Download What can modeling tell us about the threat of antiviral drug resistance?

What can modeling tell us about the threat of antiviral drug
resistance?
Sally Blowera and Paul Volberdingb
Purpose of review
Currently, antiviral resistance is a major public health concern.
Here, we review how mathematical models have been used to
provide insights into the emerging threat of antiviral resistance.
We focus mainly on the problem of drug resistance to HIV.
Recent findings
We review how antiviral models of HIV have been used: (1) to
understand the evolution of an epidemic of drug-resistant HIV,
(2) to predict the incidence and prevalence of drug-resistant
HIV, (3) to conduct biological `cost±benefit' analyses, and
(4) to make public health policy recommendations. We also
briefly discuss antiviral resistance for HSV-2 and influenza.
Recent studies indicate that for HSV-2 and influenza drug
resistance is not likely to become a major public health problem.
However, for HIV the situation is very different. Results from
several studies predict that a high prevalence of drug-resistant
HIV will be an inevitable consequence of more widespread
usage of antiretroviral therapies (ART). However more
widespread usage of ART will save a substantial number of
lives, and could even result in epidemic eradication.
Summary
Models have been used in many ways to provide insight into the
emerging threat of antiviral resistance, particularly for HIV. At
this stage in the HIV epidemic the most important future use of
models may be that they will force the goals of public health
policies to be clearly defined. Once goals have been defined it
can then be decided whether a high prevalence of drugresistant HIV is a threat or simply a justified means to an end.
Keywords
antiviral, drug resistance, mathematical model
Curr Opin Infect Dis 15:609±614.
#
2002 Lippincott Williams & Wilkins.
a
AIDS Institute and Department of Biomathematics, David Geffen School of
Medicine, University of California at Los Angeles and bUniversity of California at San
Francisco and the San Francisco Veterans Affairs Medical Center, California, USA
Correspondence to Sally Blower, AIDS Institute and Department of Biomathematics,
David Geffen School of Medicine at UCLA, 10833 Le Conte Avenue, Los Angeles,
CA 90095-1766, USA
Tel: +1 310 206 3052; fax: +1 310 206 6116; e-mail: [email protected]
Current Opinion in Infectious Diseases 2002, 15:609±614
Abbreviations
ART
HSV-2
antiretroviral therapies
herpes simplex virus type 2
# 2002 Lippincott Williams & Wilkins
0951-7375
DOI: 10.1097/01.qco.0000044780.05458.d6
Introduction
Along with our increasing ability to treat viral infections
is our fear that resistance to these new drugs will become
as limiting a barrier as has already occurred for some
bacterial pathogens. HIV drug resistance already limits
treatment success and many share the concern that drug
resistance will occur for other viral infections like herpes
simplex virus type 2 (HSV-2, the cause of genital herpes)
and hepatitis B virus. Here, we discuss a variety of ways
in which mathematical models have been used as tools
for providing insights into the emerging threat of
antiviral resistance. Mathematical models of epidemic
dynamics consist of a series of equations that describe
the speci®c transmission processes of a particular
pathogen; hence models can be used to predict
population-level outcomes such as incidence or prevalence. They are useful tools for predicting the epidemiological consequences of medical (and behavioral)
interventions, because the model contains explicit
mechanisms that link the effects of individual behaviors
with transmission dynamics. Mathematical modeling was
®rst used for analyzing how to control smallpox in 1760
[1]. Since then a wide variety of infectious diseases have
been modeled including tuberculosis, malaria, trachoma,
and in¯uenza.
The ®rst epidemic models of HIV that included the
effects of treatment were used to assess the potential
epidemiological consequences of monotherapy (with
zidovudine); these studies predicted that widespread
usage of monotherapy (under the assumptions that
zidovudine would substantially increase survival time
but would only slightly reduce infectivity) could
increase the incidence rate [1±7]. These early modeling
analyses of monotherapy did not include the possibility
of either increases in risky behavior or of the emergence
(and subsequent transmission) of drug-resistant strains.
The introduction of combination antiretroviral therapies
(ART) in the mid-1990s was accompanied by the rapid
emergence of antiviral resistance and also (in high-risk
communities) by increases in risk behavior. Thus
predicting the epidemiological consequences of these
new therapies became a more complex problem, and
led to the development and analysis of new models
[8,9 . .±11 . .,12 .,13 . .]. These new HIV models were
similar in structure to earlier epidemic models of
antibiotic resistance [14±17], as they allowed drugresistant strains to emerge during treatment and to be
transmitted.
609
Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.
610 Antimicrobial agents: parasitic/viral
The new HIV models were used to predict the effects of
widespread usage of ART in the San Francisco gay
community, under both optimistic and pessimistic
assumptions concerning changes in risky sex and the
rate of emergence of drug resistance [8]. It has been
shown that ± even in the presence of high rates of
emergence and transmission of drug resistance ± a high
usage rate of ART would signi®cantly decrease the
AIDS death rate and prevent a substantial number of
new HIV infections [8,9 . .]. Thus, treatment can act as
an effective prevention tool [8,9 . .,10 . .]. The models
have also been used to evaluate the trade-off between
decreasing transmission (due to ART) and increases in
transmission (due to increases in risky sex). An increase
in the average level of risky sex of only 10% in the San
Francisco gay community would be enough to counterbalance the bene®ts of a high usage of ART in
decreasing transmission and would result in an increase
in the incidence rate [8]. Similar results have been found
for the gay community in Australia [12 .].
Modeling antiviral resistance
To date, relatively few epidemic models have been used
to analyze problems relating to antiviral resistance;
resistance to HIV has been the main focus of attention.
A few models of antiviral resistance have also been
developed for HSV-2 [18,19] and in¯uenza [20]. Here
we review these analyses and discuss what they tell us
about the threat of antiviral resistance. We organize our
review under four topics describing how models have
been used (1) to understand the evolution of an
epidemic of drug-resistant HIV, (2) to predict the
incidence and prevalence of drug-resistant HIV, (3) to
conduct biological `cost±bene®t' analyses, and (4) to
make public health policy recommendations. Finally, we
brie¯y discuss HSV-2 and in¯uenza.
To understand the evolution of an epidemic of drugresistant HIV
Analyses of antiviral epidemic models have revealed
interesting insights into the evolution of epidemics of
drug-resistant HIV. The growth and dynamics of an
epidemic of drug-resistant strains have been shown to be
fundamentally different from the growth and dynamics
of an epidemic of drug-sensitive strains [9 . .]. These
differences are due to the ecological competitive
dynamics between drug-resistant and drug-sensitive
strains for `resources' (i.e. high-risk individuals to infect),
and to the differences in the number of processes that
fuel the epidemic [9 . .]. Drug-sensitive epidemics are
fuelled by only one process (transmission); however
drug-resistant epidemics are fuelled by two processes:
(1) transmission and (2) the conversion of treated drugsensitive infections to drug-resistant infections (acquired
resistance). Since the rate of increase in drug-resistant
infections is not rate-limited by transmission, the rate of
increase in drug-resistant infections can be much faster
than the rate of increase in drug-sensitive infections;
hence a high prevalence of drug resistance can be
reached very quickly [8,9 . .,11 . .,21]. Computational
analysis of antiviral models has been used to determine
which process is most important in fuelling the epidemic
of drug resistance: acquired resistance or transmitted
resistance [9 . .]. The vast majority of new cases of drugresistant HIV will be the result of acquired resistance;
transmitted resistance will only account for a relatively
small percentage of the new cases of drug resistance
[9 . .].
Sensitivity analyses of antiviral epidemic models have
been used to identify which factors are important in
increasing both the transmission and the prevalence of
drug-resistant strains of HIV [9 . .]. Transmission and
prevalence of drug resistance increases as treatment rates
increase, and/or as the rate of development of acquired
resistance increases. In addition, transmitted resistance
has been shown to be very dependent upon the
transmissibility of the drug-resistant strains (drugresistant strains that have a high relative ®tness generate
a high transmission rate) and the degree of treatmentinduced reduction in viral load of drug-sensitive strains
[9 . .]. Prevalence of drug resistance increases as the
average duration of time that a drug-resistant patient
spends on ineffective therapy increases. Uncertainty and
sensitivity analyses of epidemic models have revealed
how treatment changes the competitive dynamics
between the drug-sensitive and the drug-resistant
strains. High treatment rates (ranging from treating 50
to 90% of HIV-infected individuals) signi®cantly
decrease the percentage of drug-sensitive infections,
but substantially increase the percentage of drugresistant infections (Fig. 1); this effect increases over
time. The treatment rate also determines the level of
transmitted resistance [9 . .].
There has been considerable variation in the reported
prevalence of HIV drug resistance in the `real-world'
[22,23]; these empirical results may initially appear
surprising. The theoretical results, however, enable us
to understand the observed heterogeneities in the
data sets from different geographical regions. The
modeling results (Fig. 1) show (not surprisingly) that
drug resistance is a function of time and treatment
rate [9 . .]. Therefore, prevalence of resistance is
expected to be low in regions with limited drug
access and use. Also, cities where early treatment was
available and where patients were provided with the
less potent regimens that were then in vogue are
expected to have a serious problem with community
HIV drug-resistance prevalence. Populations (in the
`real world') also vary with respect to levels of
medication adherence that is related to drug-resistance
Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.
Threat of antiviral drug resistance Blower and Volberding 611
Figure 1. The evolution of drug-resistant HIV as a function of
treatment rate and time
A
Percentage 100
of prevalent 90
80
infections
70
60
50
40
30
20
10
0
50
55
60
65
70
75 80 85 90
Treatment rate (%)
50
55
60
65
70
75 80 85 90
Treatment rate (%)
B
Percentage 100
of prevalent 90
80
infections
70
60
50
40
30
20
10
0
C
Percentage 100
of prevalent 90
80
infections
70
60
50
40
30
20
10
0
50
55
60
65
70
75 80 85 90
Treatment rate (%)
Predictions calculated using model described in Blower et al. [8] and
time-dependent uncertainty analyses. Predictions show the temporal
impact of the treatment rate (in terms of the percentage of drug-sensitive
cases receiving treatment) on the prevalence of drug-sensitive infections
(black data) and the prevalence of drug-resistant infections (red data) in
San Francisco. The treatment rate ranges from 50 to 90% of HIVinfected individuals, and the rate of acquired drug resistance ranges
from 10 to 60% of treated cases per year. (A)±(C) correspond to 1997,
2000 and 2005, respectively; the median values for the prevalence of
ART-resistant infections shown in these figures is 3.3% (in 1997),
28.5% (in 2000) and 42.2% (in 2005). The results are discussed in
detail in Ref. [9 . .] (http://nature.com/medicalresearch).
selection [9 . .]; the modeling analyses predict that
variation in adherence will signi®cantly affect the
prevalence of drug resistance. In the developed
economies, these expected differences (on the basis
of the modeling analyses) in HIV drug resistance
transmission and prevalence are now being reported.
Rates of transmitted resistance in San Diego are very
different from those in San Francisco [22,23].
To predict the incidence and prevalence of drugresistant HIV
Scenario analysis (i.e. one single computer simulation of
a model) is useful for predicting the emergence of drug
resistance if the values of each parameter in the model
can be precisely estimated. Data, however, are often
sparse. For example, the values of many of the
parameters (such as the transmissibility of drug-resistant
strains) are only imprecisely known; therefore scenario
analysis has limited utility [24]. Models can still be
analyzed (even if parameter estimates are only imprecisely known), however, by using uncertainty analysis
[25±27]; uncertainty analysis is a technique developed in
the ®eld of risk assessment and engineering in order to
predict the probability of adverse events occurring
[28,29]. Uncertainty analysis can be used to predict the
future (with a degree of uncertainty) by including
uncertainty in estimating the speci®c values of each of
the models' input parameters [24,25]. By using uncertainty analysis antiviral epidemic models can be used
as predictive tools [8,9 . .,10 . .,18,19]. An uncertainty
technique based upon Latin hypercube sampling
[28,29] has previously been applied in infectious disease
modeling to predict the future of HIV epidemics
[8,9 . .,10 . .,24], the potential epidemiological consequences of HIV vaccines [30] and the emergence of
antiviral-resistance [8,9 . .,18,19,21].
Uncertainty analysis of an antiviral epidemic model has
been used to predict both the prevalence and transmission of drug-resistant HIV in the gay community in San
Francisco [9 . .,21]. Using both optimistic and pessimistic
assumptions concerning the rate of increase in risky sex
and the emergence of drug-resistant HIV, a high
prevalence of drug resistance has been predicted [21].
It has been predicted (using the pessimistic assumptions) that 42% of the HIV-infected cases in San
Francisco will be infected with drug-resistant strains by
2005 [9 . .]. The time of exponential increase for
transmitted resistance, however, is likely to be rather
short due to the effect of the competition between drugresistant and drug-sensitive strains for `resources' (i.e.
high-risk individuals to infect) [9 . .]. These competitive
dynamics ensure that transmitted resistance in San
Francisco (de®ned in terms of the percentage of new
HIV infections that are drug resistant) will remain fairly
low and is expected to stabilize in the next few years.
Even by 2005, only 15.6% (median value) of the new
HIV infections are predicted to be drug resistant [9 . .].
Recent empirical studies [23] show that these theoretical
predictions are in close agreement with the levels of
drug resistance that have actually been observed.
Goudsmit and colleagues [13 . .] have recently analyzed
the impact that therapy failure had on the transmission
of zidovudine-resistant strains of HIV in a cohort of gay
Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.
612 Antimicrobial agents: parasitic/viral
men in Amsterdam. They used a model to calculate the
number of cases of zidovudine resistance that were
expected to have occurred (as a result of transmission) in
this cohort from 1990 through to 1998. They estimated
the necessary parameter values for their model using
empirical data. The model predictions were then
compared with cohort data on temporal trends in AZT
resistance in newly infected men. Over the 8-year study
period 43 individuals in the cohort were recently
infected, but only three of these primary infections were
due to the transmission of zidovudine-resistant strains.
Model predictions, and the empirical data, showed that
the transmission and prevalence of zidovudine-resistant
strains rose and fell over the study period as the usage of
AZT rose and fell. The prevalence of AZT resistance
initially rose to 22% due to the large number of patients
receiving zidovudine monotherapy, but then prevalence
fell rapidly (after 1996) as patients were switched to
more effective therapies. The model revealed that very
few (n=3) cases of transmitted AZT resistance were
expected as the prevalence of AZT resistance quickly
fell to zero. Thus the high (but temporary) prevalence of
AZT resistance in the Amsterdam cohort was almost
completely driven by acquired resistance.
To conduct `biological cost±benefit' analyses
Medical interventions are designed to bene®t individual
patients, but can sometimes lead to detrimental epidemic-level effects; for example, HIV epidemics will
worsen if moderately effective HIV vaccines are
accompanied by an increase in risky behavior [31,32].
Models can be coupled with economic analyses to
perform cost±bene®t and cost-effectiveness analysis
[11 . .]. Modeling, however, can also be used to conduct
`biological cost±bene®t' analyses; these analyses have
two stages. First, the epidemic-level bene®ts and costs of
a particular control strategy are quanti®ed, and then a
treatment evaluation criterion is de®ned and used to
determine whether the bene®ts outweigh the costs.
Models can be used to calculate `real-world' treatment
evaluation criteria such as the annual (or cumulative)
death rate, and the annual (or cumulative) incidence
rate. Also, models can be used to de®ne theoretical
treatment evaluation criteria [14,15,18]. For example, in
the `real world' the treatment failure rate is often used as
a treatment evaluation criterion for evaluating tuberculosis control programs. The treatment failure rate,
however, is only a measure of the direct effect of
treatment in generating resistance; the indirect effect of
treatment in generating resistance is not assessed within
this treatment evaluation criterion. A theoretical treatment evaluation criterion was de®ned (by analyzing a
model of antibiotic resistance) to assess both the direct
and the indirect effects of treatment in generating
antibiotic resistance [14]. This treatment evaluation
criterion was used to calculate the number of cases of
acquired plus transmitted drug resistance that emerged
during the treatment of a single case of drug-sensitive
tuberculosis [15]. Applying this treatment evaluation
criterion to data from developing countries it was
determined that (due to high treatment failure rates)
control programs could actually make the epidemic
worse by generating (on average) 1.7 drug-resistant cases
per treated drug-sensitive tuberculosis case [15].
Antiviral models have been used to perform biological
`cost±bene®t' analyses (1) by assessing whether the
epidemic-level bene®t of ART (i.e. reduction in
transmission of drug-sensitive strains) outweighs the
epidemic-level cost of ART (i.e. increase in transmission
of drug-resistant strains) [8,9 . .], and (2) by calculating
the cumulative number of HIV infections prevented per
prevalent case of resistance [9 . .]. These analyses have
shown that the reduction in transmission of drugsensitive strains (due to widespread usage of ART)
substantially outweighs any increase in new infections
due to transmitted resistance. It has also been shown
that the high usage of ART in San Francisco has (and
will continue to) signi®cantly reduced the overall
transmission rate [8,9 . .]: by 2005 approximately one
HIV infection will have been prevented for each
prevalent case of drug resistance that is present [9 . .].
To make public health policy recommendations
Models can be useful health policy tools as they can be
used to identify how to design and improve epidemic
control strategies. Certain epidemic control strategies can
substantially reduce the morbidity and the mortality
caused by drug-sensitive strains, but substantially increase
the morbidity and mortality caused by drug-resistant
strains. In order to design and improve epidemic control
strategies, goals and evaluation criteria need to be clearly
speci®ed [15]. Many different goals can be speci®ed, for
example, disease eradication, stabilization (at a speci®c
level) of drug resistance, or a speci®c reduction in
incidence, prevalence, morbidity or mortality rates. Goals
need to be de®ned in terms of an epidemiological
measure (for both the drug-sensitive and the drugresistant strains) and by a time frame in which the goal
is to be attained [15]. The model can then be analyzed in
order to determine how to achieve the particular goal(s) in
the speci®ed time frame. Eradication is an easy goal to
specify theoretically, although it is a hard goal to achieve
in the `real world'. Analysis of antiviral models has shown
that it is theoretically possible to achieve eradication of
HIV epidemics by using a combination of ART and risk
reduction: even a high-prevalence (30%) epidemic could
be eradicated if 70% of HIV-infected cases are treated and
risky behaviors are reduced by 25% [10 . .]. When
designing epidemic control strategies both short-term
and long-term goals need to be speci®ed, and the
compatibility of these two goals needs to be carefully
Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.
Threat of antiviral drug resistance Blower and Volberding 613
evaluated [15]. An epidemic control strategy that would
be the optimal strategy to achieve the long-term goal of
eradication, can in the short term generate the highest
prevalence of drug resistance [10 . .,19].
Uncertainty analysis of antiviral resistance models has
shown that the transmission of drug-sensitive strains is a
substantially greater threat than the transmission of drugresistant strains, and that acquired resistance is a
substantially more important process than transmission
in generating cases of drug resistance [9 . .]. Sensitivity
analysis of antiviral resistance models has been used to
identify the important factors in fuelling the epidemic of
antiviral resistance. These results have been used to
suggest rational public health policies for controlling
HIV epidemics. These theoretical analyses have shown
that if the goal is to maximize the reduction in the AIDS
death rate and incidence rate then the strategy should be
to treat as many HIV-infected people as possible and to
link treatment programs with effective behavioral intervention programs [9 . .]. If the goal is to minimize the
transmission and prevalence of drug resistance then
theoretical analyses have led to four health policy
recommendations: (1) delay therapy as long as possible,
(2) reduce as much as possible the rate of development
of acquired resistance, (3) develop more effective
therapies that will completely suppress resistant isolates,
and (4) minimize the average length of time that a drugresistant case is receiving ineffective treatment [9 . .].
These recommendations are in accord with the British
[33] and the US treatment guidelines (www.hivatis.org/
guidelines/adult/April23_01/pdf.AAAPR23S) that recommend delaying therapy.
Resistance to antiretroviral drugs develops due to a
variety of factors that depend upon the virus, the
patient, the clinician and the drug regimen. One
important factor is patient adherence; a low rate of
adherence leads to a high rate of emergence of acquired
resistance. Tchetgen et al. [11 . .] have developed an
epidemic model of treatment and antiviral resistance
and have used their model to assess the effects of
adherence on the emergence of resistant virus.
Speci®cally, they have used their model in order to
answer the question of whether clinicians should screen
patients for adherence and choose to selectively treat
patients in order to minimize the emergence of drug
resistance. They combined an epidemic model with a
probabilistic model that accounted for the frequency
and accuracy with which physicians screen patients for
adherence. The model was used to compare a policy of
screening and treating only the patients that the
clinicians believe are likely to adhere to a policy of
treating all HIV-infected individuals. The results
showed that, in general, screening and selective
treatment would generate lower levels of resistance
but a higher incidence of HIV and AIDS than a policy
of treating all HIV-infected individuals.
Other diseases and antiviral resistance
Genital herpes (caused by HSV-2) is the most prevalent
sexually transmitted disease worldwide. In many developing countries, however, genital herpes is untreated,
and in the United States only 10% (or less) of HSV
infections are treated. An antiviral epidemic model of
HSV-2 has been developed and used as a health policy
tool to predict the levels of antiviral drug resistance that
would emerge if treatment rates for genital herpes were
substantially increased [18,19]. The results showed that
increasing treatment rates (in an immunocompetent
population) would signi®cantly decrease the incidence
of HSV-2 infections, and that (in contrast to HIV) the
prevalence of drug-resistant viral strains (even after
several decades) would remain low [18,19]. The same
model was also used to determine the probability of
eradicating herpes epidemics by using antivirals, and to
quantify the effect of increasing antiviral usage on
decreasing HSV-2 prevalence [19]. Further analyses
were performed to calculate the effect of antiviral usage
on individual patients in terms of the decrease in the
average number of infectious days per year, and an
individual's lifetime probability of acquiring permanent
drug resistance [19].
Stilianakis et al. [20] developed a mathematical model to
track the emergence of drug-resistant in¯uenza viruses
during an in¯uenza epidemic. They ®tted their model to
data from an in¯uenza A epidemic that occurred in 1978
in a boarding school. They used their model to evaluate
several treatment and chemoprophylaxis strategies during both an outbreak in a school and an epidemic. Three
strategies were evaluated: treating only infected persons
with clinical symptoms, mass chemoprophylaxis for all
uninfected persons, and chemoprophylaxis plus treatment. Their results showed that chemoprophylaxis of
susceptible individuals (without treatment of those who
are infected and symptomatic) would be the best
strategy for reducing transmission and would generate
only low levels of drug-resistant viruses.
Conclusion
The effects of ART at the epidemic level are complex.
Models allow us to focus on the big picture and to
evaluate simultaneously all aspects of the epidemic.
Models of antiviral resistance have many uses. They can
be used to predict how much antiviral resistance is to be
expected and over what time scale resistance will
emerge. They can also be used to identify which
biological, behavioral or treatment factors contribute to
the emergence and transmission of drug-resistant strains.
The results of these analyses can be used to suggest how
to prudently use existing (and new) treatment regimens
Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.
614 Antimicrobial agents: parasitic/viral
to control viral epidemics whilst simultaneously maximizing the public health bene®t. The models have
shown that for HSV-2 and in¯uenza, drug resistance is
not likely to become a public health problem. For HIV,
however, the situation is very different. Analyses
indicate that (not surprisingly) a high prevalence of
drug-resistant HIV will be an inevitable consequence of
more widespread usage of ART. More widespread usage
of ART, however, will save a substantial number of lives,
and could even result in epidemic eradication. At this
stage we need to determine what are the desired
epidemic-level goals for controlling HIV epidemics.
When these goals have been de®ned we can decide
whether a high prevalence of drug-resistant HIV should
be perceived as a threat or simply as a justi®ed means to
an end.
Acknowledgements
S.B. acknowledges the ®nancial support of NIH/NIAID (RO1 AI41935).
P.V. acknowledges the ®nancial support of the USCF-GIVI Center for
AIDS Research (P30 AI27763-11).
References and recommended reading
11 Tchetgen E, Kaplan EH, Friedland GH. Public health consequences of
. . screening patients for adherence to highly active antiretroviral therapy. JAIDS
2001; 26:118±129.
The first analysis to evaluate the effect of screening for adherence on the incidence
of HIV, AIDS and the emergence of drug resistance.
12 Law MG, Prestage G, Grulich A, et al. Modelling the effect of combination
.
antiretroviral treatments on HIV incidence. AIDS 2001; 15:1287±1294.
Evaluates the epidemiological trade-off between decreases in transmission due to
ART and increases in transmission due to increases in risky sex in the gay
community in Australia.
13 Goudsmit J, Weverling GJ, van der Hoak L, et al. Carrier rate of zidovudine. . resistant HIV-1: the impact of failing therapy on transmission of resistant strains.
AIDS 2001; 15:2293±2301.
Compares theory and data and evaluates the effect of changes in the usage rate of
antiretroviral therapies on the transmission of zidovudine-resistant strains.
14 Blower SM, Small PM, Hopewell PC. Control strategies for tuberculosis
epidemics: new models for old problems. Science 1996; 273:497±500.
15 Blower SM, Gerberding JLG. Understanding, predicting & controlling the
emergence of drug-resistant tuberculosis: a theoretical framework. J Mol Med
1998; 76:624±636.
16 Blower SM, Koelle K, Lietman TC. Antibiotic resistance: to treat . . . (or not to
treat)? Nat Med 1999; 5:358±359.
17 Blower SM, Porco TC, Lietman TC. Tuberculosis: the evolution of antibiotic
resistance and the design of epidemic control strategies. In: Horn, Simonett,
Webb, editors. Mathematical models in medical & health sciences. Vanderbilt
University Press; 1998.
18 Blower SM, Porco TC, Darby G. Predicting and preventing the emergence of
antiviral drug resistance in HSV-2. Nat Med 1998; 4:664±665.
19 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±142.
Papers of particular interest, published within the annual period of review, have
been highlighted as:
.
of special interest
..
of outstanding interest
20 Stilianakis NI, Perelson AS, Hayden FG. Emergence of drug resistance
during an influenza epidemic: insights from a mathematical model. J Infect Dis
1998; 177:863±873.
1
Bernoulli D. An attempt at a new analysis of the mortality caused by smallpox
and of the advantages of inoculation to prevent it [in French]. Mem Math Phys
Acad Roy Soc Paris 1760; 1±45.
22 Little SJ, Holte S, Routy JP, et al. Antiretroviral-drug resistance among
patients recently infected with HIV. N Engl J Med 2002; 347:385±394.
2
Anderson RM, Gupta S, May RM. Potential of community-wide chemotherapy or immunotherapy to control the spread of HIV-1. Nature 1991; 350:356±
359.
3
Paltiel AD, Kaplan EH. Modeling zidovudine therapy: a cost-effectiveness
analysis. J Acquir Immune Defic Syndr 1991; 4:795±804.
4
Gupta S, May RM, Anderson RM. Mathematical models and the design of
public health policy: HIV and antiviral therapy. Soc Ind Appl Math Rev 1993;
35:1±16.
21 Blower SM, Gershengorn HB, Grant RM. Supplementary data online; 2000.
Science Online www.sciencemag.org/feature/data/1044287.shl.
23 Grant RM, Hecht FM, Warmerdam M, et al. Time trends in primary HIV-1
drug resistance among recently infected persons. JAMA 2002; 288:181±
188.
24 Blower SM, Hartel D, Dowlatabadi H, et al. Drugs, sex and HIV: a
mathematical model for New York City. Phil Trans Roy Soc Series B 1991;
321:171±187.
25 Blower SM, Dowlatabadi H. Sensitivity and uncertainty analysis of complex
models of disease transmission: an HIV model, as an example. Int Stat Rev
1994; 2:229±243.
26 Blower SM, McLean AR, Porco TC, et al. The intrinsic transmission
dynamics of tuberculosis epidemics. Nat Med 1995; 1:815±821.
5
Velasco-Hernandez JX, Hsieh YH. Modeling the effect of treatment and
behavioral change in HIV transmission dynamics. J Math Biol 1994; 32:233±
249.
27 Sanchez MA, Blower SM. Uncertainty & sensitivity analysis of the basic
reproductive rate: tuberculosis as an example. Am J Epidemiol 1997;
145:1127±1138.
6
Hsieh YH, Velasco-Hernandez JX. Community treatment of HIV-1: initial
stage and asymptotic dynamics. Biosystems 1995; 35:75±81.
28 Iman RL, Helton JC, Campbell JE. An approach to sensitivity analysis of
computer models. I: Introduction, input variable selection and preliminary
variable assessment. J Qual Technol 1981; 13:174±183.
7
Velasco-HernaÂndez JX, Brauer F, Castillo-Chavez C. Effects of treatment and
prevalence-dependent recruitment on the dynamics of a fatal disease. IMA J
Math Appl Med Biol 1996; 13:175±192.
8
Blower SM, Gershengorn H, Grant RM. A tale of two futures: HIV and
antiretroviral therapy in San Francisco. Science 2000; 287:650±654.
29 Iman RL, Helton JC, Campbell JE. An approach to sensitivity analysis of
computer models. II: Ranking of input variables, response surface validation,
distribution effect and technique synopsis. J Qual Technol 1981; 13:232±
240.
9
Blower SM, Aschenbach AN, Gershengorn H, Kahn JO. Predicting the
unpredictable: transmission of drug-resistant HIV. Nat Med 2001; 7:1016±
1020.
The first analysis to predict levels of transmitted resistance. The authors use timedependent uncertainty analysis to make predictions from 1996 to 2005.
..
10 Velasco-Hernandez JX, Gershengorn HB, Blower SM. Could widespread
. . usage of combination antiretroviral therapy eradicate HIV epidemics? The
Lancet Infect Dis 2002; 2:487±493.
The first analysis to show that a high usage of antiretroviral therapies could lead to
the eradication of even a high-prevalence (30%) HIV epidemic (even if high levels
of drug resistance arise).
30 Blower S, Koelle K, Kirschner D, Mills J. Live attenuated HIV vaccines:
predicting the trade-off between efficacy and safety. PNAS 2001; 98:3618±
3623.
31 Blower SM, Koelle K, Mills J. Health policy modeling: epidemic control, HIV
vaccines & risky behavior. In: Kaplan E, Brookmeyer R, editors. Quantitative
evaluation of HIV prevention programs. New Haven, Yale University Press;
2001.
32 Blower SM, McLean AR. Prophylactic vaccines, risk behavior change and
the probability of eradicating HIV in San Francisco. Science 1994;
265:1451±1454.
33 Gazzard B, Moyle G. 1998 Revision to the British HIV Association guidelines
for antiretroviral treatment of HIV seropositive individuals. BHIVA Guidelines
Writing Committee. Lancet 1998; 352:314±316.
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