Page 1

For personal use. Only reproduce with permission from The Lancet Publishing Group.

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 drug-resistant 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 (R0

specifies the average number of new infections that one HIV

case generates during his lifetime when ARV is available

and ARV-resistant strains can evolve and be transmitted; if

R0

estimated for the HIV epidemic in the San Francisco gay

community (using uncertainty analysis), the present day

value of R0

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 R0

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. R0

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 HIV-prevention tool,

even with high levels of drug resistance and risky sex.

Furthermore, even a high-prevalence HIV epidemic could be

eradicated using current ARV.

ARV). R0

ARV

ARVis less than one epidemic eradication is possible. We

ARV, and the probability of epidemic eradication.

ARV(median

ARVdecreased

Lancet Infect Dis 2002; 2: 487–93

Introduction

Current combination antiretroviral therapies (ARV) increase

survival time of HIV-infected individuals, but do not lead to

viral eradication within individuals and hence do not cure.

These therapies are based upon three or more anti-HIV

medications that typically combine a protease inhibitor (PI),

or a non-nucleoside 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 R0; where R0is the average number

of new infections that one infectious case generates during

his/her infectious lifetime in a community of susceptible

individuals.1R0can be reduced either through behavioural or

medical interventions. If R0is 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 R0(for both drug-

sensitive and drug-resistant 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 R0for HIV in a community where ARV is

available and where both drug-sensitive and drug-resistant

strains are co-circulating (R0

and behavioural data from the gay community in San

Francisco to estimate numerical values for R0

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 R0

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 R0was first proposed by Macdonald in the

1950s2and applied to malaria. The numerical value of R0

indicates the severity of the epidemic; the greater the value of

R0(above one) the greater the severity of the epidemic. By

deriving an expression for R0, 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 R0based 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).1However, 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

ARV). We used clinical, virological,

ARVunder three

ARV.

Review

Eradicating HIV epidemics

JXV-H is at the Departamento de Matemáticas, UAM-Iztapalapa 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 90095-1766, 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 Velasco-Hernandez, H B Gershengorn, and S M Blower

Page 2

For personal use. Only reproduce with permission from The Lancet Publishing Group.

THE LANCET Infectious Diseases Vol 2 August 2002 http://infection.thelancet.com

488

drug-resistant strains during treatment,7–10and indirectly to

the transmission of drug-resistant 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 drug-sensitive

and/or drug-resistant strains of HIV.

Blower et al12,13have previously defined a mathematical

model of an HIV epidemic that includes the effects of ARV on

the transmission dynamics of both drug-sensitive and ARV-

resistant strains. The model is specified by five ordinary

differential equations;12a 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,12the AIDS death rate,12and

also to predict the transmission and

prevalence of drug-resistant strains.13

Here, we have used this model to derive

an analytical expression for R0

we define R0

new HIV-infections that one infected

individual will generate during his/her

lifetime in a community where ARV is

available and where both drug-sensitive

and ARV-resistant strains are co-

circulating. Hence, R0

single outcome measure that provides a

summary estimate of the overall

epidemic-level impact of ARV. We

calculate the values of R0

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.

ARV; where

ARVas the average number of

ARVfunctions as a

ARVthat are

Methods

We

expression for R0

used the next-generation operator

methodology.14We set the right-hand

side of the model differential equations

(given in reference 12) to zero and made

a standard change of variables to find the

disease-free 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 disease-free equilibrium of the

original model can be recovered from

the solution (?S,?R)=(0,0) of equation 1.

Linearising the right-hand side of

equation 1 around this equilibrium

point we computed the dominant eigen

value of the resulting Jacobian matrix,

thus obtaining R0

first calculated

ARV. To calculate R0

an analytical

ARVwe

ARV.

Estimating the value of R0

Estimates of the value of R0for 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;15more

recent data12,13suggest that the value of R0(in the absence of

ARV) was approximately 1·43. ARV has been widely used in

San Francisco since 1996.12,13,16We determined the epidemic-

level impact of ARV by estimating the value of R0

community (where the current prevalence of HIV is 30%16)

using clinical, virological, and behavioural data from San

Francisco12,13to set upper and lower bounds for parameter

estimates, and then applied uncertainty analysis.12,13,17–20These

data are described in reference 12 and references therein.

Uncertainty analyses were based upon Latin hypercube

ARV

ARVin the gay

Review

Eradicating HIV epidemics

1·8

1·6

1·4

1·2

1

0·8

0·6

R0ARV

R0ARV

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–

0·7 0·8 0·9 1·0

1·3– 1·4– 1·5– 1·6– 1·7–

1·4 1·51·6 1·11·2 1·3 1·71·8

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 ARV-resistance per year;

blue=increases in risky sex plus 10–60% of treated cases develop ARV-resistance per year.

(A) The 1000 estimates of R0

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 R0

three uncertainty analyses.

ARVcalculated by uncertainty analysis methodology (see text for methods)

ARVfor each of the

Page 3

For personal use. Only reproduce with permission from The Lancet Publishing Group.

THE LANCET Infectious Diseases Vol 2 August 2002 http://infection.thelancet.com

489

sampling (LHS is a type of stratified Monte Carlo

sampling17,19,20); this methodology enabled us to estimate a

range of values for R0

been used previously to calculate the value of R0 for

tuberculosis21,22and for genital herpes.23

To conduct the uncertainty analysis, each parameter in

our R0

function (PDF). We assumed that the likely treatment rates

of ARV (ie, % of prevalent HIV-infections treated) would

be between 50% and 90%;12,13thus, we used a uniform PDF

with a minimum of 50% and a maximum value of 90%

to specify the PDF for the treatment-rate parameter.

We modelled the potential effect of ARV on reducing

infectivity/transmissibility in treated patients by assuming

that ARV could cause anywhere from a two-fold to 100-fold

reduction in infectivity in treated cases by comparison

with untreated cases.12,13This uncertainty in the degree of

ARV-induced reduction in infectivity/transmissibility was

included by multiplying the infectivity/transmissibility of an

untreated individual (?S

sampled 1000 times (using LHS) from a uniform PDF (range

0·5–0·01); the infectivity/transmissibility of a treated case

(?S

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 ARV-resistant strains by

modelling the effect of 1000 different ARV-resistant strains

and assuming that each strain had a different relative fitness

(as specified by its transmissibility relative to a drug-

sensitive strain).12,13We varied the relative fitness of the 1000

different ARV-resistant strains from a maximum value (that

was set by assuming that the ARV-resistant strain was

approximately as transmissible as the drug-sensitive strain)

to a minimum value (that was set by assuming the

ARV-resistant strain was only 1% as transmissible as

the drug-sensitive strain).12,13Based upon the currently

available data, drug-resistant strains of HIV have been

found to be less infectious (and not more infectious) than

drug-sensitive 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 ARV-resistant strains. For our first uncertainty

analysis we assumed that the high rates of ARV usage

(50–90%) would be accompanied by an uncertain decrease

ARV.Uncertainty analysis methodology has

ARVexpression was assigned a probability density

U) by a multiplier (?1) that we

T) was then calculated by the relationship ?S

T=?1?S

U. This

(anywhere from no reduction to a 50% reduction) in the level

of risky sex, and that the rates of emergence of ARV-resistant

strains would be low (only 10% of the treated cases would

develop ARV-resistance per year; this value reflects the

optimal performance of ARV in clinical trials12,13). For our

second uncertainty analysis we also assumed that rates of

emergence of ARV-resistant strains would be low (10% of

treated cases per year), but in addition we assumed that no

changes in risky sex would occur.12For 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

ARV-resistance per year).12,13These high rates of emergence of

ARV resistance are based upon recent data from clinical and

community-level studies of ARV-resistance.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 drug-sensitive 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 R0

uncertainty analyses.

ARVfor each of the three

Identification of key factors that decrease, and

increase, R0

We then did sensitivity analyses,12,13,17,18,21–23using data

generated from each of the three uncertainty analyses, to

identify the key factors that substantially increase (and

decrease) the value of R0

our uncertainty analysis estimates of R0

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.17,21–23A

parameter was identified as a key factor in increasing or

decreasing the value of R0

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

ARV

ARV. For these calculations we used

ARVand the PDFs that

ARVif the absolute value of the

Review

Eradicating HIV epidemics

Values of the PRCCs for the key factors that substantially increase (PRCC >0·5) or decrease (PRCC <–0·5) the R0

ARV

Parameter ARV plus decreasing

risky behaviour

*

0·88

0·71

ARV with stable

risky behaviour

–0·81

ARV plus increasing

risky behaviour

–0·86

0·89

0·67

Treatment rate (varies from 50–90% of cases receiving ARV)

Change in risky behaviour (varies from a reduction of 50% to a doubling)

Relative fitness of ARV-resistant strain (ARV-resistant strains vary from 1%

as transmissible as drug-sensitive strains to almost as transmissible)

ARV-induced reduction in transmissibility (ie, infectivity) in a treated patient

(ARV induces a 2–100 fold reduction in transmissibility/infectivity)

0·77

–0·84 –0·91–0·71

*In this case the value of the PRCC=–0·40.

Page 4

For personal use. Only reproduce with permission from The Lancet Publishing Group.

THE LANCET Infectious Diseases Vol 2 August 2002 http://infection.thelancet.com

490

R0

relations in the scatterplots were non-linear, and monotonic;

no interactions and no discontinuities were observed.

ARVto check for monotonicity and discontinuities.32,33All

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 R0

methods.23It 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 model12with each

parameter set (of the 1000 parameter sets in the LH sample)

that generated a value of R0

ARV<1), using previously described

ARVless than one.

Results

The analytical expression for R0

not shown.

ARVis very complex and hence is

Estimated values of R0

Our calculations for the numerical values of R0

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 R0

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 R0

(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 R0

below one, and hence would eventually

lead to

Conversely, if risky sex increases (blue

data), then even with a high usage of

ARV, R0

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 R0

would remain at just above or just

below the critical threshold level for

eradication.

ARV

ARVfor each of

ARV=R0), the results of all three of the

ARVfor these three analyses are: 0·90

ARV

epidemic eradication.

ARVis highly likely to remain

ARV

Identification of key factors that

decrease, and increase, R0

Our sensitivity analyses identified two

key factors that substantially decreased

(PRCC <–0·5) the value of R0

value of R0

(1) the ARV treatment rate increased

from 50% to 90%, and/or (2) the ARV-

induced reduction

transmissibility of HIV from treated

patients increased (table). The results

reveal that R0

as the treatment rates increased even

when there was a high rate of

emergence of ARV-resistant strains

(table); however, this treatment effect

was less pronounced (PRCC= –0·40) if

it was assumed

reductions in risky behaviour also

occurred.

Our sensitivity

identified two key factors that were

most important

ARV

ARV. The

ARVdecreased substantially as:

in infectivity/

ARVdecreased substantially

that significant

analyses also

in substantially

Review

Eradicating HIV epidemics

1·8

1·6

1·4

1·2

1

0·8

0·6

0 20

Relative fitness of ARV-resistant strains (%)

4060

Change in risk behaviour (%)

80100

–50–250 25 5075100

1·8

1·6

1·4

1·2

R0ARV

R0ARV

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 ARV-resistance per year; blue=

increases in risky sex plus 10–60% of treated cases develop ARV-resistance 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 ARV-resistant strains on the value of R0

data) showing the effect of changes (increases and decreases) in risky sex on the value of R0

ARV. (B) Results (with unadjusted

ARV.

Page 5

For personal use. Only reproduce with permission from The Lancet Publishing Group.

THE LANCET Infectious Diseases Vol 2 August 2002 http://infection.thelancet.com

491

increasing (PRCC >0·5) the value of

R0

substantially as: (1) the relative fitness

(ie, the transmissibility relative to

drug-sensitive strains)

resistant strains increased, and/or (2)

the levels of risky sex increased (table).

The evolution of ARV-resistant strains

that were very transmissible (ie, very

fit) significantly increased the value of

R0

sex (green data) significantly reduced

R0

risky behaviour

significantly increased R0

2B). Thus, changes in risk behaviour

determine the effect of the value of

fitness of ARV-resistant strains on

increasing R0

ARV. The value of R0

ARVincreased

of ARV-

ARV(figure 2A). Reductions in risky

ARV(figure 2B), whereas increases in

(blue data)

ARV(figure

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)

reductions (median

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

(p=0·13).

Figures 3A and 3B show the

frequency distributions (using only

the simulations

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 epidemic-eradication 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 eradication6.

and substantial

value 25%

be unlikely

from the LHS

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 R0

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

ARV), even

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 R0

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).

ARV<1). Results

Number of simulations

Number 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

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

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 ARV-resistant 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.13Fourth,

the value of R0

sex. Our findings demonstrate unequivocally that it is

imperative that the usage of ARV should be tightly coupled

with effective risk-reduction 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 ARV-resistant strains

that evolve. If levels of risky sex increase, then even

ARV-resistant 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,12,34and it has been estimated

that ARV has also decreased the transmission rate in

this city.12,13After the widespread use of ARV in 1996,

incidence rates in San Francisco were predicted12to 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.34Therefore, 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 ARV-resistance;13by 2005 42% of the

HIV infections in San Francisco are predicted to be

ARV-resistant.13Here, we have shown by calculating a

single summary outcome measure (R0

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,35and this

reduction in average viral load translates into a reduction

in the average level of infectivity35that 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 high-prevalence (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 resistance13and high rates of increase

in risky sex;13,38,39therefore our calculations (shown in

blue in the figures) suggest that whereas high usage of

ARVis extremely sensitive to changes in risky

ARV) that a high

ARV could result in epidemic eradication in this city

it is quite unlikely under the current conditions.

Elsewhere13we 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.12,13However, the

beneficial impact of ARV on reducing transmission will

be masked if risky behaviours increase12; therefore, it

becomes necessary to theoretically estimate the “true”

impact of ARV on HIV epidemics by calculating a single

summary outcome measure (R0

that substantially reduce the HIV-infection rate and

the AIDS-death rate12,13also decrease the value of R0

and hence increase the probability of eradication. Our

current quantitative findings imply (by contrast with the

position argued by others40,41) 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 R0

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 R0

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 HIV-prevention

tool.

ARV). The same key factors

ARV

ARVshould now be calculated for HIV epidemics in

ARVthan

Acknowledgements

We gratefully acknowledge the financial support of NIH/NIAID

(Grant No. AI41935), funding from the UCLA AIDS Institute

(to SMB), and funding from UAM-Iztapalapa 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 7

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

References

1 Anderson RM, May RM. Infectious diseases of

humans: dynamics and control. Oxford: Oxford

University Press, 1991.

2Macdonald GM. The epidemiology and control of

malaria. Oxford: Oxford University Press, 1957.

3Blower SM, Small PM, Hopewell P. Control

strategies for tuberculosis epidemics: new models

for old problems. Science 1996; 273: 497–500.

4 Blower SM, Gerberding JLG. Understanding,

predicting and controlling the emergence of drug-

resistant tuberculosis: a theoretical framework.

J Mol Med 1998; 76: 624–36.

5 Lietman T, Porco TC, Dawson C, Blower SM.

Global elimination of trachoma: how frequently

should we administer mass chemotherapy? Nat

Med 1999; 5: 572–76.

6Blower S, Koelle K, Kirschner D, Mills J. Live

attenuated HIV vaccines: predicting the trade-off

between efficacy and safety. Proc Natl Acad Sci USA

2001; 98: 3618–23.

7 Hecht FM, Grant RM, Petropoulos CJ, et al. Sexual

transmission of an HIV-1 variant resistant to

multiple reverse-transcriptase and protease

inhibitors. N Engl J Med 1998; 339: 307–11.

8Boden D, Hurley A, Zhang L, et al. HIV-1 drug

resistance in newly infected individuals. JAMA

1999; 282: 1135–41.

9Little SJ, Daar ES, D’Aquila RT, et al. Reduced

antiretroviral drug susceptibility among patients

with primary HIV infection. JAMA 1999; 282:

1142–49.

10 Yerly S, Kaiser L, Race E, Bru JP, Clavel F, Perrin L.

Transmission of antiretroviral drug-resistant HIV-

1 variants. Lancet 1999; 354: 729–33.

11 Salomon H, Wainberg MA, Brenner B, et al.

Prevalence of HIV 1 resistant antiretroviral drugs

in 81 individuals newly infected by sexual contact

or IDU. AIDS 2000; 14: F17–23.

12 Blower SM, Gershengorn HB, Grant RM. A tale of

two futures: HIV and antiretroviral therapy in San

Francisco. Science 2000; 287: 650–54.

13 Blower SM, Aschenbach AN, Gershengorn HB,

Kahn JO. Predicting the unpredictable:

transmission of drug-resistant HIV. Nat Med 2001;

7: 1016–20.

14 Diekmann O, Heesterbeek JA, Metz JA. On the

definition and the computation of the basic

reproduction ratio R0 in models for infectious

diseases in heterogeneous populations. J Math Biol

1990; 28: 365–82.

15 Blower SM, McLean AR. Prophylactic vaccines,

risk behavior change and the probability of

eradicating HIV in San Francisco. Science 1994;

265: 1451–54.

16 Catania JA, Morin SF, Canchola J, Pollack L,

Chang J, Coates TJ. U.S. priorities—HIV

prevention. Science 2000; 290: 717.

17 Blower SM, Dowlatabadi H. Sensitivity and

uncertainty analysis of complex models of disease

transmission: an HIV model, as an example. Inl

Stal Rev 1994; 2: 229–43.

18 Blower SM, Porco TC, Darby G. Predicting

and preventing the emergence of antiviral

drug resistance in HSV-2. Nat Med 1998; 4:

673–78.

19 Iman RL, Helton JC, Campbell JE. An approach to

sensitivity analysis of computer models, part 1.

introduction, input variable selection and

preliminary variable assessment. J Qual Techn

1981; 13: 174–83.

20 Iman RL, Helton JC, Campbell JE. An approach to

sensitivity analysis of computer models, part 2.

ranking of input variables, response surface

validation, distribution effect and techniques

synopsis. J Qual Techn 1981; 13: 232–40.

21 Blower SM, McLean AR, Porco TC, et al. The

intrinsic transmission dynamics of tuberculosis

epidemics. Nat Med 1995; 1: 815–21.

22 Sanchez MA, Blower SM. Uncertainty and

sensitivity analysis of the basic reproductive rate:

tuberculosis as an example. Am J Epidemiol. 1997;

145: 1127–37.

23 Gershengorn HB, Blower SM. The impact of

antivirals and the emergence of drug resistance:

HSV-2 epidemic control. AIDS Patient Care STDs

2000; 14: 133–42.

24 Huang W, De Gruttola V, Fischl M, et al. Patterns

of plasma human immunodeficiency virus type 1

RNA response to antiretroviral therapy. J Infect Dis

2001; 183: 1455–65.

25 Hansel A, Bucher HC, Nuesch R, Battegay MJ.

Reasons for discontinuation of first highly active

antiretroviral therapy in a cohort of proteinase

inhibitor-naive HIV-infected patients. J Acquir

Immune Defic Syndr 2001; 26: 191–93.

26 Gallant JE. Strategies for long-term success in the

treatment of HIV infection. JAMA 2000; 283:

1329–34.

27 Descamps D, Flandre P, Calvez V, et al.

Mechanisms of virologic failure in previously

untreated HIV-infected patients from a trial of

induction-maintenance therapy. JAMA 2000; 283:

205–11.

28 Pialoux G, Raffi F, Brun-Vezinet F, et al.

A randomized trial of three maintenance regimens

given after three months of induction therapy

with zidovudine, lamivudine, and indinavir in

previously untreated HIV-1-infected patients.

N Engl J Med 1998; 339: 1269–76.

29 Havlir DV, Hellmann NS, Petropoulos CJ, et al.

Drug susceptibility in HIV infection after viral

rebound in patients receiving indinavir-containing

regimens. JAMA 2000; 283: 229–34.

30 Ghani AC, Henley WE, Donnelly CA, Mayer S,

Anderson RM. Comparison of the effectiveness of

non-nucleoside reverse transcriptase inhibitor-

containing and protease inhibitor-containing

regimens using observational databases. AIDS

2001; 15: 1133–42.

31 Paredes R, Mocroft A, Kirk O et al. Predictors of

virological success and ensuing failure in HIV-

positive patients starting highly active antiretroviral

therapy in Europe: results from the EuroSIDA

study. Arch Intern Med 2000; 160: 1123–32.

32 Iman RL, Helton JC, An investigation of

uncertainty and sensitivity analysis techniques for

computer models. Risk Anal 1988; 8: 71–90.

33 Kleijnen JPC, Helton JC. Statistical analyses of

scatter plots to identify important factors in large-

scale simulations, 1: review and comparison of

techniques. Reliability Engineering and System

Safety 1999; 65: 147–85.

34 HIV Seroepidemiology and Surveillance Section

AIDS Surveillance Unit. San Francisco annual

surveillance report 2000. San Francisco: San

Francisco Department of Public Health, 2001.

http://www.dph.sf.ca.us.

35 Quinn TC, Wawer MJ, Sewankambo N, et al. Viral

load and heterosexual transmission of human

immunodeficiency virus type 1. N Engl J Med 2000;

342: 921–29.

36 Velasco-Hernandez JX, Hsieh YH. Modelling the

effect of treatment and behavioral change in HIV

transmission dynamics. J Math Biol 1994; 32:

233–49.

37 Hsieh YH, Velasco-Hernandez JX. Community

treatment of HIV-1: initial stage and asymptotic

dynamics. Biosystems 1995; 35: 75–81.

38 Centers for Disease Control. Increases in unsafe sex

and rectal gonorrhoea among men who have sex

with men—San Francisco, California, 1994–1997.

MMWR Morb Mortal Wkly Rep 1999; 48: 45–48.

39 Katz MH, Schwarz SK, Kellog TA, et al. Impact of

highly active antiretroviral treatment on HIV

seroincidence among men who have sex with men:

San Francisco. Am J Public Health 2002; 92:

388–94.

40 Creese A, Floyd K, Alban A, Guiness L. Cost-

effectiveness of HIV/AIDS interventions in Africa:

a systematic review of the evidence. Lancet 2002;

359: 1635–43.

41 Marseille E, Hofmann PB, Kahn JG. HIV

prevention before HAART in sub-Saharan Africa.

Lancet 2002; 359: 1851–56.

Review

Eradicating HIV epidemics