T
;
is the concentration of viral particles in plasma, is the rate of loss of infected
is the number of new virions produced per infected cell during its lifetime, and
c
is the rate constant for viral clearance 9 . The loss of infected cells could be due to viral
cytopathicity, immune elimination, or other processes such as apoptosis. Virion clearance
could be due to binding and entry into cells, immune elimination, or nonspecic removal
by the reticuloendothelial system.
4
We assume that ritonavir does not aect the survival or rate of virion production of
infected cells, and that after the pharmacological delay all newly produced virions are noninfectious. However, infectious virions produced before drug eect are still present until
they are cleared. Therefore, after treatment with ritonavir,
d =
d
T
t
kVI T
d I =;
d
V
t
d
=
VNI
d
t
where
VI
;
T
(3)
cVI (4)
;
(5)
N T
cVN I is the plasma concentration of virions in the infectious pool (produced before
drug eect I ( = 0) = 0),
VNI
(produced after drug eect
VNI t
V
t
V
is the concentration of virions in the non-infectious pool
( = 0) = 0), and = 0 is the time of onset of the drug
t
eect. In our analyses, it is assumed that viral inhibition by ritonavir is 100%, although
the model can be generalized for non-perfect drugs 10.
Assuming that the system is at quasi-steady state before drug treatment 11, and that
the uninfected cell concentration, , remains at approximately its steady-state level,
T
T0
,
for one week after drug administration 15, we nd from Eqs. (3)-(5) that the total concentration of plasma virions, =
V
()=
t
+
VI
;ct
+ ;
V0 e
V
VNI
cV0
c
, varies as
; (
c
c
;t
e
;
;ct
e
);
te
;ct
(6)
which diers from the equation derived by Wei et al (2, see ref. 12). Allowing to increase
T
necessitates using numerical methods to predict ( ), but does not substantially alter the
V
outcomes of the analyses given below 13.
5
t
Using nonlinear regression analysis (Fig. 1, legend), we estimated , the viral clearance
c
rate constant, and , the rate of loss of virus-producing cells, for each of the patients by
tting Eq. (6) to the plasma HIV-1 RNA measurements (Table 1, ref 13). The theoretical
curves generated from Eq. (6), using the best-t values of and , gave an excellent t to
c
the data for all patients (3 examples shown in Fig. 1).
Clearance of free virions is the more rapid process, occurring on a time scale of hours.
The values of ranged from 2.06 to 3.81 day;1 with a mean of 3 07 0 64 day;1 (Table 1).
c
:
The corresponding
t1=2
:
of free virions ( 1=2 = ln 2 ) ranged from 0.18 days to 0.34 days
t
=c
with a mean of 0 24 0 06 days ( 6 hours).
:
:
Conrmation of the virion clearance rate was obtained from an independent experiment
that measured by quantitative cultures 14 the rate of loss of viral infectivity in plasma for
patient 105 (Fig. 1B). The loss of infectious virions occurred by rst-order decay, with a
rate constant of 3 0 day;1, which is within the 68% condence interval of the estimated
:
c
value for that patient (Table 1).
At steady state, the production rate of virus must equal its clearance rate,
the estimate of and the pretreatment viral level,
c
V0
cV
. Using
, we obtained an estimate for the
rate of viral production before ritonavir administration. Estimating each patient's plasma
and extracellular uid volumes based on body weight, the total daily viral production and
clearance rates ranged from 0 4 109 to 32 1 109 virions per day, with a mean of 10 3 109
:
:
:
virions per day released into the extracellular uid (Table 1) 15.
The loss of virus-producing cells, as estimated from the t of Eq. (6) to the HIV-1
RNA data, was slower than that of free virions, with values of ranging from 0 26 to
6
:
0 68 day;1, and a mean of 0 49 0 13 day;1, corresponding to
:
:
:
t1=2
values between 1.02
and 2.67 days, with a mean of 1 55 0 57 days (Table 1). A prediction of the kinetics of
:
:
virus-producing cells can be obtained by solving Eq. (3) 16.
Several features of the replication cycle of HIV-1 in vivo could be discerned from our
analysis. Given that and represent the decay rate constants for plasma virions and
c
productively infected cells, respectively, then 1 and 1 are the corresponding average
=c
=
lifespans of these two compartments. Thus, the average lifespan of a virion in the extracellular phase is 0 3 0 1 days, whereas the average lifespan of a productively infected cell
:
:
is 2 2 0 8 days (Table 2). The average generation time of the virus, , dened as the
:
:
time from release of a virion until it infects another cell and causes the release of a new
generation of viral particles, should equal the sum of the average lifespan of a free virion
and the average lifespan of a productively infected cell, or = 1 + 1 , a relationship
=c
=
that can be shown formally (Table 2 legend). Table 2 shows the average value of for the
patients to be 2 6 0 8 days.
:
:
By a heuristic procedure, we can nd minimal estimates for the average duration of
the HIV-1 life cycle and its intracellular or eclipse phase (from virion binding to the release
of the rst progeny). We estimate the duration of the HIV-1 life cycle, , dened as the
S
duration from release of a virion until the release of its rst progeny virus, by the lag in the
decay of HIV-1 RNA in plasma (Fig. 1) after the pharmacologic delay (Table 1) has been
subtracted. The shoulder in the RNA decay curve is explained by the fact that virions
produced before the pharmacologic eect of ritonavir are still infectious and capable of
producing, for a single cycle, viral particles that would be detected by the RNA assay.
7
Thus, the fall in the RNA level should begin when target cells interact with drug-aected
virions and do not produce new virions. These \missing virions" would rst have been
produced at a time equal to the minimum time for infection plus the minimum time for
production of new progeny. As shown in Table 2, the estimated values for
S
were quite
consistent for the ve patients, with a mean duration of 1 2 0 1 days. In steady state,
:
1 =1
=c
=N kT0
:
is the average time for infection (Table 2, legend). Assuming this average
time is greater than the minimal time for infection, ; 1 = 0 9 day, is a minimal estimate
S
=c
:
of the average duration of the intracellular phase of the HIV-1 life cycle 17.
Using potent antiretroviral agents to perturb the quasi-steady state in vivo, previous
studies provided a crude estimate of the
t1=2
of viral decay in which the lifespan of produc-
tively infected cells could not be separated from that of plasma virions (1,2). Here, using a
new mathematical model to analyze a detailed set of data collected after the administration
of a protease inhibitor, we have determined the average lifespan of a productively infected
cell (presumably an activated CD4 lymphocyte) to be 2.2 days. Thus, such cells are lost
with an average
t1=2
of 1.6 days (Fig. 2). Note that the lifespans of productively infected
cells are not dramatically dierent among the study subjects (Table 2), even though patients with low CD4 lymphocyte counts generally have decreased numbers of virus-specic,
MHC class I-restricted cytotoxic T lymphocytes 18 .
The average lifespan of a virion in blood was calculated to be 0.3 days. Therefore, a
population of plasma virions is cleared with a
t1=2
of 0.24 days, i.e., on average, half of
the plasma virions turns over approximately every 6 hours (Fig. 2). Because our analysis
assumed that the antiviral eect of ritonavir was complete and that target cells did not
8
recover during treatment, our estimates of the virion clearance rate and infected cell loss
rate are minimal estimates 1317. Consequently, the true virion
t1=2
may be shorter than 6
hours. For example, Nathanson and Harrington 19 found that monkeys clear the Langat
virus from their circulation on a time scale of about 30 minutes. Thus, the total number
of virions produced and released into the extracellular uid is at least 10 3 109 particles
:
per day 15, which is about 15-fold higher than our previous minimum estimate (1). At
least 99% of this large pool of virus is produced by recently infected cells (1,2) (Fig. 2).
At quasi-steady state viral clearance,
cV
, equals viral production,
N T
. Because has
c
similar values for all patients studied (Table 1), the level of plasma viremia is a reection
of the total virion production, which in turn is proportional to the number of infected cells,
T
, and their viral burst size, .
N
The average generation time of HIV-1 was determined to be 2.6 days. This suggests
that 140 viral replication cycles occur each year, about half the number estimated by
Con 20.
It is now apparent that the repetitive replication of HIV-1, shown on the left side
of Fig. 2, accounts for 99% of the plasma viruses in infected individuals
1220
, as
well as for the high destruction rate of CD4 lymphocytes. The demonstration of the
highly dynamic nature of this cyclic process provides a number of theoretical principles to
guide the development of treatment strategies. First, an eective antiviral agent should
detectably lower the viral load in plasma after only a few days of treatment. Second,
based on previous estimates of the viral dynamics (1,2) along with the mutation rate of
HIV-1 (3 4 10;5 per base pair per replication cycle) 21 and the genome size (104 bp),
:
9
Con has cogently argued that on average every mutation at every position in the genome
would occur numerous times each day 20. The larger turnover rate of HIV-1 described in
the present study only makes this type of consideration even more applicable. Therefore,
the failure of the current generation of antiviral agents, when used as monotherapy, is the
inevitable consequence of the dynamics of HIV-1 replication. Eective treatment must,
instead, force the virus to mutate simultaneously at multiple positions in one viral genome
by using a combination of multiple, potent antiretroviral agents. Moreover, that the process
of producing mutant viruses is repeated for 140 generations each year argues strongly
for aggressive therapeutic intervention early if a dramatic clinical impact is to be achieved
22
. Third, from the current study and previous reports (1,2,5), it is now clear that the
\raging re" of active HIV-1 replication (left side of Fig. 2) could be put out by potent
antiretroviral agents in 2-3 weeks. However, the dynamics of other viral compartments
must also be understood. Although they contribute 1% of the plasma virus, each
viral compartment (right side of Fig. 2) could serve as the \ember" to re-ignite highlevel viral replication when the therapeutic regimen is withdrawn. In particular, we must
determine the decay rate of long-lived, virus-producing population of cells such as tissue
macrophages, as well as the activation rate of cells latently carrying infectious proviruses.
This information, someday, will enable the design of a treatment regimen to block de novo
HIV-1 replication for a time sucient to permit each viral compartment to \burn out."
10
REFERENCES AND NOTES
1. D. D. Ho et al, Nature 373, 123 (1995).
2. X. Wei et al, Nature 373, 117 (1995).
3. M. A. Nowak et al, Nature 375, 193 (1995).
4. D. J. Kempf et al, Proc. Natl. Acad. Sci. USA 92, 2484 (1995).
5. M. Markowitz et al, N. Engl. J. Med., 333, 1534 (1995).
6. C. Pachl et al, J. AIDS 8, 446. (1995).
7. Y. Cao et al, AIDS Res. Human Retroviruses 11, 353 (1995) .
8. D. L. Winslow and M. J. Otto, AIDS 9 (Suppl A), S183 (1995).
9. The rate of viral production is expressed as the product
N
to convey either of two
possibilities: that HIV-1 is produced continuously at an average rate given by the
total production of virus particles, , divided by the cell lifespan, 1 , or that
N
=
N
virions are produced in lytic bursts occurring at the rate of cell death, .
10. The eect of a non-perfect drug can be modeled by simply adding the term
(1 ; )
N T
to Eq. (4) and multiplying the rst term in Eq. (5) by the factor ,
where represents the drug's inhibitory activity, e.g., =
( +
D= D
E C50
), where
D
is the plasma concentration of drug and EC50 is the concentration required for 50%
eectiveness.
11. In quasi-steady state
cV0
dT
=dt
= 0 and
dV =dt
= 0. Thus,
kV0 T0
=
T0
and
N T0
=
, where the subscript 0 indicates a steady-state value. Combining these equations,
11
we nd
N kT0
= . Each virion infects cells at rate
c
on average to the production of
new virions at rate
N kT0
N
kT0
, with each infection leading
new virions. At steady-state, the production of
must balance the virion clearance at rate .
c
12. Equation (6) diers from the equation, ( ) =
V
t
V0
c;
;t
ce
;
;ct
e
], introduced by
Wei et al. 2 for analyzing the eects of drug treatment on viral load. Their analysis
is based on Eqs. (1) and (2) and the assumption that no new infections occur after
drug treatment ( = 0 after treatment). Equation (6) is a new model appropriate
k
for protease inhibitors, which do not prevent infections from pre-existing mature
infectious virions. Note that because of the symmetry between and in the Wei
c
et al. equation, one cannot distinguish by data tting the viral clearance rate from
the infected cell death rate.
13. Because our parameter estimates are based on the assumption of complete inhibition
of the production of new infectious virions and no increase in target cells, we expect
that our parameter estimates to be minimal estimates. Generalizing our model to
relax these two assumptions, we can show that is always a minimal estimate and
that with target cell growth , typically, is also a minimal estimate. We tested how
c
the estimates of and depend on the assumption that ritonavir is 100% eective
c
as follows: We generated viral load data assuming dierent drug eectivenesses with
c
= 3 and = 0 5. With this \data" we used our tting procedure to estimate
:
c
and under the assumption that the drug is 100% eective. For data generated with
= 1 0 0 99 0 95, and 0.90, we estimated = 3 000 3 003 3 015 and 3.028,
: :
:
:
c
:
:
respectively, and that = 0 500 0 494 0 470 and 0.441, respectively. Thus, our
:
:
12
:
estimate of remains essentially unchanged, while that of is a slight underestimate,
c
(e.g., for = 0 95, = 0 47 rather than the true 0.5). Consequently, if a drug is
:
:
not completely eective, cell lifespans may be somewhat less than we estimate. If
the target cells are allowed to increase by the maximum factor observed in the ve
patients, ve-fold, we nd that the derived values of and are minimal estimates.
c
Thus, for example, for data generated with = 1, with = 3 00 and = 0 500, we
c
:
:
nd that our tting procedure estimates = 2 76 and = 0 499.
c
:
:
321, 1621 (1989).
14. D. D. Ho, T. Moudgil, M. Alam, N. Engl. J. Med.
15. Virions that are not released into the extracellular uid are not included in this
estimate. Thus, the total production in the body is even larger.
16. The solution to Eq. (3) is
T
( ) = ;0
T
t
c
;t
ce
;
;ct e
:
If cellular RNA data were obtained, this equation could be tted to that data, and
the parameter estimates for and could be veried for consistency with the viral
c
kinetics.
17. In principle, more accurate estimates of the duration of the intracellular or eclipse
phase of the viral life cycle can be obtained using a model in which one explicitly
includes a delay from the time of infection until the time of viral release. For
example, one can replace Eq. (2) by
dV =dt
=
N
R1
0
T
( ; 0) ( 0)
t
t
! t
dt
0
;
cV
,
where ( 0 ) is the probability that a cell infected at time ; 0 produces virus at
! t
t
t
time . Explicit solutions to our model, with ( 0 ) given by a gamma distribution,
t
! t
13
will be published elsewhere. Alternatively, one can keep track not of infected cells,
, but of virally producing cells, p , where now Eq. (1) is replaced by
T
T
kT
R1
0
V
( ; 0) ( 0)
t
t
! t
0
dt
;
Tp
dTp =dt
=
. Models of this type can also be solved explicitly when
( 0 ) is given by a gamma function. M. Nowak and A. Herz, Oxford Univ. (personal
! t
commun.), have solved this model for the case of ( 0 ) being a delta-function, in
! t
which case the delay simply adds to the pharmacologic delay and one regains Eq.
(6) after this combined delay. Analysis of current data by nonlinear least squares
estimation has so far not allowed accurate simultaneous estimation of , and the
c
intracellular delay. However, the qualitative eect of including the delay in the
model is to increase the estimate of , consistent with our claim that the values of
c
c
in Table 1 are minimal estimates. Increasing , will decrease 1 , and increase the
c
=c
estimate, ; 1 , of the intracellular delay. Thus, the duration of the intracellular
S
=c
phase, as derived in the text and given in Table 2, is still a minimal estimate.
18. A. Carmichael, X. Jin, P. Sissons, L. Borysiewicz, J. Exp. Med.
19. N. Nathanson and B. Harrington, Amer. J. Epidemiol.
177, 249 (1993).
85, 494 (1966).
20. J. M. Con, Science 267, 483 (1995).
21. L. M. Mansky and H. M. Temin, J. Virol.
22. D. D. Ho, N. Engl. J. Med.
69, 5087 (1995).
333, 450 (1995).
23. B. Efron and R. Tibshirani, Stat. Sci. 1, 54 (1986).
24. We thank the patients for participation, A. Hurley, Y. Cao, and scientists at Chiron
for assistance, B. Goldstein for the use of his nonlinear least squares tting package,
14
and G. Bell, T. Kepler, C. Macken, E. Schwartz, and B. Sulzer for helpful discussions
and calculations. Portion of this work were performed under the auspices of the
U.S. Department of Energy. This work was supported by Abbott Laboratories, the
NIH (NO1 AI45218 and RR06555), the NYU Center for AIDS Research (AI27742)
and the General Clinical Research Center (MO1 RR00096), the Aaron Diamond
Foundation, the Joseph P. Sullivan and Jeanne M. Sullivan Foundation, and the Los
Alamos National Laboratory LDRD program.
15
Figure and Table Captions
Figure 1. (A) Plasma levels of HIV-1 RNA (circles) for two representative patients after
ritonavir treatment was begun on day 0. The theoretical curve (solid line) was obtained
by nonlinear least-square tting of Eq. (6) to the data. The parameters, , viral clearance
c
rate, , the rate of loss of infected cells, and 0, the initial viral load, were simultaneously
V
estimated. To account for the pharmacokinetic delay, = 0 in Eq. (6) was assumed to
t
correspond to the time of the pharmacokinetic delay (if measured) or was chosen as the
best t value among 2, 4, and 6 hours (see Table 1). The logarithm of the experimental
data was tted to the logarithm of Eq. (6) by a nonlinear least squares method employing
the subroutine, DNLS1, from the Common Los Alamos Software Library, which is based
on a nite dierence Levenberg-Marquardt algorithm. The best t, with the smallest sum
of squares per data point, was chosen after eliminating the worst outlying data point for
each patient using the jacknife method. (B) Plasma levels of HIV-1 RNA (circles) and the
plasma infectivity titer (squares) for patient 105. (Top panel) The solid curve is the best
t of Eq. (6) to the RNA data. With the best t parameters, we also show (short-dashed
line) the curve of noninfectious pool of virions,
( ), and (long-dashed line) the curve of
VNI t
infectious virions I ( ). (Bottom panel) The long-dashed line is the best t of the equation
V
t
for I ( ) to the plasma infectivity data. TCID50 : 50% tissue culture infectious dose.
V
t
Figure 2. Schematic summary of the dynamics of HIV-1 infection in vivo. Shown in
the center is the cell-free virion population that is sampled when the viral load in plasma
is measured.
16
Table 2 Legend. The viral life cycle, , and the minimal estimate of the intracellular
S
phase, ; 1 , were obtained by a heuristic procedure and should be viewed as rough
S
=c
estimates. The standard deviations (STD) indicate the dierences between patients and
not the accuracy of the estimates. To estimate the in vivo value of the average viral
generation time, , the fate of a large population of virions is followed. For a system
in quasi-steady state, the average generation time can be dened as the time it takes
V0
particles to produce the same number of virions in the next generation. After a protease
inhibitor has been administered, assume all newly produced virions are noninfectious. In
order to keep track of the number of noninfectious particles, we assume for the purposes
of this calculation that noninfectious particles are not cleared and act as a perfect marker
recording the production of virions after one round of infection. Thus, from Eq. (5),
dVNI =dt
i.e.
T
=
N T
. We also assume that before drug is given there are no infected cells,
(0) = 0, so that only new infections are tracked. Under these circumstances,
is the average time needed for
V0
virions to produce
V0
noninfectious particles after
ritonavir administration. Following treatment, no further infectious particles are produced
and hence infectious particles, I , decline exponentially, i.e., I ( ) =
V
V
t
;ct
V0 e
, where = 0
t
is the time at which the drug takes aect after pharmacokinetic delays. The existing
infectious particles infect cells, and the number of infected cells,
the solution of Eq. (3), with the initial condition
mean number of virions produced from the initial
T
T
, varies as given by
(0) = 0. At any given time, , the
V0
t
virions is
( ) = ( ) 0 , where
VN I t
P t V
( ) is the (cumulative) probability that a virion is produced by time . The probability
P t
t
density of a virus being produced at time is ( ) =
t
of virion production
=
R1
0
p t
dP =dt
, and thus the average time
( ) . Using the above, we nd
tp t dt
17
=
R
1 1 dVNI
V0 0 t dt dt
=
1 R1
V0 0 tN T
. Substituting the solution of Eq. (3) for
dt
= ( 1 + 1c ). Because the system is at steady state 11, =
c
T
and integrating, we nd
N kT0
, and thus the clearance
rate and rate of new cell infection are coupled. Thus, the viral generation time can also
be viewed as the time for an infected cell to produce
plus the time for this cohort of
i.e., 1 (
= N kT0
N
N
new virions, i.e., its lifespan 1 ,
virions to infect any of the
).
18
=
T0
uninfected target cells,