Table S1: Main Model Parameters.
Model
Parameter
Population Size
(Year 2000)
Symbol¥
_
Population
Growth Rate
_
Calibration
antenatal clinic
population.
Urban: 962168
UN Population
Rural: 4631832
Division [1].
Urban: 4.7%/year
UN Population
Rural: 1.8%/year
Division [1].
Normal(-
Based on a
0.0037653,0.04457)
comparison of HIV
d
(Difference in
prevalence, on
prevalence in DHS
Rural:
and ANC surveillance
Normal(-
estimate. [2]
Year epidemic
prevalence at
Urban
Rural
_
_
_
_
_
_
Data from US Census
T0
Uniform(1980,1990)
Bureau [3] indicate
1983.77 (1980.01-
epidemic established
1986.62)
1982.05 (19801986.74)
0.49 (0.21-0.79)
0.61 (0.2-0.8)
0.63 (0.2-0.8)
0.51 (0.2-0.8)
0.22 (0-1)
0.62 (0-1)
0.1%)
by 1990.
Extent of mixing
Studies suggest weak
between high-
[Mean (Range)]
0.074831,0.02047)
probit scale).
starts (with
Assumptions In Prior
Posterior π
Urban:
between
and general
Prior Distribution*
Notes On

Uniform(0.2,0.8)
risk groups.
assortative mixing. [4,
5]
Extent to which
male determine
the pattern of
sexual
Cannot be directly

Uniform(0.2,0.8)
R
Bernoulli(0.5)
c2
Uniform(0.2,4)
2.08 (0.31-3.99)
1.47 (0.2-4)
c1
Uniform(0.2,4)
1.91 (0.22-3.98)
1.48 (0.2-4)
estimated from data.
partnership
formation.
Replacement (0
for no
replacement; 1
Cannot be directly
estimated from data.
for replacement.)
Mean partner
change rate: men
Mean partner
change rate:
women
Fraction of men
in high risk
1   2,3
groups (groups I
  2,1   2, 2
Uniform(0.05,0.50)
Cannot be directly
estimated from data.
0.42 (0.05-0.5)
0.22 (0.05-0.5)
0.6 (0.2-0.79)
0.46 (0.2-0.8)
0.25 (0.06-0.49)
0.19 (0.05-0.5)
0.46 (0.21-0.8)
0.45 (0.2-0.8)
40.09 (2.2-49.7)
22.92 (2.0249.92)
48.77 (10.69-99.9)
63.07 (10.0199.99)
24.89 (2.17-49.99)
22.84 (2.0249.98)
52.22 (10.09-99.54)
65.98 (10.08100)
0.25 (0.02-0.49)
0.21 (0-0.49)
and II).
Fraction of men
with casual
partners that
have large
 2,1 1   2,3 
numbers of
Uniform(0.20,0.80)
Cannot be directly
estimated from data.
partners (group I
as a fraction of
groups I and II).
Fraction of
women in high
1  1,3
risk groups
 1,1  1, 2
Uniform(0.05,0.50)
Cannot be directly
estimated from data.
(groups I and III).
Fraction of
women with
casual partners
that have large
1,1 1  1,3 
numbers of
Uniform(0.20,0.80)
Cannot be directly
estimated from data.
partners (group I
as a fraction of
groups I and II).
Relative rates of
partner change:
group II versus
 2, 2
Uniform(2,50)
 2,1
Uniform(10,100)
 1, 2
Uniform(2,50)
 1,1
Uniform(10,100)
Cannot be directly
estimated from data.
group III: men.
Relative rates of
partner change:
group I versus
Cannot be directly
estimated from data.
group III: men.
Relative rates of
partner change:
group II versus
Cannot be directly
estimated from data.
group III: women.
Relative rates of
partner change:
group I versus
Cannot be directly
estimated from data.
group III: women.
Fraction of sex
acts in casual
q1
Triangular(0.1,0.50,0.15)
Modal value based on
point estimate of
partnerships
reported partners in
protected by
last year by men,
condom.
2000 DHS [6].
Number of sex
Limits based on
acts in casual
partnerships per
n1
Uniform(10,80)
reports in
observational cohort
year.
in rural Zimbabwe b.
Number of sex
Limits based on
acts in regular
partnerships per
n2
Uniform(50,300)
Chance of HIV
147.27 (52.46-
observational cohort
298.73)
captures influence of
sex act from

Triangular(0.000666,0.00
2,0.001)
(average value
co-factor STIs as well
0.00118 (0.00069-
and other aspects of
0.00192)
risk not explicitly
0.00114
(0.000680.00197)
captured in the model
for men and
[7].
women).
Relative coital
Cannot be directly
frequency for
estimated from data,
those with
but available data do
symptoms of
131.5 (50.03299.81)
This parameter
transmission per
latent infection
reports in
46.23 (10.0879.94)
in rural Zimbabwe b.
year.
individuals with
50.03 (12.45-79.99)
h
Uniform(0.0,0.5)
suggest reduction in
immune
coital frequency for
suppression
those in stable
versus others. c
partnerships. [7]
0.29 (0-0.5)
0.26 (0-0.5)
0.54 (0.32-0.65)
0.49 (0.31-0.66)
Bbased on observed
survival rate in cohort
studies [8, 9]. Overall
survival time is
manipulated by
changing duration of
Rate of
progression of
_
Uniform(0.313,0.655)
latent infection stage
( 1  3 1  4 1  5 )
HIV.
and stated range
corresponds to net
survival with infection
between 8.5 and 12.5
years.
Year behaviour
change starts

Uniform(2000,2004)
Years of surveys
2000.44 (2000-
between which
2003.25)
-π
behaviour changes
observed.
Years until new
value for
behavioural
F
Uniform(1,5)
Vague prior.
2.39 (1.02-4.94)
-π
1.13 (0.54-1.47)
-π
0.64 (0.52-1.06)
-π
0.84 (0.52-1.33)
-π
0.8 (0.8-0.8)
0.36 (0.12-0.78)
parameters
reached
Modal value based on
point estimate of
Relative change
change in fraction of
in condom use in
casual
partnerships
men and women that
3
Triangular(0.5,1.5,1.23)
used condom in last
sex act with non-
(1=stays the
regular partner,
same)
between the 2004
and 2000 DHS [6, 10].
Modal value based on
point estimate of
change in mean
Relative change
in mean partner
2
Triangular(0.5,1.5,0.62)
change rate: men
numbers of partners
reported by women
in the last year,
between the 2004
and 2000 DHS [6, 10].
Modal value based on
point estimate of
Relative change
in mean partner
change rate:
change in mean
1
Triangular(0.5,1.5,1.00)
numbers of partners
reported by women
women
in the last year,
between the 2004
and 2000 DHS [6, 10].
It is estimated that in
2006, coverage of
treatment (=number
on treatment / total
Rate of scale-up
of access to ART
arate
Triangular(0.11,0.80,0.17
in need of treatment)
7)
was 27% (credible
interval 43-89%)
(based on need at
CD4 cell counts below
200 cells per
microlitre) [11]. In the
model, this
corresponds to the
stated scale-up rates
of access to
treatment; the mode
of the prior is the
estimated value, and
the limits are the
bounds of the
credible interval.
Notes to Table 1:
¥Following
notation in Hallett et al., 2009 [12].
*The distribution as parameterised in the following way: Uniform (lower limit, upper limit); Triangular(lower limit, upper
limit, mode); Normal(mean, standard deviation) (If not parameters specified, a fixed value was assumed).
π:Values reported are the model with behaviour change for Urban population and the model without behaviour change for
the Rural populations (in each case, this is the preferred model).
b: To assess the location and potential ranges for some model parameters, point estimates of behavioural indicators were
calculated for various sub-groups in a population-based study in rural Eastern Zimbabwe conducted 1998-2000 [13]. The
population was divided by sex, age (<20; 20-29; 30-39; 40-49), type of location (estate, subsistence farming area, roadside
trading venue or small town) and church (Traditional, Anglican, Roman Catholic or Other). Sub-groups in which the number
of respondents was less than 10 were ignored. The limits of the prior as the 1st and 99th percentiles across these 128 strata.
c: Individuals with symptoms of immune-suppressions include individuals with pre-AIDS or AIDS.
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