Article
VelascoHernandez, J.X., Gershengorn, H.B. & Blower, S.M. Could widespread use of combination antiretroviral therapy eradicate HIV epidemics? Lancet Infect. Dis. 2, 487493
Departamento de Matemáticas, UAMIztapalapa and PIMAYC Instituto Mexicano del Petroleo, Atepehuacan, San Bartolo, Mexico.
The Lancet Infectious Diseases (Impact Factor: 22.43). 09/2002; 2(8):48793. DOI: 10.1016/S14733099(02)003468 Source: PubMed
Fulltext
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THE LANCET Infectious Diseases Vol 2 August 2002 http://infection.thelancet.com
487
Current combination antiretroviral therapies (ARV) are
widely used to treat HIV. However drugresistant strains of
HIV have quickly evolved, and the level of risky behaviour
has increased in certain communities. Hence, currently the
overall impact that ARV will have on HIV epidemics remains
unclear. We have used a mathematical model to predict
whether the current therapies: are reducing the severity of
HIV epidemics, and could even lead to eradication of a high
prevalence (30%) epidemic. We quantified the epidemic
level impact of ARV on reducing epidemic severity by
deriving the basic reproduction number (R
0
ARV
). R
0
ARV
specifies the average number of new infections that one HIV
case generates during his lifetime when ARV is available
and ARVresistant strains can evolve and be transmitted; if
R
0
ARV
is less than one epidemic eradication is possible. We
estimated for the HIV epidemic in the San Francisco gay
community (using uncertainty analysis), the present day
value of R
0
ARV
, and the probability of epidemic eradication.
We assumed a high usage of ARV and three behavioural
assumptions: that risky sex would (1) decrease, (2) remain
stable, or (3) increase. Our estimated values of R
0
ARV
(median
and interquartile range [IQR]) were: 0·90 (0·85–0·96) if risky
sex decreases, 1·0 (0·94–1·05) if risky sex remains stable,
and 1·16 (1·05–1·28) if risky sex increases. R
0
ARV
decreased
as the fraction of cases receiving treatment increased. The
probability of epidemic eradication is high (p=0·85) if risky
sex decreases, moderate (p=0·5) if levels of risky sex remain
stable, and low (p=0·13) if risky sex increases. We conclude
that ARV can function as an effective HIVprevention tool,
even with high levels of drug resistance and risky sex.
Furthermore, even a highprevalence HIV epidemic could be
eradicated using current ARV.
Lancet Infect Dis 2002; 2: 487–93
Introduction
Current combination antiretroviral therapies (ARV) increase
survival time of HIVinfected individuals, but do not lead to
viral eradication within individuals and hence do not cure.
These therapies are based upon three or more antiHIV
medications that typically combine a protease inhibitor (PI),
or a nonnucleoside reverse transcriptase inhibitor (nnRTI),
with at least two nucleoside reverse transcriptase inhibitors
(nRTI). However, to eradicate an epidemic it is not necessary
to cure any individuals, but simply to reduce the transmission
rate to below a certain threshold value that is specified by the
basic reproduction number R
0
; where R
0
is the average number
of new infections that one infectious case generates during
his/her infectious lifetime in a community of susceptible
individuals.
1
R
0
can be reduced either through behavioural or
medical interventions. If R
0
is reduced to below one then
epidemic eradication occurs, because each infected individual
(on average) will generate less than one new infection. Here,
we have quantified the effect of ARV on R
0
(for both drug
sensitive and drugresistant infections) and we have answered
the question, “Could widespread usage of ARV eradicate HIV
epidemics?”
We addressed this question by deriving an analytical
expression for R
0
for HIV in a community where ARV is
available and where both drugsensitive and drugresistant
strains are cocirculating (R
0
ARV
). We used clinical, virological,
and behavioural data from the gay community in San
Francisco to estimate numerical values for R
0
ARV
under three
different assumptions: ARV plus decreases in risky sex, ARV
with no change in risky sex, and ARV plus increases in risky
sex. For each assumption, we then identified the key factors
that substantially increase (or decrease) the value of R
0
ARV
.
Finally, we calculated the probability that a high usage of ARV
could eradicate the current high prevalence (30%) HIV
epidemic in San Francisco, and we also determined the time
dynamics of eradication.
The concept of R
0
was first proposed by Macdonald in the
1950s
2
and applied to malaria. The numerical value of R
0
indicates the severity of the epidemic; the greater the value of
R
0
(above one) the greater the severity of the epidemic. By
deriving an expression for R
0
, and setting the value equal to
one, the specific levels of treatment, vaccination, or reductions
in risky behaviour that are necessary to achieve epidemic
eradication can be determined for any infectious disease.
3–6
The expression for R
0
based upon the transmission dynamics
of sexually transmitted HIV in an untreated community is
simple and is dependent upon only three parameters:  (the
probability that sexual transmission of HIV occurs during a
sexual partnership), c (the average number of new sexual
partners per unit time), and D (the average duration of
infectiousness).
1
However, the situation is more complex if
one needs to compute a reproduction number for HIV where
ARV is available, since ARV leads: directly to the emergence of
Review
Eradicating HIV epidemics
JXVH is at the Departamento de Matemáticas, UAMIztapalapa and
PIMAYC Instituto Mexicano del Petroleo, San Bartolo, Atepehuacan,
Mexico; HBG is at the Harvard Medical School, Boston, USA; and
SMB is at the Department of Biomathematics & UCLA AIDS
Institute, UCLA School of Medicine, 10833 Le Conte Avenue, Los
Angeles, CA 900951766, USA.
Correspondence: Dr S M Blower. Tel +1 310 206 3052;
fax +1 310 206 6116; email sblower@biomath.ucla.edu
Could widespread use of combination
antiretroviral therapy eradicate HIV epidemics?
J X VelascoHernandez, H B Gershengorn, and S M Blower
Page 1
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THE LANCET Infectious Diseases Vol 2 August 2002 http://infection.thelancet.com
488
drugresistant strains during treatment,
7–10
and indirectly to
the transmission of drugresistant strains.
7,9–11
. Under these
circumstances it is necessary to calculate a reproduction
number based upon the transmission potential of treated and
untreated individuals infected with either drugsensitive
and/or drugresistant strains of HIV.
Blower et al
12,13
have previously defined a mathematical
model of an HIV epidemic that includes the effects of ARV on
the transmission dynamics of both drugsensitive and ARV
resistant strains. The model is specified by five ordinary
differential equations;
12
a web version can be run at
http://www.biomath.ucla.edu/faculty/sblower. Previously, this
model has been used to assess the effect of ARV (over a 10 year
period) on the incidence of HIV,
12
the AIDS death rate,
12
and
also to predict the transmission and
prevalence of drugresistant strains.
13
Here, we have used this model to derive
an analytical expression for R
0
ARV
; where
we define R
0
ARV
as the average number of
new HIVinfections that one infected
individual will generate during his/her
lifetime in a community where ARV is
available and where both drugsensitive
and ARVresistant strains are co
circulating. Hence, R
0
ARV
functions as a
single outcome measure that provides a
summary estimate of the overall
epidemiclevel impact of ARV. We
calculate the values of R
0
ARV
that are
generated due to a variety of different
treatment rates; hence we assessed
whether ARV has an overall beneficial
or detrimental impact at the epidemic
level.
Methods
We first calculated an analytical
expression for R
0
ARV
. To calculate R
0
ARV
we
used the nextgeneration operator
methodology.
14
We set the righthand
side of the model differential equations
(given in reference 12) to zero and made
a standard change of variables to find the
diseasefree equilibrium in terms of the
forces of infection of the resistant (
R
)
and sensitive (
S
) strains. The problem
was then reduced to a system of two
nonlinear algebraic equations given in
equation 1.
(1)
S
=F (
S
,
R
),
R
=G (
S
,
R
)
The diseasefree equilibrium of the
original model can be recovered from
the solution (
S
,
R
)=(0,0) of equation 1.
Linearising the righthand side of
equation 1 around this equilibrium
point we computed the dominant eigen
value of the resulting Jacobian matrix,
thus obtaining R
0
ARV
.
Estimating the value of R
0
ARV
Estimates of the value of R
0
for HIV before the introduction of
ARV in the San Francisco gay community ranged from 2
(lower bound) to 5 (upper bound) in the early 1990s;
15
more
recent data
12,13
suggest that the value of R
0
(in the absence of
ARV) was approximately 1·43. ARV has been widely used in
San Francisco since 1996.
12,13,16
We determined the epidemic
level impact of ARV by estimating the value of R
0
ARV
in the gay
community (where the current prevalence of HIV is 30%
16
)
using clinical, virological, and behavioural data from San
Francisco
12,13
to set upper and lower bounds for parameter
estimates, and then applied uncertainty analysis.
12,13,17–20
These
data are described in reference 12 and references therein.
Uncertainty analyses were based upon Latin hypercube
Review
Eradicating HIV epidemics
1·8
1·6
1·4
1·2
1
0·8
0·6
R
0
ARV
R
0
ARV
450
Number of simulations
400
350
300
250
200
150
100
50
0
0·6– 0·7– 0·8– 0·9– 1·0– 1·1– 1·2– 1·3– 1·4– 1·5– 1·6– 1·7–
0·7 0·8 0·9 1·0 1·1 1·2 1·3 1·4 1·5 1·6 1·7 1·8
ARV + decreasing
risky behaviour
ARV + increasing
risky behaviour
ARV + stable
risk behaviour
A
B
Figure 1. Results from three uncertainty analyses; all have high ARV usage (50–90% of cases receive
treatment). Pink=no change in risky sex plus only 10% of treated cases develop ARV resistance per
year; green=decreased risky sex plus only 10% of treated cases develop ARVresistance per year;
blue=increases in risky sex plus 10–60% of treated cases develop ARVresistance per year.
(A) The 1000 estimates of R
0
ARV
calculated by uncertainty analysis methodology (see text for methods)
for each of the three different assumptions concerning risky sex and rates of emergence of ARV
resistance are plotted as box plots; these plots show the median value, upper and lower quartiles, and
the outlier cutoffs. (B) The frequency distributions for the estimated values of R
0
ARV
for each of the
three uncertainty analyses.
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489
sampling (LHS is a type of stratified Monte Carlo
sampling
17,19,20
); this methodology enabled us to estimate a
range of values for R
0
ARV
. Uncertainty analysis methodology has
been used previously to calculate the value of R
0
for
tuberculosis
21,22
and for genital herpes.
23
To conduct the uncertainty analysis, each parameter in
our R
0
ARV
expression was assigned a probability density
function (PDF). We assumed that the likely treatment rates
of ARV (ie, % of prevalent HIVinfections treated) would
be between 50% and 90%;
12,13
thus, we used a uniform PDF
with a minimum of 50% and a maximum value of 90%
to specify the PDF for the treatmentrate parameter.
We modelled the potential effect of ARV on reducing
infectivity/transmissibility in treated patients by assuming
that ARV could cause anywhere from a twofold to 100fold
reduction in infectivity in treated cases by comparison
with untreated cases.
12,13
This uncertainty in the degree of
ARVinduced reduction in infectivity/transmissibility was
included by multiplying the infectivity/transmissibility of an
untreated individual (
S
U
) by a multiplier (␣
1
) that we
sampled 1000 times (using LHS) from a uniform PDF (range
0·5–0·01); the infectivity/transmissibility of a treated case
(
S
T
) was then calculated by the relationship 
S
T
=␣
1

S
U
. This
sampling procedure ensured that treated cases (as a result of
ARV) were anywhere from only 1% to as much as 50% as
transmissible/infectious as untreated cases.
We also included uncertainty in the degree of
infectivity/transmissibility of ARVresistant strains by
modelling the effect of 1000 different ARVresistant strains
and assuming that each strain had a different relative fitness
(as specified by its transmissibility relative to a drug
sensitive strain).
12,13
We varied the relative fitness of the 1000
different ARVresistant strains from a maximum value (that
was set by assuming that the ARVresistant strain was
approximately as transmissible as the drugsensitive strain)
to a minimum value (that was set by assuming the
ARVresistant strain was only 1% as transmissible as
the drugsensitive strain).
12,13
Based upon the currently
available data, drugresistant strains of HIV have been
found to be less infectious (and not more infectious) than
drugsensitive strains. The remaining PDFs used in the
uncertainty analyses have been discussed in detail and
justified previously.
12,13
We did three uncertainty analyses, each with a different set
of assumptions concerning changes in risky sex and the rate of
emergence of ARVresistant strains. For our first uncertainty
analysis we assumed that the high rates of ARV usage
(50–90%) would be accompanied by an uncertain decrease
(anywhere from no reduction to a 50% reduction) in the level
of risky sex, and that the rates of emergence of ARVresistant
strains would be low (only 10% of the treated cases would
develop ARVresistance per year; this value reflects the
optimal performance of ARV in clinical trials
12,13
). For our
second uncertainty analysis we also assumed that rates of
emergence of ARVresistant strains would be low (10% of
treated cases per year), but in addition we assumed that no
changes in risky sex would occur.
12
For our third uncertainty
analysis we assumed that the high rates of ARV usage
(50–90%) would be accompanied by uncertain increases in
risky sex (anywhere from no increase to doubling), and that
the rates of emergence of ARV resistance would be high (we
assumed that 10–60% of the treated cases would develop
ARVresistance per year).
12,13
These high rates of emergence of
ARV resistance are based upon recent data from clinical and
communitylevel studies of ARVresistance.
24–31
For each of the three uncertainty analyses, LHS was used
to randomly sample (without replacement) each PDF for
each parameter 1000 times. For example, in the third
analysis we included uncertainty in the rate of emergence of
drug resistance during the treatment of drugsensitive cases
(r) using LHS to sample 1000 values of r from a uniform
PDF (minimum=0·1, maximum=0·6). In this analysis, we
also included uncertainty in the degree of increase in risky
behaviour (I) using LHS to sample 1000 values of I from
a uniform PDF (minimum=0·0, maximum=1·0); hence,
risky behaviour varied from no increase (I=0·0) to
doubling (I=1·0). This sampling procedure produced
1000 different estimates of R
0
ARV
for each of the three
uncertainty analyses.
Identification of key factors that decrease, and
increase, R
0
ARV
We then did sensitivity analyses,
12,13,17,18,21–23
using data
generated from each of the three uncertainty analyses, to
identify the key factors that substantially increase (and
decrease) the value of R
0
ARV
. For these calculations we used
our uncertainty analysis estimates of R
0
ARV
and the PDFs that
specified each of the virological, clinical and behavioural
parameters (described previously in references 12 and 13) to
calculate sensitivity coefficients; a partial rank correlation
coefficient (PRCC) was calculated for each parameter.
17,21–23
A
parameter was identified as a key factor in increasing or
decreasing the value of R
0
ARV
if the absolute value of the
PRCC was greater than 0·5. For each of the three sensitivity
analyses, before calculating PRCCs we examined scatterplots
of each model parameter versus the 1000 estimated values of
Review
Eradicating HIV epidemics
Values of the PRCCs for the key factors that substantially increase (PRCC >0·5) or decrease (PRCC <–0·5) the R
0
ARV
Parameter ARV plus decreasing ARV with stable ARV plus increasing
risky behaviour risky behaviour risky behaviour
Treatment rate (varies from 50–90% of cases receiving ARV) * –0·81 –0·86
Change in risky behaviour (varies from a reduction of 50% to a doubling) 0·88 0·89
Relative fitness of ARVresistant strain (ARVresistant strains vary from 1% 0·71 0·77 0·67
as transmissible as drugsensitive strains to almost as transmissible)
ARVinduced reduction in transmissibility (ie, infectivity) in a treated patient –0·84 –0·91 –0·71
(ARV induces a 2–100 fold reduction in transmissibility/infectivity)
*In this case the value of the PRCC=–0·40.
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490
R
0
ARV
to check for monotonicity and discontinuities.
32,33
All
relations in the scatterplots were nonlinear, and monotonic;
no interactions and no discontinuities were observed.
Probability of epidemic eradication, and the time
course
We used the results from our three uncertainty analyses
to calculate the probability that widespread usage of ARV
could eradicate the HIV epidemic in San Francisco (ie,
the probability that R
0
ARV
<1), using previously described
methods.
23
It should be noted, that these methods slightly
understate the chance of eradication. Finally, we determined
the time course of epidemic eradication using the LHS data
generated for each of our three uncertainty analyses and
numerically simulating the transmission model
12
with each
parameter set (of the 1000 parameter sets in the LH sample)
that generated a value of R
0
ARV
less than one.
Results
The analytical expression for R
0
ARV
is very complex and hence is
not shown.
Estimated values of R
0
ARV
Our calculations for the numerical values of R
0
ARV
for each of
the three uncertainty analyses are shown as boxplots in figure
1A, and as frequency distributions in figure 1B. Since the value
of the reproduction number is 1·43 if ARV is not used (ie, if
ARV is not used then R
0
ARV
=R
0
), the results of all three of the
uncertainty analyses reveal that a high usage of ARV (ie,
50–90% of cases receiving ARV) would significantly reduce the
severity of the HIV epidemic in the gay community in San
Francisco (figure 1). The median values (and interquartile
range [IQR]) of R
0
ARV
for these three analyses are: 0·90
(0·85–0·96; data shown in green, assuming reductions in risky
sex), 1·0 (0·94–1·05; data shown in pink, assuming no change
in risky sex) and 1·16 (1·05–1·28; data
shown in blue, assuming increases in
risky sex) (figure 1A). The results clearly
reveal that a high usage of ARV if
combined with substantial decreases in
risky sex (green data) could drive R
0
ARV
below one, and hence would eventually
lead to epidemic eradication.
Conversely, if risky sex increases (blue
data), then even with a high usage of
ARV, R
0
ARV
is highly likely to remain
greater than one. If no change in risky
sex (pink data) occurs then a high usage
of ARV would reduce the severity of the
HIV epidemic, but the value of R
0
ARV
would remain at just above or just
below the critical threshold level for
eradication.
Identification of key factors that
decrease, and increase, R
0
ARV
Our sensitivity analyses identified two
key factors that substantially decreased
(PRCC <–0·5) the value of R
0
ARV
. The
value of R
0
ARV
decreased substantially as:
(1) the ARV treatment rate increased
from 50% to 90%, and/or (2) the ARV
induced reduction in infectivity/
transmissibility of HIV from treated
patients increased (table). The results
reveal that R
0
ARV
decreased substantially
as the treatment rates increased even
when there was a high rate of
emergence of ARVresistant strains
(table); however, this treatment effect
was less pronounced (PRCC= –0·40) if
it was assumed that significant
reductions in risky behaviour also
occurred.
Our sensitivity analyses also
identified two key factors that were
most important in substantially
Review
Eradicating HIV epidemics
1·8
1·6
1·4
1·2
1
0·8
0·6
0 204060
Relative fitness of ARVresistant strains (%)
Change in risk behaviour (%)
80 100
–50 –25 0 25 50 75 100
1·8
1·6
1·4
1·2
R
0
ARV
R
0
ARV
1
0·8
0·6
A
B
Figure 2. Results from three uncertainty analyses; all have high ARV usage (50–90% of cases receive
treatment). Pink=no change in risky sex plus only 10% of treated cases develop ARV resistance per year;
green=decreased risky sex plus only 10% of treated cases develop ARVresistance per year; blue=
increases in risky sex plus 10–60% of treated cases develop ARVresistance per year. (A) The graphical
results (with unadjusted data from the three uncertainty analyses) show the effect of the relative fitness
(in terms of transmissibility) of the ARVresistant strains on the value of R
0
ARV
. (B) Results (with unadjusted
data) showing the effect of changes (increases and decreases) in risky sex on the value of R
0
ARV
.
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491
increasing (PRCC >0·5) the value of
R
0
ARV
. The value of R
0
ARV
increased
substantially as: (1) the relative fitness
(ie, the transmissibility relative to
drugsensitive strains) of ARV
resistant strains increased, and/or (2)
the levels of risky sex increased (table).
The evolution of ARVresistant strains
that were very transmissible (ie, very
fit) significantly increased the value of
R
0
ARV
(figure 2A). Reductions in risky
sex (green data) significantly reduced
R
0
ARV
(figure 2B), whereas increases in
risky behaviour (blue data)
significantly increased R
0
ARV
(figure
2B). Thus, changes in risk behaviour
determine the effect of the value of
fitness of ARVresistant strains on
increasing R
0
ARV
(figure 2A).
Probability of eradicating HIV
epidemics, and the time course
We calculated that if ARV was widely
used (median value 70% of cases
received ARV) and substantial
reductions (median value 25%
decrease) in risky sex occurred the
probability of eradication of the HIV
epidemic would be high (p=0·85). We
determined that if levels of risky sex
remain stable the probability of
eradication would be only 0·5, and if
levels of risky sex increased (median
value 50% increase) then epidemic
eradication would be unlikely
(p=0·13).
Figures 3A and 3B show the
frequency distributions (using only
the simulations from the LHS
that eventually lead to epidemic
eradication) for the predicted HIV
prevalence in San Francisco after
50 and 100 years of continuous ARV.
These results clearly show that,
although epidemic eradication is
possible (with either high levels of ARV alone [pink data] or
else high levels of ARV combined with risk reductions [green
data]), it would be likely to take 100 years or more to
achieve. These estimates of eradication times are upper
bound estimates; clearly, if parameter values change over
time (as is to be expected as new and more effective therapies
are developed) then eradication will occur more quickly. An
eradication strategy based upon current ARV will be slow as
all patients with prevalent infections would have to die, and
patients on ARV have a fairly long survival time. However,
clearly any HIV epidemiceradication strategy will take a
long time; it has been shown that even widely deployed and
highly effective HIV vaccines would take several decades to
achieve eradication
6
.
Discussion
Our findings have four significant clinical and public
health implications. First, increasing the percentage of
cases receiving ARV would substantially reduce the
severity of the HIV epidemic (ie, the value of R
0
ARV
), even
in the presence of high levels of ARV resistance and
increases in risky behaviour. However, ARV should not be
used as an epidemic control strategy to improve public
health unless increasing usage rates would also produce
clinical benefits for the treated individuals. Second,
even fairly moderate reductions in the infectivity/
transmissibility of treated cases will be extremely beneficial
in reducing the severity of the HIV epidemic. Reductions
in infectivity/transmissibility could be achieved either
Review
Eradicating HIV epidemics
Figure 3. Frequency distributions of the prevalence of HIV infection in the gay community in San
Francisco after (A) 50 years and (B) 100 years of continuous high usage of ARV. Only simulations in
which eradication of HIV from the population would occur are shown (ie, only if R
0
ARV
<1). Results
from the three uncertainty analyses are shown; all have high ARV usage (50–90% of cases receive
treatment). Pink=no change in risky sex plus only 10% of treated cases develop ARV resistance per
year (N=506), green=decreased risky sex plus only 10% of treated cases develop ARV resistance
per year (N=847); blue=increases in risky sex plus 10–60% of treated cases develop ARV resistance
per year (N=130).
Number of simulationsNumber of simulations
0%
0
0
50
100
150
200
250
300
350
400
10
20
30
40
50
60
70
80
90
100
1% 2% 3% 4% 5%
Prevalence of HIV infection
Prevalence of HIV infection
6% 7% 8% 9% 10% 11%
0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11%
A
B
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492
by developing new drugs and drug regimens that more
effectively suppress virus, and/or by significantly
increasing the use of condoms by treated cases. Third,
if highly transmissible ARVresistant strains emerge
(even though they are less transmissible than the drug
sensitive strains), they will significantly reduce the
beneficial overall impact of ARV on the HIV epidemic.
Great efforts should be made to prevent cases of acquired
resistance developing during treatment, because these
cases can lead to cases of transmitted resistance.
13
Fourth,
the value of R
0
ARV
is extremely sensitive to changes in risky
sex. Our findings demonstrate unequivocally that it is
imperative that the usage of ARV should be tightly coupled
with effective riskreduction strategies. It is imperative
that levels of risky sex are substantially reduced. We have
also shown that the impact of changes in risky sex on
reducing the HIV epidemic will be very dependent upon
the biological characteristics of the ARVresistant strains
that evolve. If levels of risky sex increase, then even
ARVresistant strains with a low transmissibility will
increase epidemic severity; conversely, reducing the
level of risky behaviours will significantly reduce the
transmission rate even if highly transmissible ARV
resistant strains emerge.
High usage of ARV in San Francisco has substantially
reduced the AIDS death rate,
12,34
and it has been estimated
that ARV has also decreased the transmission rate in
this city.
12,13
After the widespread use of ARV in 1996,
incidence rates in San Francisco were predicted
12
to first
rise (due to increases in risky sex) and then to fall (when
the beneficial effects of ARV on decreasing transmission
outweigh the effects of increases in risky sex on increasing
transmission). The first of these theoretical predictions
has been confirmed by recent empirical studies: the
incidence rate in the gay community in San Francisco has
increased.
34
Therefore, based upon current empirical
data, it is unclear whether the overall impact of ARV on
the HIV epidemic will be beneficial. Furthermore, the high
usage of ARV in San Francisco has already led to a
high prevalence of ARVresistance;
13
by 2005 42% of the
HIV infections in San Francisco are predicted to be
ARVresistant.
13
Here, we have shown by calculating a
single summary outcome measure (R
0
ARV
) that a high
usage of ARV will substantially reduce the severity of the
HIV epidemic in the gay community in San Francisco.
This beneficial impact of ARV at the epidemic level
occurs because widespread usage of ARV reduces (at the
population level) the average viral load,
35
and this
reduction in average viral load translates into a reduction
in the average level of infectivity
35
that hence reduces
transmission.
12,13,36,37
Our results show that although
the current therapies do not cure individuals they could
be used to eradicate a highprevalence (30%) HIV
epidemic. However, we have shown that the probability
of eradication is very sensitive to changes in the level of
risky sex. Currently in San Francisco there are high rates
of emergence of drug resistance
13
and high rates of increase
in risky sex;
13,38,39
therefore our calculations (shown in
blue in the figures) suggest that whereas high usage of
ARV could result in epidemic eradication in this city
it is quite unlikely under the current conditions.
Elsewhere
13
we have advocated the widespread usage of
ARV in Africa and other developing countries, because
of the beneficial effect of ARV on reducing HIV
transmission and AIDS death rates.
12,13
However, the
beneficial impact of ARV on reducing transmission will
be masked if risky behaviours increase
12
; therefore, it
becomes necessary to theoretically estimate the “true”
impact of ARV on HIV epidemics by calculating a single
summary outcome measure (R
0
ARV
). The same key factors
that substantially reduce the HIVinfection rate and
the AIDSdeath rate
12,13
also decrease the value of R
0
ARV
and hence increase the probability of eradication. Our
current quantitative findings imply (by contrast with the
position argued by others
40,41
) that widespread usage of
ARV in Africa and other developing countries would
be extremely beneficial in reducing HIV epidemics.
The methodology we propose is generalisable to other
geographical locations. Hence, we suggest that estimates
of R
0
ARV
should now be calculated for HIV epidemics in
other locations to predict and to quantify the effect of
ARV on reducing the severity of HIV epidemics in
these countries. Such analyses should reveal that a high
usage of ARV would much more easily eradicate HIV
epidemics that are less severe than the current high
prevalence epidemic in San Francisco. The development
of more effective drugs and drug regimens that render
patients completely uninfectious will obviously benefit
the treated individuals, but will also result in a much
more substantial reduction in the value of R
0
ARV
than
we have calculated for our current analyses. Hence
epidemic eradication using ARV could then become
significantly quicker and easier than we have calculated.
However, our findings clearly show that a high usage
of the currently available combination ARV therapies
(as well as benefiting the individual patients receiving
treatment) would also serve as an effective HIVprevention
tool.
Acknowledgements
We gratefully acknowledge the financial support of NIH/NIAID
(Grant No. AI41935), funding from the UCLA AIDS Institute
(to SMB), and funding from UAMIztapalapa and CONACYT (
to JVH). We are grateful to Nelson, Jake, and Dan Freimer for
helpful discussions. We also thank Nick Aschenbach for assistance
in producing the figures. This paper is dedicated to the memory of
Bob Blower (aka Popeye) 9/7/1929–13/2/2002.
Conflicts of interest
None declared.
Review
Eradicating HIV epidemics
Search strategy and selection criteria
Data for this review were identified by searches of Medline,
Current Contents, and references from relevant articles;
numerous articles were identified through searches of the
extensive files of the authors. Search terms were “antiretroviral
therapy”, “prediction models”, “mathematical model”, “HIV
transmission dynamics”, “epidemic control strategies”. English
language papers were reviewed.
Page 6
For personal use. Only reproduce with permission from The Lancet Publishing Group.
THE LANCET Infectious Diseases Vol 2 August 2002 http://infection.thelancet.com
493
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Review
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 "In Fig. 6, we see the densities of the basic and invasion reproduction numbers that were obtained from our parameter ranges, with their mean identified by the point on the lower axis. These reproduction number ranges are consistent with literature [8,[25][26][27]. In calculating the invasion reproduction numbers, we numerically calculated the equilibrium values to be used in the simulations. "
Article: A model for the coupled disease dynamics of HIV and HSV2 with mixing among and between genders
[Show abstract] [Hide abstract] ABSTRACT: Evidence indicates that those with genital herpes (HSV2) infections have greater risks of infection by HIV; and, once coinfected, are more likely to transmit HIV. To better understand the interactions between HIV and HSV2, we construct a mathematical model that describes the joint dynamics. A new feature of this model is the inclusion of both heterosexual and homosexual interactions. We derive and interpret the basic and invasion reproduction numbers for HIV and HSV2 using the approach of nextgeneration matrices. We then perform scenario analyses and conduct a sensitivity analysis to investigate the impact of the model parameters on the reproduction numbers and disease prevalences. We conclude that homosexual transmission drastically changes the disease prevalences; hence, it is important to account for this interaction as models that ignore homosexuality may greatly underestimate the disease burden. Copyright © 2015. Published by Elsevier Inc. 
 "In these couples, the index case (infected participant) is equally likely to be a man or woman [32], and HIV transmission risk persists for couples over the duration of their relationship, although the risk is highest when one partner first acquires HIV [1,3233343536. As noted previously, several observational studies and one randomized controlled trial have demonstrated that suppressive ART provided to an index case can prevent sexual transmission of HIV to their HIV negative partner [1, 2,37383940 from either (or both) the direct impact of ARV and from couples' counseling. Couples enrolled in HPTN 052 also received repeated optimized counseling that focused on safer sex behavior, including condoms, and adherence of the index case to ART when offered. "
[Show abstract] [Hide abstract] ABSTRACT: Serodiscordant couples play an important role in maintaining the global HIV epidemic. This review summarizes biobehavioral and biomedical HIV prevention options for serodiscordant couples focusing on advances in 2013 and 2014, including World Health Organization guidelines and best evidence for couples counseling, couplebased interventions, and the use of antiviral agents for prevention. In the past few years, marked advances have been made in HIV prevention for serodiscordant couples and numerous ongoing studies are continuously expanding HIV prevention tools, especially in the area of preexposure prophylaxis. Uptake and adherence to antiviral therapy remains a key challenge. Additional research is needed to develop evidencebased interventions for couples, and especially for malemale couples. Randomized trials have demonstrated the prevention benefits of antiretroviralbased approaches among serodiscordant couples; however, residual transmission observed in recognized serodiscordant couples represents an important and resolvable challenge in HIV prevention. 
 "In the USA, many clinicians are already prescribing ART for many of their HIVpositive patients at CD4 counts well in excess of 500 cells/μL. Some mathematical models have demonstrated that if UTT can be delivered with high coverage, HIV incidence could be reduced substantially [1820,22]. "
[Show abstract] [Hide abstract] ABSTRACT: Effective interventions to reduce HIV incidence in subSaharan Africa are urgently needed. Mathematical modelling and the HIV Prevention Trials Network (HPTN) 052 trial results suggest that universal HIV testing combined with immediate antiretroviral treatment (ART) should substantially reduce incidence and may eliminate HIV as a public health problem. We describe the rationale and design of a trial to evaluate this hypothesis. A rigorouslydesigned trial of universal testing and treatment (UTT) interventions is needed because: i) it is unknown whether these interventions can be delivered to scale with adequate uptake; ii) there are many uncertainties in the models such that the populationlevel impact of these interventions is unknown; and ii) there are potential adverse effects including sexual risk disinhibition, HIVrelated stigma, overburdening of health systems, poor adherence, toxicity, and drug resistance.In the HPTN 071 (PopART) trial, 21 communities in Zambia and South Africa (total population 1.2 m) will be randomly allocated to three arms. Arm A will receive the full PopART combination HIV prevention package including annual homebased HIV testing, promotion of medical male circumcision for HIVnegative men, and offer of immediate ART for those testing HIVpositive; Arm B will receive the full package except that ART initiation will follow current national guidelines; Arm C will receive standard of care. A Population Cohort of 2,500 adults will be randomly selected in each community and followed for 3 years to measure the primary outcome of HIV incidence. Based on model projections, the trial will be wellpowered to detect predicted effects on HIV incidence and secondary outcomes. Trial results, combined with modelling and cost data, will provide shortterm and longterm estimates of costeffectiveness of UTT interventions. Importantly, the threearm design will enable assessment of how much could be achieved by optimal delivery of current policies and the costs and benefits of extending this to UTT.Trial registration: ClinicalTrials.gov NCT01900977.