# Estimating the impact of vaccination on acute simian-human immunodeficiency virus/simian immunodeficiency virus infections.

**ABSTRACT** The dynamics of HIV infection have been studied in humans and in a variety of animal models. The standard model of infection has been used to estimate the basic reproductive ratio of the virus, calculated from the growth rate of virus in acute infection. This method has not been useful in studying the effects of vaccination, since, for the vaccines developed so far, early growth rates of virus do not differ between control and vaccinated animals. Here, we use the standard model of viral dynamics to derive the reproductive ratio from the peak viral load and nadir of target cell numbers in acute infection. We apply this method to data from studies of vaccination in SHIV and SIV infection and demonstrate that vaccination can reduce the reproductive ratio by 2.3- and 2-fold, respectively. This method allows the comparison of vaccination efficacies among different viral strains and animal models in vivo.

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**ABSTRACT:**Cytotoxic T-lymphocytes (CTLs) recognize viral protein fragments displayed by major histocompatibility complex molecules on the surface of virally infected cells and generate an anti-viral response that can kill the infected cells. Virus variants whose protein fragments are not efficiently presented on infected cells or whose fragments are presented but not recognized by CTLs therefore have a competitive advantage and spread rapidly through the population. We present a method that allows a more robust estimation of these escape rates from serially sampled sequence data. The proposed method accounts for competition between multiple escapes by explicitly modeling the accumulation of escape mutations and the stochastic effects of rare multiple mutants. Applying our method to serially sampled HIV sequence data, we estimate rates of HIV escape that are substantially larger than those previously reported. The method can be extended to complex escapes that require compensatory mutations. We expect our method to be applicable in other contexts such as cancer evolution where time series data is also available.Frontiers in Immunology 01/2013; 4:252. - SourceAvailable from: Kei SatoHiroki Ikeda, Rob J de Boer, Kei Sato, Satoru Morita, Naoko Misawa, Yoshio Koyanagi, Kazuyuki Aihara, Shingo Iwami[Show abstract] [Hide abstract]

**ABSTRACT:**Mathematical modeling of virus dynamics has provided quantitative insights into viral infections such as influenza, the simian immunodeficiency virus/human immunodeficiency virus, hepatitis B, and hepatitis C. Through modeling, we can estimate the half-life of infected cells, the exponential growth rate, and the basic reproduction number (R0). To calculate R0 from virus load data, the death rate of productively infected cells is required. This can be readily estimated from treatment data collected during the chronic phase, but is difficult to determine from acute infection data. Here, we propose two new models that can reliably estimate the average life span of infected cells from acute-phase data, and apply both methods to experimental data from humanized mice infected with HIV-1.Theoretical Biology and Medical Modelling 05/2014; 11(1):22. · 1.27 Impact Factor - SourceAvailable from: Vitaly V GanusovVitaly V Ganusov, Nilu Goonetilleke, Michael K P Liu, Guido Ferrari, George M Shaw, Andrew J McMichael, Persephone Borrow, Bette T Korber, Alan S Perelson[Show abstract] [Hide abstract]

**ABSTRACT:**HIV-1 often evades cytotoxic T cell (CTL) responses by generating variants that are not recognized by CTLs. We used single-genome amplification and sequencing of complete HIV genomes to identify longitudinal changes in the transmitted/founder virus from the establishment of infection to the viral set point at 1 year after the infection. We found that the rate of viral escape from CTL responses in a given patient decreases dramatically from acute infection to the viral set point. Using a novel mathematical model that tracks the dynamics of viral escape at multiple epitopes, we show that a number of factors could potentially contribute to a slower escape in the chronic phase of infection, such as a decreased magnitude of epitope-specific CTL responses, an increased fitness cost of escape mutations, or an increased diversity of the CTL response. In the model, an increase in the number of epitope-specific CTL responses can reduce the rate of viral escape from a given epitope-specific CTL response, particularly if CD8+ T cells compete for killing of infected cells or control virus replication nonlytically. Our mathematical framework of viral escape from multiple CTL responses can be used to predict the breadth and magnitude of HIV-specific CTL responses that need to be induced by vaccination to reduce (or even prevent) viral escape following HIV infection.Journal of Virology 08/2011; 85(20):10518-28. · 4.65 Impact Factor

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JOURNAL OF VIROLOGY, Dec. 2008, p. 11589–11598

0022-538X/08/$08.00?0

Copyright © 2008, American Society for Microbiology. All Rights Reserved.

Vol. 82, No. 23

doi:10.1128/JVI.01596-08

Estimating the Impact of Vaccination on Acute Simian-Human

Immunodeficiency Virus/Simian Immunodeficiency Virus Infections?

Janka Petravic,1Ruy M. Ribeiro,2Danilo R. Casimiro,3Joseph J. Mattapallil,4

Mario Roederer,5John W. Shiver,3and Miles P. Davenport1*

Complex Systems in Biology Group, Centre for Vascular Research, University of New South Wales 2052, New South Wales, Australia1;

Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico 875452; Merck Research Laboratories,

West Point, Pennsylvania3; Department of Microbiology and Immunology, Uniformed Services University of Health Sciences,

Bethesda, Maryland 208244; and ImmunoTechnology Section, National Institute of Allergy and Infectious Diseases,

National Institutes of Health, Bethesda, Maryland 208925

Received 28 July 2008/Accepted 8 September 2008

The dynamics of HIV infection have been studied in humans and in a variety of animal models. The standard

model of infection has been used to estimate the basic reproductive ratio of the virus, calculated from the

growth rate of virus in acute infection. This method has not been useful in studying the effects of vaccination,

since, for the vaccines developed so far, early growth rates of virus do not differ between control and vaccinated

animals. Here, we use the standard model of viral dynamics to derive the reproductive ratio from the peak viral

load and nadir of target cell numbers in acute infection. We apply this method to data from studies of

vaccination in SHIV and SIV infection and demonstrate that vaccination can reduce the reproductive ratio by

2.3- and 2-fold, respectively. This method allows the comparison of vaccination efficacies among different viral

strains and animal models in vivo.

Human immunodeficiency virus (HIV) infects approxi-

mately 0.5% of the world population and is a major cause of

morbidity and mortality worldwide. A vaccine for HIV is ur-

gently required, and a variety of vaccine modalities have been

tested in animal models of infection. A number of these studies

have shown protection in monkey models of infection, al-

though the ability of the vaccine to protect appears to vary with

the viral strain and animal model used (8). The recent failure

of a large vaccine study in humans (1) suggests that further

understanding of the basic dynamics of infection and the im-

pact of vaccination are required in order to understand the

variable efficacies of vaccination in different infections.

The initial ability of HIV to propagate within the host is

determined by the abundance of target cells (e.g., CD4?T

lymphocytes) the virus can infect in order to produce progeny,

by the replicative capacity of the virus, and by how cytopathic

it is to infected cells. At later stages of the disease, in addition

to changes in the target cell availability, there may also be

changes in virus-specific properties, such as the ability of the

virus to reproduce and the survival of productively infected

cells as a result of changes in immune pressure and viral evo-

lution. These parameters may be variable among individuals

and within one individual over time and affect the impact of

vaccination. In order to compare the efficacies of vaccination

strategies, we need a quantitative measure of the factors that

influence virus replication.

In this work, we focus on the basic reproductive ratio (R0) as

a measure of vaccine efficacy in the acute phase of infection. In

epidemiology, R0measures the potential for the spread of an

epidemic and is defined as the average number of people

infected by one infected individual in a susceptible population.

If this number is below 1, the disease will not spread in a

population. Therefore, the knowledge of R0allows one to

estimate the fraction of a population that needs to be vacci-

nated in order to eradicate the disease. Analogously, in host-

pathogen dynamics, the basic reproductive ratio is defined as

the number of infected cells generated by one infected cell

during its lifetime at the start of infection, i.e., before any

depletion of target cells. In order for the infection to spread

within the host, this number has to be larger than 1; otherwise,

the infection will be cleared before it has a chance to spread.

The basic reproductive ratio will depend on the ability of virus

to infect cells (“infectivity”), on the rate of virion production by

infected cells, on the lifetime of infected cells, and on the rate

at which free virus is cleared. The aim of vaccines is therefore

to create virus-specific immunity that changes any of these

parameters and thus decreases the basic reproductive ratio of

the virus, preferably below 1 (so that infection does not spread

beyond the initially infected cells). The importance of R0in

HIV vaccination, in order to assess how much protection a

particular vaccine can achieve, has been stressed previously

(11). Specifically, a variety of different animal models have

been used to study HIV vaccination. They differ in a number of

ways, particularly in the virulence and cell tropism of the virus.

Comparison between models may be difficult because of dif-

ferences in the underlying dynamics of infection. For example,

it may be more difficult to prevent CD4?T-cell depletion in a

very virulent animal model than in other infections, because of

the higher underlying growth rate. Thus, a vaccine may appear

efficacious in one model but ineffective in another, despite the

fact that it may have the same impact on viral growth. Mea-

surement of R0allows comparison of the effectiveness of dif-

* Corresponding author. Mailing address: Complex Systems in Bi-

ology Group, Centre for Vascular Research, University of New South

Wales 2052, New South Wales, Australia. Phone: 612 9385 2762. Fax:

61-2-9385 1389. E-mail: m.davenport@unsw.edu.au.

?Published ahead of print on 17 September 2008.

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ferent vaccines within a given animal model, as well as across

different models. It could be a very useful and common stan-

dard to compare different vaccination protocols.

The basic reproductive ratio can be determined from the

rate of exponential growth of virus in the initial period, during

which the target cell levels are almost constant (14, 20, 29).

However, in monkeys infected with the same type of simian

immunodeficiency virus (SIV) there is in fact very little varia-

tion in the basic reproductive ratio determined from the initial

exponential growth between controls and vaccinees, despite

the variety of outcomes later in infection. Different factors

identified as possible predictors of disease progression (29),

such as the peak viral load, target cell nadir, decay rate of virus

following peak viremia, set point viral load, and chronic target

cell levels, all correlate poorly or not at all with the differences

in the reproductive ratio determined from the primary expo-

nential growth phase (29). In particular, it is not possible to

assess the efficacy of cytotoxic-T-lymphocyte (CTL)-based vac-

cines on the basis of the basic reproductive ratio, because there

is no effect of vaccination on viral growth before approximately

10 days postinfection, which is at the end of the exponential

growth period (4, 6).

We have recently shown the existence of a strong correlation

between the viral load at peak and the target cell depletion in

the acute phase (7, 32). Using this correlation, one can show

that vaccination results in the reduction of the peak viral load

and of acute CD4?T-cell depletion, thus improving the chronic-

phase prognosis.

The dependence of the nadir in the CD4?T-cell count on

the viral peak can be obtained from the standard model of

virus dynamics (7, 32). Here, we show that this relationship

between the viral peak and the number of target cells 1 week

after the peak (corresponding approximately to the minimum

number of target cells in primary infection) is parameterized

by the basic reproductive ratio of the virus. In other words, the

decrease in the peak viral load leads to less target cell deple-

tion at nadir, and both are a consequence of a lower basic

reproductive ratio. Thus, we can in principle determine the

basic reproductive ratio from experimental data on the viral

peak and target cell nadir. We show that this relationship is

indeed supported by experimental data from CXCR4-tropic

simian-human immunodeficiency virus (SHIV) infection (for

viral loads and CD4?T-cell counts in peripheral blood) and

for CCR5-tropic SIV infection data (for plasma viral loads and

memory CD4?T-cell depletion in the gut).

We show that the reproductive ratio estimated from the viral

peak and the target cell nadir, which we call the “reproductive

ratio at the peak,” is significantly lower than the basic repro-

ductive ratio estimated from the exponential growth. In addi-

tion, we found that in vaccinated animals the reproductive

ratio at the peak is on average twofold lower than in control

animals. We attribute this difference to the cellular immune

response appearing before the peak viral load, around day 10

of infection, and changing the properties of the virus and

infected-cell dynamics (e.g., decreasing the lifetime of infected

cells through the cytolytic function of CTLs or changing infec-

tivity or virus production through the release of cytokines).

Thus, we propose that the “reproductive ratio at the peak,” a

measurement that includes information on both the viral peak

and the target cell nadir, can be useful as a standard to com-

pare vaccine protocols.

MATERIALS AND METHODS

In the CXCR4-tropic virus study, 35 rhesus macaques (Macaca mulatta) were

vaccinated with a variety of regimens, consisting of SIV gag-containing plasmid

DNA (with different adjuvants), modified vaccinia virus Ankara, and adenovirus

type 5 vectors, as previously reported (27). Animals were challenged intrave-

nously at 6 weeks (study A) or at 12 weeks (study B) after the final boost with 50

monkey infectious doses of SHIV-89.6P. Viral loads and CD4?T-cell counts

were monitored in peripheral blood every 2 to 4 days until 4 weeks after infection

and then weekly. The results of the two studies were combined for the purpose

of this work.

In the CCR5-tropic virus study, 20 rhesus macaques were challenged intrave-

nously with 100 monkey infectious doses of uncloned SIVmac251. Six of these

animals received prior vaccination with plasmid DNA encoding SIV envelope,

Gag, and Pol, and were boosted with recombinant adenovirus encoding the same

antigens. Plasma and jejunum tissue samples were collected at various time

points by biopsy or at necropsy, and tissue CD4?T-cell percentages and plasma

viral loads were determined (17, 18).

RESULTS

Reproductive ratio in the initial exponential growth phase of

disease. The standard model of virus dynamics (15, 21) de-

scribes the relationships between the change in the number of

uninfected cells, T, that are targets for the virus; infected cells,

I; and free virus particles, V, in a given volume of blood or

tissue.

dT

dt? ? ? dTT ? ?VT(1)

dI

dt? ?VT ? ?I(2)

dV

dt? pI ? cV(3)

The parameters ?, the production rate of new target cells, and

dT, the loss rate of uninfected cells, describe the disease-free

target cell dynamics. The disease-free equilibrium number of

target cells is equal to T0, which is equal to ?/dT. The infectiv-

ity, ?, characterizes the rate at which a virus particle infects a

target cell, and ? is the death rate of infected cells; ? ? ? dT.

Free virus is produced by infected cells at rate p and is cleared

at rate c. In this model, the immune response is assumed to be

constant, and its effects are contained in the virus parameters

?, c, ?, and p. All the parameters are assumed to be constant

in time (28). The basic reproductive ratio, R0, for this model is

as follows (15, 21):

R0? T0

?p

?c

(4)

The virus infection can spread only if R0is ?1. In this case, the

viral load generally increases to the peak and then decays, in

order to finally reach the steady-state value, V*. Target cells

drop to the minimum and then partly recover and settle at the

steady-state value, T*, which is equal to T0/R0. The standard

model has been used to investigate different aspects of HIV/

SIV/SHIV infection, such as the turnover of infected cells (7,

12, 31), the clearance rate of virus (23), and the “burst size” of

infected cells (3, 13).

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The basic reproductive ratio of a virus is determined from

the initial rate of exponential expansion, r0, during which the

number of target cells is approximately constant (14, 20, 25).

Thus, if we know the initial exponential growth rate of a virus

(r0' 1/V dV/dt) and the death rate of infected cells (?), we can

estimate R0:

r0? ??R0? 1?

(5)

In Fig. 1A, we show viral-load data during the first weeks of

infection from the Shiver et al. study (27), in which 21 out of 35

rhesus macaques were vaccinated with seven different SIV

gag-containing vaccines, and all 35 were challenged intrave-

nously with CXCR4-tropic SHIV-89.6P. The initial exponen-

tial growth rate and the decay rate of virus after the peak were

remarkably similar between monkeys, irrespective of whether

they were vaccinated. The results of the statistical analysis are

summarized in Fig. 1C and D and Table 1.

Equation 5 indicates how to measure R0from the initial

growth rate of virus and the death rate of infected cells. The

initial growth rate of virus (r0) is directly estimated from the

experimental data. The death rate of infected cells (?) can be

estimated from the rate of decline of the viral load after the

peak in each animal. Using this approach, we estimate that R0

is 2.4 for vaccinated animals (95% confidence interval [CI], 2.3

to 2.6) and almost the same, 2.5, for control animals (95% CI,

2.3 to 2.7). The two values are not statistically different (Mann-

Whitney, P ? 0.391).

On the basis of the similarity in virus growth and decay rates

between control and vaccinated animals, we (4, 6) and others

(24) concluded that the cellular (CD8?T-cell) immune re-

sponse does not emerge before at least 10 days postinfection

(reviewed in reference 5). This is why it has not been possible

to assess the effects of vaccination from the reproductive ratio

of the virus calculated from its growth rate within this initial

period of 10 days.

Equation 5 considerably underestimates R0because it ne-

glects the delay between the time when a cell becomes infected

and the time when it starts producing the virus. In a model with

FIG. 1. Dynamics of acute SHIV-89.6P infection. The time courses of the viral load (A) and CD4?T-cell numbers (B) are shown over the first

40 days of SHIV infection for control (black lines) and vaccinated (red lines) animals. The initial viral growth rates (r0) (C) and viral decay rates

(?) (D) after the peak viral load of SHIV-89.6P do not differ significantly between controls (black dots) and vaccinees (red dots). However, the

peak viral load (E) and the nadir CD4?T-cell number (F) are significantly different between controls and vaccinees. In panels C to F, the gray

rectangles represent the confidence intervals.

TABLE 1. Summary of statisticsa

Parameter

r0(per day)b

? (per day)c

LogVPd

Tmin(no. of cells/?l)e

Control VaccinatedControl VaccinatedControl Vaccinated ControlVaccinated

Mean

SE

95% CI

1.42

0.055

1.30–1.54

1.38

0.043

1.29–1.47

0.991

0.058

1.01

0.046

8.03

0.12

7.19

0.13

29.4

13.7

238

48

0.866–1.12 0.913–1.107.75–8.286.92–7.49 1.13–57.6137–339

aFor initial exponential growth rate, r0; decay rate of virus after the peak, ?; peak viral load, VP; and the target cell nadir, Tmin, in vaccinated and unvaccinated

animals.

bMann-Whitney P value, 0.83.

cMann-Whitney P value, 0.90.

dMann-Whitney P value, 0.00018.

eMann-Whitney P value, 0.00015.

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a fixed intracellular delay, ? (and assuming that all infected

cells survive the delay period) (10), R0is found from the initial

growth rate as follows (15, 25):

R0? ?1 ? r0/??er0?

(6)

With a delay of 1 day (22), we obtain an R0of 9.9 for vacci-

nated animals (95% CI, 8.6 to 11) and an R0of 11 for control

animals (95% CI, 8.6 to 12), again not different for the two

groups and consistent with previous studies of the basic repro-

ductive ratio in SIV infection (20).

As demonstrated above, the traditional approach to measur-

ing R0in vaccinated animals shows no significant difference in

R0between controls and vaccinees, despite clear differences in

infection outcomes. Thus, we aimed to develop a new measure

of viral growth that can quantify vaccine effects.

Virus peak and target cell nadir in the standard model of

virus dynamics. In contrast to the exponential growth and

decay rates of the viral load, the peak of the viral load and the

nadir of CD4?T-cells were significantly different between con-

trol and vaccinated animals (Fig. 1B, E, and F and Table 1).

Since the peak viral load and level of depletion of CD4?T cells

were important factors that were clearly affected by vaccination

and were correlated with outcome, we aimed to develop a

measurement of viral growth and vaccine efficacy based on

them. Obtaining an expression for the peak viral load or nadir

target cell numbers is quite difficult using the standard model

(equation 1 to equation 3), since they are dependent on a large

number of other parameters. Thus, we needed to simplify the

standard model to identify which parameters can be ignored

because in practice they have negligible influence on the peak

viral load and nadir targets. Before infection, target cells are at

a constant level, which implies that the daily production (?)

and death (dTT0) are balanced, and it is thought that ?1% of

cells turn over in this way each day. Thus, early in infection,

while there is very little depletion in target cell numbers (T ?

T0) (Fig. 2), we can neglect those two terms in equation 1

because they balance each other. Around the peak of viremia,

there is massive infection of target cells (?VT becomes very

large), and up to 99% of cells disappear over a period of 1 to

2 weeks. During this period, the normal production and loss of

target cells (? and dT) are much smaller than the loss due to

infection (i.e., ?VT ? ? ? ? dTT), and we can safely ignore the

effects of normal turnover on the target cell number. That is,

we can simplify the standard model to the following (7):

dT

dt? ? ?VT(7)

dI

dt? ?VT ? ?I (8)

dV

dt? pI ? cV. (9)

In this reduced model, the viral load always vanishes at long

times (i.e., infection is always cleared if there is no natural loss

and replacement of target cells), with target cells steadily de-

clining toward a low steady-state value, Tmin. However, we can

further justify our approximation by noting that the profile of

viral-load and target cell dynamics during primary infection

(up to the target cell nadir, days 18 to 20 in Fig. 2) is only mildly

affected. As expected, the exponential growth rate of the virus

is the same as in the full standard model, and the viral load has

a maximum, VP, with a value very close to the peak of the

standard model (Fig. 2A).

Figure 2 also shows that the steady-state target cell number,

Tmin, in the reduced model is slightly lower, but still a very

good approximation for the uninfected target cell nadir of the

standard model in equation 1 to equation 3 if around 1% of

CD4?T cells turn over each day (i.e., for the parameters ? ?

10 cells/?l/day and dT? 0.01/day [28] usually attributed to

CD4?T cells in HIV/SIV/SHIV infection). The condition for

equation 7 to be a good approximation to the full model, that

is, ?VT ? ? ? ? dTT, is violated only very close to the nadir of

target cells, as the viral load decreases, and that is why we

obtain a good estimate of the nadir from this approximation.

This is true whenever the normal replacement or turnover of

CD4?T cells is relatively small.

Instead of uninfected target cells, the quantity that is usually

measured experimentally is the total number of uninfected and

infected cells (T ? I). Figure 2B shows that the minimum of

FIG. 2. A reduced model of viral dynamics. The time courses of virus growth and decay (A) and CD4?T-cell (target cell) decline in primary

infection (B) are shown, obtained by numerical integration of equation 1 to equation 3 and equation 7 to equation 9. (A) The peak viral loads for

the reduced model (?, dT? 0) and the standard model (? ? 10 cells/?l/day; dT? 0.01 day?1). (B) The nadir numbers of uninfected CD4?T cells

are indicated for the reduced model and the standard model. The total CD4?T-cell number (infected plus uninfected) is also indicated for the

standard model. The other parameters were as follows: ? ? 8 ? 10?8ml/copy/day, ? ? 0.8 day?1, P ? 103?l/ml ? 500 copies/cell/day, and c ?

20/day. The initial inoculum was 50 copies/ml.

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the total T-cell number is again very close to the minimum of

target cells. Therefore, we can compare the experimental nadir

target cell counts to the steady-state number of uninfected

cells, Tmin, in the reduced model.

An advantage of the reduced system in equation 7 to equa-

tion 9 is that one can estimate VPand Tminanalytically. We

shall use the analytical results as estimates for the viral peak

and the target cell nadir in the full standard model.

The basic reproductive ratio of the reduced model, R0, is still

given by equation 4 (with T0being an arbitrary initial target cell

number). The peak of viremia, as a function of R0, is as follows

(see the Appendix for the derivation):

?RP?1 ?

VP??

1

RP?lnRP

RP?

(10)

which is valid for the reduced model (equation 7 to equation 9)

and a good approximation for the standard model, with low

target cell replacement and loss (equation 1 to equation 3).

Tminis found as the solution of the equation (see the Ap-

pendix).

Tmin

T0

?

1

RPlnTmin

T0

? 1(11)

The fraction of uninfected target cells at the nadir in the full

standard model, approximately equal to Tmin/T0in equation

11, depends only on the basic reproductive ratio, R0. The

solution is illustrated in Fig. 3. For an R0of ?5, the value of

Tmin/T0is practically zero and the depletion at nadir is almost

100%. In Fig. 3, we plotted both Tmin/T0(the ratio at the target

cell nadir) and T*/T0(the ratio in chronic infection, i.e., in the

steady state, given by 1/R0) as functions of R0, showing that

Tminis always (for all R0) less than the steady-state target cell

count, T*.

Relationship between the virus peak and the target cell

nadir in the model. In the context of acute infection, i.e., the

time between the virus peak and the target cell nadir, we shall

call the expression in equation 4 the reproductive ratio at the

peak (and use the symbol RP) instead of the basic reproductive

ratio, in order to stress that the parameter values in this period

may have changed from those of initial infection. Thus, one

should replace the symbol R0by RPin equation 10 and equa-

tion 11. For a very low target cell replacement rate ? and loss

rate dT, the depletion (D) at the target cell nadir (D ? 1 ?

Tmin/T0[from equation 11]) depends only on the reproductive

ratio at the peak, RP, since this is the only free parameter in the

equation. The peak viral load (equation 10) depends on RP

and, in addition, on the ratio ?/?. This means that, for viruses

with different characteristic infectivities, ?, or different cyto-

toxicities and cellular immune responses resulting in different

death rates of infected cells, ?, the relationship between the

virus peak and the target cell minimum will be described by a

family of parallel sigmoid curves (Fig. 4A). RPvaries along

each curve with the characteristic ratio ?/?. Increases in infec-

tivity shift the curve to the left, while decreases in infectivity

shift it to the right.

Reducing the reproductive ratio at the peak for a given virus

decreases the peak viral load. The reduction of the peak by,

say, 0.5 log unit will have little effect on target cell depletion for

very high viral loads (when RPis high, there is a plateau at

nearly 100% depletion [Fig. 4]), but the same reduction can

significantly reduce CD4?T-cell depletion and change the

prognosis for lower viral loads (Fig. 4B).

The relationship between the peak viral load and the CD4?

T-cell nadir in experimental infection. The analysis above pro-

FIG. 3. The target cell nadir, Tmin, is lower than the steady-state

value, T*, for all values of R0.

FIG. 4. (A) The curve describing the relationship between the logarithm of the peak viral load and target cell depletion at the nadir has a

universal S shape and moves left or right only with the change in log(?/?). The constant ?/? is assumed to be characteristic of the virus type. Points

higher on the same curve have higher reproductive ratios at the peak RP. (B) The effect of lowering the virus peak depends on the basic

reproductive ratio and the peak viral load (i.e., on the value of ?/? and the peak viral load, which are likely characteristic of a particular virus).

For example, reducing the peak viral load by 0.5 log10copies/ml has a negligible impact on CD4?T-cell depletion in the shaded area to the right,

because depletion remains near 100%. However, for an infection with a lower R0and a lower peak viral load, the same reduction in the peak viral

load reduces CD4?T-cell depletion significantly (shaded area to left).

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vided a theoretical relationship between the peak viral load

and the CD4?T-cell nadir. We then investigated whether this

relationship was observed in experimental models of HIV in-

fection. As an illustration, we present the SHIV-89.6P data

(27) for the peak of virus and the depletion at the CD4?T-cell

minimum. The advantage of considering a CXCR4-tropic virus

is that it infects “all” CD4?T cells, so that the target pool in

peripheral blood is well defined and can be measured. In ad-

dition, for the total number of CD4?T cells, it is safe to

assume that the net replacement rate, ?, from the external

source (thymus) and, consequently, the loss rate, dT, are low

(i.e., that less than 1% of the normal uninfected CD4?T-cell

number is replaced from the thymus per day).

In Fig. 5A we show the measured values of depletion of

CD4?T cells at the nadir, defined as (1 ? Tmin/T0) ? 100%,

against the peak viral load for the control and vaccinated

animals. The theoretical relationship between the virus peak

(equation 10) and the CD4?nadir (Tminin equation 11) for

each value of the reproductive ratio RPdepends on ?/?. We

have shown in our earlier work that ? and ? do not vary much

between individual monkeys, whether vaccinated or not.

Briefly, the death rate of infected cells is the main determinant

of the slope of the viral load after the peak, and it does not

differ between controls and vaccinees (Fig. 1A and D) (4, 6).

Also, we have estimated the infectivity of SHIV-89.6P in rhe-

sus macaques on the same data set and found that there is no

significant difference between vaccinated and unvaccinated an-

imals (7). As explained in Fig. 4A, the shape of the theoretical

sigmoid curve, D(VP), cannot be changed by fitting, since it is

parameterized only by RP. It is universal for all diseases that

are well described by the standard model, with low replace-

ment and loss rates of target cells. However, by shifting the

curve along the x axis, we can determine the best-fit value of

the factor ?/? that minimizes the sum-of-squares deviation of

experimental data from the theoretical curve (Fig. 4A). Since

the quantities described by both axes have errors, the squared

deviation of each point is defined as the sum of squares of the

deviations in x and y directions from the closest point on the

theoretical curve (a form of type 2 regression). We found that

the best-fit value of log(?/?) is 7.53 (?/? ? 3.39 ? 107copies/

ml) with a CI of 7.45 to 7.65 found by bootstrapping. The

correlation coefficient (r2) was 0.985.

In our previous work (7), we estimated infectivity from the

relationship between the peak viral load and the number of

CD4?T cells 1 week after the peak, using the experimental

viral-load timeline and the first two equations of the reduced

model, equation 7 and equation 8. The procedure required

advance knowledge of the death rate of infected cells, ?, which

we estimated from the maximum decay rate of the viral load

after the peak as follows: ? ? 0.84/day. This led to the best-fit

average infectivity, ?, of 4.4 ? 10?8ml copy?1day?1(95% CI,

between 3.4 ? 10?8and 5.6 ? 10?8ml copy?1day?1). Our

present estimate of ?/? as 3.39 ? 107copies/ml with a ? of

0.84/day would give a lower best-fit infectivity of 2.48 ? 10?8

ml copy?1day?1for the same death rate of infected cells.

However, since the death rate of infected cells used in the

previous work was the minimum estimate of the actual death

rate, it is possible that both ? and our best-fit infectivity are

higher.

Analyzing infection by CCR5-tropic viruses is complicated

because the number of target cells (CCR5?CD4?T cells) is

more difficult to measure. However, in the gastrointestinal

tract, most CD4?T cells express CCR5 coreceptor, so most

gut CD4?T cells are targets for CCR5-tropic viruses. In recent

studies, Mattapallil et al. (17, 18) measured CD4?depletion in

the jejunum in 20 rhesus macaques infected with CCR5-tropic

SIVmac251, 6 of which were previously vaccinated.

Nine animals were euthanized before the viral load reached

the first peak, so they could not be analyzed. Figure 5B con-

tains data points from the remaining 11 animals (7 control

animals and 4 vaccinated animals). The longitudinal data for

each animal contain only three results of gut biopsies with

percentages of CD4?T-cells out of all CD3?lymphocytes, and

the lowest percentage was always the last point. We considered

this point to be close to the target cell nadir.

We assumed slow turnover of memory CD4?T cells prior to

infection, consistent with the lack of reconstitution of these

cells during antiretroviral therapy (19). The decay rate of

SIVmac251-infected cells has been independently estimated as a

? of 1.49/day (2). By means of the same procedure using equa-

tion 7, equation 8, and the experimental viral load, we esti-

mated the infectivity as a ? of 1.45 ? 10?7ml copy?1day?1, so

that ?/? was 1.02 ? 107(32).

The line corresponds to the value of log(?/?), which is equal

to 7.20 (?/? ? 1.58 ? 107copies/ml), which minimizes the

sum-of-squares deviation of experimental data from the theo-

FIG. 5. Fitting theoretical curves to experimental data. Best-fit curves for the relationship between CD4?T-cell depletion at the nadir and the

peak of virus (from equation 10 and equation 11) for SHIV-89.6P data (7, 27) (A) and for SIVmac251data (B) (17, 18, 32). The solid lines are the

best-fit curves obtained by optimization of the value of ?/?.

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retical curve [the CI for log(?/?) is 7.09 to 7.59; the correlation

coefficient, r2, is 0.874). The scatter of the experimental points

around the theoretical curve is much larger than for SHIV

infection in Fig. 5A. One reason for the larger scatter is the

infrequent sampling in the longitudinal data (each animal had

only one biopsy before challenge and one postchallenge and a

necropsy), which probably caused imprecision in the estimates

of the minimum. One would need in principle several samples

in the 2- to 3-week period after the peak in order to correctly

estimate the nadir. Another reason for the scatter could be that

the depletion was calculated from the change in the fraction of

CD4?T cells (out of all CD3?cells) instead of the CD4?

T-cell count used in the model. The two ways of calculating

depletion would be equivalent only if the number of CD3?

lymphocytes stayed constant during the infection. The in-

creased scatter of experimental data compared to SHIV infec-

tion can also be observed in the curve fit in reference 32.

Vaccination reduces the reproductive ratio at the peak of the

virus. The fitting of the model to experimental data suggests

that the theoretical curves are a good predictor of the relation-

ship between the viral load and CD4?T-cell depletion in

SHIV/SIV infection. Thus, we went on to use this approach to

estimate the impact of vaccination on the reproductive ratio at

peak. We first applied this approach to the experimental data

on SHIV89.6P infection. Figure 5A shows that vaccinated an-

imals have on average significantly lower peak viral loads (vac-

cinated logVP? 7.19 [95% CI, between 6.92 and 7.47]; unvac-

cinated logVP? 8.03 [95% CI, 7.78 and 8.28]; Mann-Whitney,

P ? 0.0004) and lower CD4?T-cell depletion at minimum

(vaccinated Dmin? 81.7% [95% CI, 71.4 and 92.1%]; unvac-

cinated Dmin? 97.4% [95% CI, 95.2 and 99.7%]; Mann-Whit-

ney, P ? 0.0003), so we expect the average reproductive ratio

at the peak to be lower in vaccinated animals. The results are

summarized in Fig. 6.

The change in the reproductive ratio from R0to RPis as-

sumed to be the result of the change in the virus-dependent

parameters due to the onset of cellular immunity a few days

before the peak of the viral load, i.e., before significant deple-

tion of target cells (5). The relationship between the virus peak

and the CD4?T-cell nadir in SHIV-89.6P is consistent with

slow replacement of uninfected cells, so that in this case, the

depletion at nadir can be considered to be completely deter-

mined by the peak reproductive ratio, RP, of the virus (equa-

tion 11). From the range of the nadir CD4?T-cell depletions

and peak viral loads, we can determine the range of the repro-

ductive ratios at the peak of SHIV-89.6P in the infected ani-

mals in the Shiver et al. study (18). Therefore, we estimate the

range of RPfrom the range of peak viral loads and the line of

best fit in Fig. 5A, assuming ?/? ? 107.53. The obtained range

of RPis between 1.5 and 19.2. The peak reproductive ratio, RP,

for vaccinated animals is 3.81, with a 95% CI between 2.3 and

4.6. For unvaccinated animals, RPis 8.87 with a 95% CI be-

tween 4.8 and 11.0. Vaccinated animals have on average a

significantly lower peak reproductive ratio (Mann-Whitney,

P ? 0.0007).

Since the 21 animals in the Shiver study were vaccinated with

seven different types of vaccines, all we can conclude is that, in

general, the effect of vaccination is to reduce the peak repro-

ductive ratio of the virus. The amount by which RPis reduced

with respect to the average in control animals would reflect the

effectiveness of a particular vaccine.

We obtained similar reduction in the reproductive ratio at

the peak for SIVmac251in the jejunum tissues of the macaques

in the Mattapallil et al. study (17, 18). The vaccinated animals

had an RPvalue of 1.8, and control animals had an RPvalue of

3.6; however, the difference did not reach significance (Mann-

Whitney, P ? 0.073) due to the small sample size (11 animals).

DISCUSSION

Vaccination trials have been used to compare the effective-

ness of different vaccines in a number of monkey species, and

using a wide variety of vaccine modalities. The efficacies of

different vaccines can then be ranked by comparison of their

abilities to preserve CD4?T-cell numbers or reduce peak viral

loads. Such comparisons can be misleading at times, since in

viruses with a higher R0, it is much more difficult to prevent

CD4 T-cell depletion than in viruses with low R0. Thus, the

ideal metric for ranking vaccines would allow comparison of

efficacies both within one infection model and across multiple

infection models. Moreover, such a metric should also allow

consideration of whether a given vaccine may be more effective

in more virulent infections (with high R0) or less virulent in-

fections, in order to predict which will perform best in HIV.

Previous approaches to comparing viral virulence have mea-

sured the basic reproductive ratios (R0) of different infection

models. The basic reproductive ratio contains all model pa-

rameters in the initial exponential growth phase of the virus.

While R0may be useful in comparing different animal models

of infection, it is not useful in quantifying the impact of vacci-

nation. In particular, it does not reflect the effects of the cel-

lular immune responses (or, consequently, the effects of vac-

cination) in primary infection, because in current vaccines

these effects become evident only at the end of the early ex-

pansion period (4, 5).

In order to overcome this limitation, we used a modeling

approach to develop a new method of estimating both the

FIG. 6. Measuring the impact of vaccination. The values of the

basic reproductive ratio (R0) and the reproductive ratio at peak (RP)

were estimated for SHIV-89.6P infection. Distributions of values of

the basic reproductive ratio, R0, obtained from the initial exponential

growth rate with a fixed intracellular delay of 1 day show no difference

between control (solid circles) and vaccinated (solid diamonds) ani-

mals. The values of the peak reproductive ratio, RP, (estimated from

the virus peak and the target cell nadir) are reduced approximately

twofold in vaccinated animals (open diamonds) compared to controls

(open circles).

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virulence of infection and the impact of vaccination, which we

term the reproductive ratio at peak. We first showed that the

relationship between the virus peak and the target cell nadir in

the acute phase of the CXCR4-tropic SHIV infection and

CCR5-tropic SIV infection is consistent with the standard

model of virus dynamics. This relationship allowed us to esti-

mate the decrease in reproductive capacity of the virus caused

by vaccination. We have defined the reproductive ratio at the

peak as the same function of the standard model parameters as

in the basic reproductive ratio but evaluated in the period

between the viral peak and the CD4?T-cell nadir. In this

period, CTL response is the main factor responsible for the

change of parameters. We found that in both SHIV and SIV

infections, vaccination on average reduced the reproductive

ratio at the peak between 2 and 2.5 times. This was not suffi-

cient to clear the virus. In order to suppress the infection

during the first few weeks, vaccines should decrease the repro-

ductive ratio below unity, i.e., approximately eightfold for

SHIV and fourfold for SIV. In the absence of CTL responses,

the basic and the peak reproductive ratios would probably be

the same (this is in principle testable in macaques with anti-

CD8 treatment). However, our method cannot determine spe-

cifically which parameters have changed as a result of the CTL

response, only that the compound quantity RPhas changed

considerably as a result of vaccination.

The disadvantage of using the reproductive ratio at the peak

as a measure of immune pressure is that the method requires

knowledge of the target cell numbers, which is straightforward

to measure in blood for CXCR4-tropic viruses but may require

sampling of mucosal sites for CCR5-tropic viruses, like HIV

(9). In the present study, we have also focused on CD4?T cells

as the major targets for HIV infection; however, macrophages

and other cells may also play a minor role (26, 30). With this

limitation, the method would be applicable to a variety of viral

infections.

The basic reproductive ratio at peak permits comparisons of

vaccine efficacies between studies performed in different ani-

mal models of infection. In addition, it also has the inherent

threshold of unity in its definition. The idea of reducing the

basic reproductive ratio of the virus below unity by inducing

specific immune response has been present in the context of

HIV vaccination for a long time (11). However, we believe that

we present the first method that allows evaluation of the im-

pact of vaccination using such a concept, in this case, the

“reproductive ratio at the peak.”

APPENDIX

Derivation of equation 10 for virus peak. Let us assume that

at the start of infection, t ? 0, we have an initial target cell

number T0and an initial viral load V0, with an initial number

of infected cells, I0, equal to 0. If the peak viral load, VP, occurs

at time tPand the target and infected cell numbers at tPare TP

and IP, respectively, then

dV

dt? pIp? cVP? 0(A1)

leads to

IP?c

pVP

(A2)

If we assume that V and I peak at the same time, which is true

when c is ? ??I, then from

dI

dt? ?VPTP? ?Ip? 0 (A3)

it follows that

TP??c

?p? T* ?T0

RP

(A4)

where T* is the steady-state target cell number in the full

standard model, equation 1 to equation 3. The lag between the

peak of infected cells and the viral load becomes negligible in

the limit ? ? ? c. This is justified in the case of HIV/SIV/SHIV

infection, where the parameter estimates are as follows: ? ?

1.0/day and c ? 20/day (16, 23).

Integrating

dT

dt? ? ?VT(A5)

and equations A1 and A3 from t ? 0 to t ? tPand using

equations A2 and A4, we get the following expression for the

virus peak:

c ? ?T0?1 ?

VP?

?

c ? ?V0?

p1

RP

?

lnRP

RP?

(A6)

Since ? is ? ?c and the initial virus concentration in blood, V0,

is usually much lower than T0, the first term on the right-hand

side of equation A6 can be neglected compared to the second

term. The peak viral load then depends only on the constant

parameters of the system (Fig. 7A). Since ? is ? ?c, from equa-

tion A6 we obtain the approximate expression for the virus

peak:

?RP?1 ?

VP??

1

RP

?

lnRP

RP?

(A7)

Derivation of equation 11 for the target cell minimum. In the

infinite time limit, all three derivatives, equation 7 to equation

9, must vanish. This means that the steady-state values of both

V and I are zero, while the steady-state value of target cells,

Tmin, is undetermined.

We can find Tminby integration. We substitute the expres-

sion for the viral load from equation A5,

V ? ?1

?

d

dtlnT (A8)

into the second term on the right-hand side of equation A1 and

integrate over time from zero to infinity. Taking into account

that the infection is always cleared, i.e., that the viral load

vanishes in the long time limit, we obtain the following result:

?

0

?

Idt ?

c

?pln

T0

Tmin

?1

pV0

(A9)

Next, we integrate both sides of equation A3 and substitute the

expression A9 for the integral of infected cells. We note that

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the integral on the left-hand side of equation A3 vanishes at

both limits (at t ? 0 and at t ? ?), leading to

??

0

?

VTdt ?T0

RPln

T0

Tmin

?

?

pV0

(A10)

After substituting equation A10 into equation A5 and integrat-

ing from zero to infinity, we finally obtain the equation for

Tmin/T0,

Tmin

T0

?

1

RPlnTmin

T0

? 1 (A11)

In deriving equation A11, we have again neglected the initial

viral load in the inoculum (V0? 0).

ACKNOWLEDGMENTS

This work was supported by the James S. McDonnell Foundation

21st Century Research Award/Studying Complex Systems and the Aus-

tralian National Health and Medical Research Council. M.P.D. is a

Sylvia and Charles Viertel Senior Medical Research Fellow. R.M.R.

was supported by grant P20-RR18754 from the National Institutes of

Health.

REFERENCES

1. Anonymous. 2007. HIV vaccine failure prompts Merck to halt trial. Nature

449:390.

2. Brandin, E., R. Thorstensson, S. Bonhoeffer, and J. Albert. 2006. Rapid viral

decay in simian immunodeficiency virus-infected macaques receiving qua-

druple antiretroviral therapy. J. Virol. 80:9861–9864.

3. Chen, H. Y., M. Di Mascio, A. S. Perelson, D. D. Ho, and L. Zhang. 2007.

Determination of virus burst size in vivo using a single-cycle SIV in rhesus

macaques. Proc. Natl. Acad. Sci. USA 104:19079–19084.

4. Davenport, M. P., R. M. Ribeiro, and A. S. Perelson. 2004. Kinetics of

virus-specific CD8?T cells and the control of human immunodeficiency

virus infection. J. Virol. 78:10096–10103.

5. Davenport, M. P., R. M. Ribeiro, L. Zhang, D. P. Wilson, and A. S. Perelson.

2007. Understanding the mechanisms and limitations of immune control of

HIV. Immunol. Rev. 216:164–175.

6. Davenport, M. P., L. Zhang, A. Bagchi, A. Fridman, T. M. Fu, W. Schleif,

J. W. Shiver, R. M. Ribeiro, and A. S. Perelson. 2005. High-potency human

immunodeficiency virus vaccination leads to delayed and reduced CD8?

T-cell expansion but improved virus control. J. Virol. 79:10059–10062.

7. Davenport, M. P., L. Zhang, J. W. Shiver, D. R. Casmiro, R. M. Ribeiro, and

A. S. Perelson. 2006. Influence of peak viral load on the extent of CD4?

T-cell depletion in simian HIV infection. J. Acquir. Immune Defic. Syndr.

41:259–265.

8. Feinberg, M. B., and J. P. Moore. 2002. AIDS vaccine models: challenging

challenge viruses. Nat. Med. 8:207–210.

9. Guadalupe, M., E. Reay, S. Sankaran, T. Prindiville, J. Flamm, A. McNeil,

and S. Dandekar. 2003. Severe CD4?T-cell depletion in gut lymphoid tissue

during primary human immunodeficiency virus type 1 infection and substan-

tial delay in restoration following highly active antiretroviral therapy. J. Vi-

rol. 77:11708–11717.

10. Herz, A. V., S. Bonhoeffer, R. M. Anderson, R. M. May, and M. A. Nowak.

1996. Viral dynamics in vivo: limitations on estimates of intracellular delay

and virus decay. Proc. Natl. Acad. Sci. USA 93:7247–7251.

11. Ho, D. D., and Y. X. Huang. 2002. The HIV-1 vaccine race. Cell 110:135–138.

12. Ho, D. D., A. U. Neumann, A. S. Perelson, W. Chen, J. M. Leonard, and M.

Markowitz. 1995. Rapid turnover of plasma virions and CD4 lymphocytes in

HIV-1 infection. Nature 373:123–126.

13. Hockett, R. D., J. M. Kilby, C. A. Derdeyn, M. S. Saag, M. Sillers, K. Squires,

S. Chiz, M. A. Nowak, G. M. Shaw, and R. P. Bucy. 1999. Constant mean

viral copy number per infected cell in tissues regardless of high, low, or

undetectable plasma HIV RNA. J. Exp. Med. 189:1545–1554.

14. Little, S. J., A. R. McLean, C. A. Spina, D. D. Richman, and D. V. Havlir.

1999. Viral dynamics of acute HIV-1 infection. J. Exp. Med. 190:841–850.

15. Lloyd, A. L. 2001. The dependence of viral parameter estimates on the

assumed viral life cycle: limitations of studies of viral load data. Proc. Biol.

Sci. 268:847–854.

16. Markowitz, M., M. Louie, A. Hurley, E. Sun, M. Di Mascio, A. S. Perelson,

and D. D. Ho. 2003. A novel antiviral intervention results in more accurate

assessment of human immunodeficiency virus type 1 replication dynamics

and T-cell decay in vivo. J. Virol. 77:5037–5038.

17. Mattapallil, J. J., D. C. Douek, A. Buckler-White, D. Montefiori, N. L.

Letvin, G. J. Nabel, and M. Roederer. 2006. Vaccination preserves CD4

memory T cells during acute simian immunodeficiency virus challenge. J.

Exp. Med. 203:1533–1541.

18. Mattapallil, J. J., D. C. Douek, B. Hill, Y. Nishimura, M. Martin, and M.

Roederer. 2005. Massive infection and loss of memory CD4?T cells in

multiple tissues during acute SIV infection. Nature 434:1093–1097.

19. Mehandru, S., M. A. Poles, K. Tenner-Racz, P. Jean-Pierre, V. Manuelli, P.

Lopez, A. Shet, A. Low, H. Mohri, D. Boden, P. Racz, and M. Markowitz.

2006. Lack of mucosal immune reconstitution during prolonged treatment of

acute and early HIV-1 infection. PLoS Med. 3:e484.

20. Nowak, M. A., A. L. Lloyd, G. M. Vasquez, T. A. Wiltrout, L. M. Wahl, N.

Bischofberger, J. Williams, A. Kinter, A. S. Fauci, V. M. Hirsch, and J. D.

Lifson. 1997. Viral dynamics of primary viremia and antiretroviral therapy in

simian immunodeficiency virus infection. J. Virol. 71:7518–7525.

21. Nowak, M. A., and R. M. May. 2000. Virus dynamics: Mathematical principles of

immunology and virology. Oxford University Press, Oxford, United Kingdom.

22. Perelson, A. S., A. U. Neumann, M. Markowitz, J. M. Leonard, and D. D. Ho.

1996. HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span,

and viral generation time. Science 271:1582–1586.

23. Ramratnam, B., S. Bonhoeffer, J. Binley, A. Hurley, L. Zhang, J. E. Mittler,

M. Markowitz, J. P. Moore, A. S. Perelson, and D. D. Ho. 1999. Rapid

production and clearance of HIV-1 and hepatitis C virus assessed by large

volume plasma apheresis. Lancet 354:1782–1785.

24. Reynolds, M. R., E. Rakasz, P. J. Skinner, C. White, K. Abel, Z. M. Ma, L.

Compton, G. Napoe, N. Wilson, C. J. Miller, A. Haase, and D. I. Watkins.

2005. CD8?T-lymphocyte response to major immunodominant epitopes

after vaginal exposure to simian immunodeficiency virus: too late and too

little. J. Virol. 79:9228–9235.

25. Ribeiro, R. M., N. M. Dixit, and A. S. Perelson. 2006. Modeling the in vivo

growth rate of HIV: implications for vaccination, p. 231–246. In R. Paton and

L. A. McNamara (ed.), Multidisciplinary approaches to theory in medicine.

Elsevier, Amsterdam, The Netherlands.

26. Schacker, T., S. Little, E. Connick, K. Gebhard, Z. Q. Zhang, J. Krieger, J. Pryor,

D.Havlir,J.K.Wong,R.T.Schooley,D.Richman,L.Corey,andA.T.Haase.2001.

Productive infection of T cells in lymphoid tissues during primary and early human

immunodeficiency virus infection. J. Infect. Dis. 183:555–562.

27. Shiver, J. W., T. M. Fu, L. Chen, D. R. Casimiro, M. E. Davies, R. K. Evans,

Z. Q. Zhang, A. J. Simon, W. L. Trigona, S. A. Dubey, L. Huang, V. A. Harris,

R. S. Long, X. Liang, L. Handt, W. A. Schleif, L. Zhu, D. C. Freed, N. V.

Persaud, L. Guan, K. S. Punt, A. Tang, M. Chen, K. A. Wilson, K. B. Collins,

FIG. A1.The virus peak (A) and target cell nadir (B) do not depend on the amount of virus in the inoculum (i.e., on the initial conditions) unless

it is greater than the peak. Increasing the initial viral load only causes the peak/nadir to appear earlier.

VOL. 82, 2008ESTIMATING VACCINATION IMPACT ON ACUTE SHIV/SIV INFECTION 11597

at UNIVERSITY OF NEW SOUTH WALES on November 11, 2008

jvi.asm.org

Downloaded from

Page 10

G. J. Heidecker, V. R. Fernandez, H. C. Perry, J. G. Joyce, K. M. Grimm,

J. C. Cook, P. M. Keller, D. S. Kresock, H. Mach, R. D. Troutman, L. A.

Isopi, D. M. Williams, Z. Xu, K. E. Bohannon, D. B. Volkin, D. C. Monte-

fiori, A. Miura, G. R. Krivulka, M. A. Lifton, M. J. Kuroda, J. E. Schmitz,

N. L. Letvin, M. J. Caulfield, A. J. Bett, R. Youil, D. C. Kaslow, and E. A.

Emini. 2002. Replication-incompetent adenoviral vaccine vector elicits ef-

fective anti-immunodeficiency-virus immunity. Nature 415:331–335.

28. Stafford, M. A., L. Corey, Y. Cao, E. S. Daar, D. D. Ho, and A. S. Perelson.

2000. Modeling plasma virus concentration during primary HIV infection. J.

Theor. Biol. 203:285–301.

29. Staprans, S. I., P. J. Dailey, A. Rosenthal, C. Horton, R. M. Grant, N.

Lerche, and M. B. Feinberg. 1999. Simian immunodeficiency virus disease

course is predicted by the extent of virus replication during primary infec-

tion. J. Virol. 73:4829–4839.

30. van der Ende, M. E., M. Schutten, B. Raschdorff, G. Grossschupff, P. Racz,

A. Osterhaus, and K. Tenner-Racz. 1999. CD4 T cells remain the major

source of HIV-1 during end stage disease. AIDS 13:1015–1019.

31. Wei, X., S. K. Ghosh, M. E. Taylor, V. A. Johnson, E. A. Emini, P. Deutsch,

J. D. Lifson, S. Bonhoeffer, M. A. Nowak, B. H. Hahn, M. S. Saag, and G. M.

Shaw. 1995. Viral dynamics in human immunodeficiency virus type 1 infec-

tion. Nature 373:117–122.

32. Wilson, D. P., J. J. Mattapallil, M. D. Lay, L. Zhang, M. Roederer, and M. P.

Davenport. 2007. Estimating the infectivity of CCR5-tropic simian immuno-

deficiency virus SIVmac251in the gut. J. Virol. 81:8025–8029.

11598 PETRAVIC ET AL.J. VIROL.

at UNIVERSITY OF NEW SOUTH WALES on November 11, 2008

jvi.asm.org

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