Transcript Modeling the AIDS outbreak

AIDS 23 years into the outbreak;
why is the pandemic not contained?
Wayne X Shandera, MD
Baylor College of Medicine
August 30, 2004
Topics to be covered
1
The current epidemiology of HIV/AIDS
Unique problem areas of the world today
2
Pathogenesis of disease
The impact of simple models
Modeling the coreceptor phenomenon
3
Treatment and prevention
How can resistance or adherence better be studied?
Does governmental policy make a difference?
4
Need for interactions today
mathematicians, virologists, and physicians
1 - Epidemiology
• A study of the unexpected (knowing the denominator)
• In 1981 Pneumocystis pneumonia or Kaposi’s
sarcoma among homosexual men was unexpected
• These are opportunistic infections which developed
because of HIV (isolated, 1983) infection
• In 23 years the prevalence of HIV infection increased
from zero to 1 in 150 globally
• Profound demographic impact in some cultures
HIV Prevalence in Adults, end 2003, 38 million infected
40 million in a world with 6 billion: 1/150
Adults and children estimated to be living
with HIV/AIDS as of end 2003
Western Europe
Eastern Europe
& Central Asia
520 000 – 680 000 1.2 – 1.8 million
East Asia & Pacific
790 000 – 1.2 million
700 000 – 1.3 million
North Africa & Middle East
Caribbean
South
350 000 – 590 000 470 000 – 730 000 & South-East Asia
Sub-Saharan Africa 4.6 – 8.2 million
Latin America
25.0 – 28.2 million
Australia
1.3 – 1.9 million
& New Zealand
12 000 – 18 000
North America
Total: 34 – 46 million
00002-E-1 – 1 December 2003
61-73% in Sub-Saharan Africa
Sub-Saharan Africa
• About 90% of HIV-infected Africans do not
know that they are infected
• Only about 11% of the HIV-infected have
been tested
• The percentage of Africans on HAART is
clearly under 1%
Spread of HIV over time
in sub-Saharan Africa, 1982–1997
Estimated percentage of adults
(15–49) infected with HIV
16.0% – 32.0%
8.0% – 16.0%
2.0% – 8.0%
0.5% – 2.0%
0% – 0.5%
trend data unavailable
outside region
WA D-E N 1998
Why is Southern sub-Saharan
Africa so impacted?
• Viral factors?
• Host factors?
• Transmission determinants?
Viral factors
• Transfer of a simian virus, separately for
HIV-1 and HIV-2, probably through hunting
accidents
– HIV-2 from sooty mangabees in West Africa
– HIV-1 from chimpanzees in Central Africa
• Unique clades for southern sub-Saharan
Africa may explain its meteoric rise there?
The HIV prevalence saw its exponential growth among
CSWs in Africa after it was already prevalent among
homosexual men in the US
HIV types (clades): Red is A, Green is B, Blue is C
Isolates are most diverse where the virus was
present the longest
Type C virus shows unique properties that
may explain some added pathogenicity
Clade distribution within Africa
In Cameroon, 40% of isolates are
nonrecombinant forms, making
vaccine production more difficult
Host factors
• Human immunogenetic determinants to some
degree affect progression of disease
– Are there unique such determinants in southern Africa?
This needs modeling!
• The age of first marriage may be important
• Concomitant sexually transmitted diseases put one
at higher risk for infection with HIV
• Lack of circumcision does the same
– Circumcision rates correlate in one study (at +0.9,
Pearson correlation coefficient) with absence of HIV
We know that age of marriage is
important because:
• It correlates directly with
the age of first child
(which is the best correlate
of population growth)
In the most HIV-impacted African
countries, marriage occurs later
• Three of the African
nations with the
highest HIV rate are at
the bottom of this
table, suggesting that
age at marriage is not
the primary factor for
spread in southern
sub-Saharan Africa
Do transmission factors explain
the HIV rise in Southern Africa?
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Poverty
Literacy
Women’s education
Migration of peoples
Political factors and degree of corruption
Inappropriate use and reuse of contaminated
needles
Is there a correlation between
poverty and AIDS?
• Because most sub-Saharan African
countries are poor, it is difficult to find
sufficient variation to study this relationship
• Namibia and Botswana are heavily
impacted with HIV infection, yet their per
capita gross national income (GNI) and per
capita purchasing power parity (PPP) are
among the highest in Africa
per capita Purchasing Power Parity
for sub-Saharan Africa nations
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•
1
2
64
70
84
85
118
139
156
205
208
Luxembourg
United States
South Africa
Mauritius
Botswana
Namibia
Swaziland
Lesotho
Zimbabwe
Congo, DR
Sierra Leone
$48,560
$34,280
$10,910
$ 9,860
$ 7,410*
$ 7,410
$ 4,430*
$ 2,980*
$ 2,220*
$ 630
$ 460
What about literacy in sub-Saharan Africa?
A moderate correlation, but HIV prevalence appears to be higher in
countries that show higher literacy
Could this reflect poor surveillance in the less literate nations?
Ted Conover, "The Road Is Very Unfair:
Trucking Across Africa in the age of Aids“
New Yorker, Aug 16, 1993
Along the remote routes of eastern Africa, longdistance truck drivers have been affectionately
revered as cowboys in convoy. But now they are also
identified as the unwitting carriers of AIDS,
particularly in Rwanda, at the heart of the AIDS belt,
where their H.I.V. infection rate is fifty-one per cent
A truck in Mali that traverses the migratory routes and
spreads a message of HIV prevention to 16,000 persons
along its routes
Other worrisome foci in the
world today
• Eastern Europe especially among drug users
• China and India
– 40% of the world’s population
– India already may have the largest case load
• Southeast Asia
– A diverse outbreak, IVDU and CSWs
– Cambodia with 4% and highest prevalence
Is Texas exempt in the era of
combination therapy?
The changes in prevalence are
worrisome
What models describe the
outbreak at large?
• May and Anderson, compartmental models
– Importance of mixing among subgroups
• Size of outbreak assessed by back calculation
– use of convolution
• Incubation period (t, exposure to disease) is a
bugaboo:
– Highly variable
– Infectivity is high early in disease, low, then high, hence
when does disease actually begin?
Isham V, Stochastic models for epidemics with
special reference to AIDS Ann Appl Prob 1993;3:1.
• Stochastic vs deterministic models
– Acquiring infection is stochastic
– Consequences of infection are both
deterministic and stochastic
• How do you accounting for variability in
– sexual activity
– incubation period
– infectivity
Phenomenon of mixing
The ideal?
The reality
How do you account for mixing I
sexual activity?
• Xi(t) = # susceptibles in i
subgroup
• Yi(t) = # infected
in i
subgroup
• κi = rate of partner change in
i subgroup
• pij = mixing matrix that
partner in subgroup i will
choose partner in subgroup j
• β = transmission probability
• ni = number of individuals in
I subgroup
Rate of infections
in subgroup i =
β Xi κi Σ pij Yj /nj
Incubation period for AIDS
• Truncated on the left
at time of infection
• Interval to
development of AIDS
• Best modeled with
– Weibull or
– gamma distribution
• scale ~2.6
Example of gamma distributions
Isham: divide the outbreak into i
periods of differing infectivity (3)
Practical tools for
epidemiologists
• AIDS Impact Model (AIM) – incidence,
progression and fertility to make demographic
predictions for a give country (SPECTRUM)
• Epimodel – uses point prevalence,
assumptions about progression rates and
putative start of outbreak to calculate
incidence curves, used by UN
Practical tools (continued)
• iwgAIDS – “complex continuous simulation” ,
calculate incidence and deaths by age and sex,
modes of transmission, US Census Bureau models
– Both Epimodel and iwgAIDS treat HIV+/-infected as
separate entities, limiting demographic predictions
• SimulAIDS – age structured “microstimulation”
model of AIDS using full complement of variables
(coital frequency, condom usage, # sex partners,
frequency of sexually transmitted infections) to
assess transmission dynamics
Practical tools (continued)
• May and Anderson compartmental models
– Demographic predictions
– Aimed primarily at affect on heterosexual populations
in developing world
– Importance of Ro, the basic reproductive rate
which must be >1 to sustain an outbreak
• STDSIM – a Monte Carlo model of sexual
transmission of HIV and 4 sexually transmitted
diseases
Ro = reproductive rate of the
outbreak
βc
Ro =
(μ + v)
• β = probability of
acquiring infection from
infected person
• c = average rate of
acquiring sexual contacts
• μ = underlying mortality
• v = disease-assd
mortality
Is Ro < or > 1?
• The primary drive is to push Ro < 1
• Is this best done through decreasing β?
– Condoms
– HAART
• Is this best done through decreasing c?
– Sexual education, religious based programs
• Increasing v is not a good alternative
– A reminder that patients living longer may sustain the outbreak
– Boily et al: Changes in transmission dynamics of the HIV epidemic after the widescale use of antiretroviral therapy could explain increases in sexually transmitted
infections. STD 2004;31:100
Criteria for a good model
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Good fit to observed data
Reasonable biological interpretation
Conceptual and computational simplicity
Applicability to low-quality, less frequent data
Convenient for statistical inferences,
interpretation
• Low costs economically and computationally
Courtesy, Wu and Ding, Biometrics
1999;55:418
Pathogenesis
(how disease develops)
• Challenge in the mid-1990s to the
prevailing idea of how AIDS is maintained
during its “years of latency”
• Models that incorporate new biologic
findings on coreceptor usage
– HIV binds to a cell receptor (CD4) but also
requires a coreceptor (“CCR5”) in which the
deletion of a segment provides complete
protection from infection
Early simple models
• Data of Ho et al, Wei et al, challenged the
prevailing notion of viral dynamics
• Modeled the level of actively replicating
virus in blood after administering a protease
inhibitor (which inhibits final viral particle
production)
• Best fit was a negative log function
During years of “latency”, is the virus quiescent or
replicating?
Source: Alimonti, J Gen Virol 2003
The empiric data, Ho et al, Nature 1995;373:124
Math formulation
• V(t) = V(0)e-St
– where S is the slope from the previous graph
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V(t1/2) = V(0)/2 = V(0)e-S(t1/2)
t1/2 = ln(2)/S
S = -0.34 (range, -0.21 to –0.54)
t1/2 = 2.04 days (range, 1/3 – 3.3 days)
Consequence of these data
• Recognition that HIV is not merely virally
stagnant within a sequestered site (such as the
herpes viruses within neurologic tissue)
• Instead 109 particles are produced daily
• Therapy was hence changed from single agents
(which began in 1987) to multiagent, combination
therapy in the mid-1990s
• HAART: Highly Active Anti-Retroviral Therapy
Some reservoirs show a half-life of months, making eradication
next to impossible by current therapy, Ho, Science, 1998, 1866
Another aspect of pathogenesis
that has been modeled
• Infection is a consequence of virus/host cell
interactions
• The main interaction is between viral
glycoprotein 41 (gp41) and a cellular
determinant (CD4) receptor
• A second “co-receptor” is required for
virus/host cell interaction
What is known about these
“coreceptors”?
Named as acronym (CCR5 and CXCR4) for a type
of chemokine (protein that attracts cells) Receptor
CCR5 is a protein (composed of amino acids made
of base pairs of DNA)
A deletion of 32 base pairs (referred to as the delta
32 deletion) changes the receptor and if found in
both genomes (“homozygous”) provides absolute
protection against HIV infection
Delta-32 deletion of CCR5
• It is known that some individuals can be
repeatedly exposed yet not acquire HIV infection
• This deletion is found selectively among
Caucasians
• By studies of isolate diversity, it is suggested the
deletion entered the human genome about 800
years ago (!)
• This fact regarding pathogenesis is being used by
Schering-Plough to introduced the newest line of
antiretrovirals
Modeling the Δ32 deletion
• Sullivan AD et al: The coreceptor mutation
CCR5Δ32 influences the dynamics of HIV
epidemics and is selected for by HIV.
PNAS 2001:98:10214
• A compartmental model that accounts for
varying transmission and progression rates
based on the Δ32 deletion status
What this model looks like
Calculating the changes in levels
of susceptibles
• Χ = entering
susceptibles
• i = genotype (coded)
• j = gender
• μ = natural mortality
• λ = infectivity
• k = stage of infection
infectivity, λ
• C = rate of partner
acquisition (mean plus
variance)
• Φ = number of contacts in
a partnership
• β = likelihood of
transmission in encounter
of S/I
• I/N = odds of
encountering an infected
The β transmission probabilities
estimates
WW
Partner Status
WΔ32
Δ32Δ32
WW
0.1
0.1
0.000010
WΔ32
0.03
0.03
0.000005
These probabilities are different, acute primary
infections vs late disease (higher for former)
Prevalence of HIV/AIDS in the adult population as predicted by the model
Wild type
CCR5Δ32 allele
Sullivan, Amy D. et al. (2001) Proc. Natl. Acad. Sci. USA 98, 10214-10219
Effects of HIV-1 on selection of the CCR5[Delta]32 allele
Sullivan, Amy D. et al. (2001) Proc. Natl. Acad. Sci. USA 98, 10214-10219
Aspects of treatment and prevention
• With the current 4 classes of HAART, there
are 19 drugs against AIDS (21, all other
human viruses)
• Prevention is inadequately funded both in the
developing and developed world
• More than clean needles and condoms
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Ensuring a safe blood supply
Education about the disease to teenagers
Encouraging voluntary and early testing
Adherence to treatment
Estimated AIDS Spending and Projected Need in Low- and Middle-Income Countries
Steinbrook, R. N Engl J Med 2004;351:738-742
Where HAART is available, the disease is manageable
Current status of therapy
• Reverse transcriptase inhibitors (2 current classes)
– Inhibits the enzyme HIV needs to replicate
• Protease inhibitors (1 current class)
– Inhibits an enzyme needed to form virus
• Fusion inhibitors (1 current class, agent)
– Inhibits fusion of the virus with the cell
• Integrase inhibitors (under investigation)
– Inhibits integration of the virus into the human genome
• Coreceptor inhibitors (under investigation)
– Inhibits the viral interaction with “coreceptors”
How is resistance modeled?
X = # susceptible
YR = # infected w resistant
isolates
YU = # infected w sensitive
isolates
U, T superscript = +/- rx
r = rate of resistance
Μ = mortality
What needs modeling today?
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Resistance to therapy
Adherence to therapy
Developing countries and their unique epidemiology
Immunopathogenesis (how disease develops)
– The body contains exposure to HIV better than any vaccine
to date
• Immunogenetic determinants in different racial groups
• The impacts of governmental policy
What about political factors,
corruption
AIDS appears to progress more rapidly in
nations with less stable regimes
Examples:
Uganda and the legacy of Idi Amin
Zaire (Congo) and the Mobutu years
President Mbeki in RSA, refusing to
accept the fact that HIV causes AIDS
The hazards of a
government failing to
recognize a major
epidemic in its midst
Can this phenomenon of
corruption be quantified?
• Transparency International – an NGO based in
Berlin, independently financed, designed to expose
corruption
• Produces an annual Corruptions Perceptions Index but
only for nations with data (101 of 200, 2000-2)
• Data collected from 15 sources
– Examples: World Economic Forum, Price Waterhouse
Coopers, World Bank survey, Columbia University
– Available at www.globalcorruptionreport.org
– Sources must rank data and may include other measures
such as nationalism, xenophobia, political instability
• Findings are robust with high correlation
Which governments are least
corrupt (0-10, 10 best)?
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1-Finland
2-Denmark
-New Zealand
4-Iceland
5-Singapore
-Sweden
7-Canada
-Luxembourg
-Netherlands
9.7
9.5
9.5
9.4
9.3
9.3
9.0
9.0
9.0
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10-United Kingdom
11-Australia
17-United States
18-Germany
24-Botswana
25-France
71-India
101-Nigeria
102-Bangladesh
8.7
8.6
7.7
7.3
6.4
6.3
2.7
1.6
1.2
Where are the sub-Saharan
African nations?
• Only 21 African nations, 18 of these subSaharan, were ranked with this index
• Not being ranked means data are not
available which usually suggests that
corruption is more rampant
• The median for all nations was 3.8, for the
18 SSA nations it was 2.7
Corruption index, African nations
(10 least corrupt, 1 most corrupt)
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Botswana
Namibia
Tunisia
Rep So Africa
Mauritius
Ghana
Morocco
Ethiopia
Egypt
Senegal
Malawi
6.4
5.7
4.8
4.8
4.5
3.9
3.7
3.5
3.4
3.1
2.9
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Cote d’Ivoire
Tanzania
Zimbabwe
Zambia
Cameroon
Uganda
Kenya
Angola
Madagascar
Nigeria
2.7
2.7
2.7
2.6
2.2
2.1
1.9
1.7
1.7
1.6
Does this suggest corruption
correlates with HIV infection?
• The 3 sub-Saharan African nations with the best
scores all arise from the areas with high HIV
prevalence (Namibia, Botswana, and the Republic of
South Africa)
• Nigeria, with the most corrupt government in Africa,
and one of the most corrupt in the world, is not
impacted as significantly with HIV/AIDS as other
regions of sub-Saharan Africa
• Governmental corruption is not the final answer
(corrupt governments can exercise AIDS prevention)
AIDS 23 years into the outbreak;
why have we not contained this pandemic?
• In particular, what needs modeling today ?
• How do we impact “at risk” behavior
• Correlates of sexual activity
– Initiation
– Partner choice
– Level of sexual behavior
• The real need - interactions between social scientists,
psychologists, physicians, mathematicians
• How do you model nondichotomous variables?
“behavior” “corruption”
Potentiating factors
Migration
Sexually Transmitted
Infections
HIV
C?
No genetic
protection
Uncircumcised
men
Literacy??
Wealth??
Government
corruption
Contaminated needles
in medical settings
Contaminated blood
products
IV Drug Usage
Multiple sex partners
In the end, a behavior and/or
injection is necessary
HIV infection