Modelling changes in HIV prevalence
among women attending antenatal
clinics in Uganda
Brian Williams
Behaviour change in Uganda
20
Prevalence (%)
ANC women
15
10
5
0
1970
1990
2010
2030
N
S
 SI /N
mS
I
I
mI
 = birth rate
N =S+I
 = rate at which new infections occur
 = mortality
The basic model
Prevalence (%)
100
80
R0 -1
= 70%
R0
60
40
R0 = 3.3
20
0
1970
1990
2010
10
9
8
7
6
5
4
3
2
1
0
2030
Incidence/Mortality (%/yr)
ANC women in Uganda
N
S
 SI /N
I
I
I
mS
1.0
Normal (Weibull 2)
 = birth rate
N =S+I
 = infection rate
I = Weibull mortality
P(surviving)
0.8
0.6
Exponential
(Weibull 1)
0.4
0.2
0.0
0
10
20
Time (years)
30
80
12
Prevalence (%)
10
60
8
40
6
4
20
2
0
1970
1990
2010
0
2030
Incidence/Mortality (%/yr)
ANC women in Uganda
~
N
S
SI /N
I
mI
~
N = population
 =
e–P
I = Weibull mort.
Relative transmission .
mS
 = birth rate
I
1.0
0.8
e–P
0.6
0.4
0.2
0.0
0
10
20
Prevalence (%)
Heterogeneity in sexual behaviour
30
Prevalence (%)
15
2
10
1
5
0
1970
1990
2010
0
2030
Incidence/Mortality (%/yr)
ANC women in Uganda
~
N
~
S
SI /N
I
I
~
N
~

= birth rate
= population
= C(t)
I = mortality
Relative transmission .
mS

I
1.0
C(t)
0.8
0.6
0.4
0.2
0.0
1985
Including control
1990
1995
Year
2000
Prevalence (%)
15
2
10
1
5
0
1970
1990
2010
0
2030
Incidence/Mortality (%/yr)
ANC women in Uganda
~
N
S
*
SI /N
I
I
~
N
*
= birth rate
= population
= e –M
I = mortality
Relative transmission .
mS

I
e –M
1.0
0.8
0.6
0.4
0.2
0.0
0
2
Annual mortality (%)
4
Mortality leads to behaviour change
Prevalence (%)
15
2
10
1
5
0
1970
1990
2010
0
2030
Incidence/Mortality (%/yr)
ANC women in Uganda
Nairobi
6 yr
Nunn P et al. Tuberculosis control in the era of HIV. Nat Rev Immunol. 2005 Oct;5(10):819-26.
Annual incidence (%) .
10
HIV-
9.4
HIV+
8
5.9
6
4
2
2.2
1.0
1.1
1.1
0
1991-1994
1995-1997
1998-1999
TB incidence among gold miners in SA
Corbett EL Stable incidence rates of tuberculosis (TB) among human immunodeficiency virus (HIV)-negative South African gold miners during a decade of
epidemic HIV-associated TB. J Infect Dis. 2003;188: 1156-63.
Prevalence
(%)
HIV+ 0.44 (0.02-1.05)
HIV- 0.55 (0.14–0.95)
SS+ Tuberculosis
Incidence
Disease Duration
(%/yr)
(yr)
2.87 (1.94-4.25)
0.15 (0.05-0.48)
0.48 (0.27-0.84)
1.15 (0.48-1.13)
DDR = 0.13 (0.09–0.20)
Gold miners in South Africa
We define disease duration as prevalence divided by incidence
TB-HIV model
Repeat the model 4
times, once for each
stage of HIV. Use time
series of HIV prevalence
to determine incidence.
Incidence gives rate at
which people enter first
stage; overall (Weibull)
survival determines rate
at which people move to
next stage.
Williams BG et al. The impact of HIV/AIDS on the control of tuberculosis in India. PNAS 2005 102: 9619-9624.
Impact of interventions on TB cases in Kenya
800
.
Baseline
TB incidence/100k/yr
ARV 80%
TLTI (6 m)
600
TLTI (life)
ARV 100%
400
TB detect.
TB cure
HIV incid
200
0
1980
2000
2020
Year
2040
Base line:
CDR = 50%
CR = 70%
Interventions:
1% increase
Currie, C. et al. Cost, affordability and cost-effectiveness of strategies to control tuberculosis in countries with high HIV prevalence. BMC, 2005. 5: 130.
Percent
HIV negative
Percent
HIV positive
Williams BG et al. HIV Infection, Antiretroviral Therapy, and CD4+ Cell Count Distributions in African
Populations. J Infect Dis, 2006 194: 1450-8.
Initial CD4/mL
2,000
Model 1

CD4 decline independent of
starting value
1,000
Survival determined by preinfection CD4
20
Initial CD4/mL
10
2,000
Time to death (yrs)
Model 2

Survival independent of starting
value
1,000
CD4 decline determine entirely
by starting value and survival
distribution
10
20
Time to death (yrs)
Spatial Epidemiology of HIV
Doubling time = 1 year
Life expectancy = 10 years
Number of partners = 4
Proportion of random partners chosen
at random = 0 (left hand set) or 10%
(right hand set) in the following slides.
Note that in this model migrants have
exactly the same sexual behaviour and
individual risk as non-migrants.
Questions for all of us
1. Can we combine spatial/network models
with our more conventional continuous
time models of HIV?
2. Can we get a better understanding of the
host-viral interaction?
3. What are the population level implications
of 2?
4. Do we have enough data to explore fully
the joint dynamics of TB and HIV?
Advice to young epidemiologists
Never make a calculation until you know the
answer. Make an estimate before every calculation,
try a simple biological argument (R0, generation
time, selection, survival, control). Guess the answer
to every puzzle. Courage: no one else needs to
know what the guess is. Therefore, make it quickly,
by instinct. A right guess reinforces this instinct. A
wrong guess brings the refreshment of surprise. In
either case, life as an epidemiologist, however long,
is more fun.
Plagiarised from E.F. Taylor and J.A. Wheeler Space-time Physics 1963