Supplementary material 1: Model equations
The Hd and Ng components of the model are identical with each having a SIS structure, i.e.
individuals become infected and once they recover return to the original susceptible class. The
equations for Ng are defined in equation 1 and 2 with xnri denoting those that are susceptible to
Ng and ynri denoting those that are infected with Ng. For these variables and elsewhere, the
superscript 'n' denotes the variable is for Ng ('hd' denotes Hd), first subscript 'r' denotes the sex of
the individual (r=1 for FSWs and r=0 for their clients) and the second subscript 'i' denotes
whether the individual is or will be reached by the intervention. For FSW, i=0 means the FSW
will not be reached, i=1 means they will be reached but have not received their first presumptive
treatment and i=2 means they are currently participating in the intervention. For clients, i is
always zero because they are not targeted by the intervention. The variable pn is only relevant for
FSWs and represents the number of FSWs that have recently received a PPT dose and are still
resistant to re-infection. For all clients and for the FSWs that are not reached by the intervention,
the model equations are:

dx n r 0
yhr0
 N r 0   r  
dt
Nr0

n
dy r 0
 n r x n r 0
dt


yhr0
  n r x n r 0   n r y n r 0    r  
Nr0



yhr0  n
 y r0
  n r y n r 0    r  
N r 0 

 n
 x r 0

Equation 1,
where n r is the force of infection for Ng to sex r (see equation 3),  r is the rate at which clients
(r=0) or FSWs (r=1) stop buying or selling sex,  n r is the rate at which clients or FSWs recover
from Ng (including local treatment),  is the mortality rate amongst the proportion of
individuals in each group that have chronic HIV, Nr0 is the number of individuals in sex r and PPT
intervention state i ( N r 0  xrn0  y rn0 ), and yrih is the number of clients or FSWs that are in
intervention state i (see above - i=0 means not reached by intervention) that are in the low
viraemia phase of HIV. For FSWs reached by the intervention, the model equations are:

dx n 11
y h 11
  N 11  N 12  1  
dt
N 11  N 12

dy n 11
 n 1 x n 11   n 1 y n 11  y n 11
dt


y h 11
  n 1 x n 11   n 1 y n 11  x n 11   1  
N 11  N 12



 n
y h 11
 y 11
  1  
N 11  N 12 

 n
 x 11


 n
dp n
y h 11
p
  x n 11  y n 11   n p n   x n 12  y n 12   1  
dt
N 11  N 12 


 n
dx n 12
y h 11
 x 12
 n 1 x n 12   n 1 y n 12  x n 12   n p n   1  
dt
N 11  N 12 






dy n 12
y h 11
 n 1 x n 12   n 1 y n 12  y n 12   1  
dt
N 11  N 12

 n
 y 12

Equation 2,
where  is the rate at which the reached FSWs are recruited on to the PPT intervention,  n is the
rate at which individuals lose protection to re-infection from Ng following PPT,  is the rate at
which FSWs receive their next PPT dose, and N11 and N12 are the number of FSWs in PPT
n
n
n
n
intervention state i=1 or i=2 ( N11  x11
and N12  x12
 y12
 p n ). The force of infection
 y11
( n r ) is estimated as:

n
0
  y n10  y n11  y n12  n

  1 1  ef 
 1  1  

N1

 


n1  1  1 

n
y 00 n
 0 1  ef
N0


n0
and
Equation 3,
n1

where  n r is the per act transmission probability for Ng from an infected individual of sex r, and
Nr is the number of clients (r=0) or FSWs (r=1). The Hd model is identical to the Ng model.
The Ct model has a type of SIR structure, with a proportion of infected individuals recovering
into a resistant class that has a lower risk of re-infection, and once re-infected enter a different
infection class that returns back to the resistant class when the infection is resolved. The model is
defined in equations 4 and 5 with xcri, ycri and pc being as for the Hd/Ng model, but now for Ct,
and xrcri, yrcri and prc denoting the number of individuals that have partial resistance to Ct reinfection and are either currently uninfected, infected or have recently taken a PPT dose,
respectively. The subscripts r and i are defined as before, and the equations are as follows for all
clients and for FSWs that are not reached by the intervention:

y h r0
dx c r 0
 N r 0   r  
dt
N r0



y h r0
  c r x c r 0   c r 1    y c r 0    r  
N r0


c
h

dy r 0
y r0  c
 y r0
 c r x c r 0   c r y c r 0    r  
dt
N r 0 


y h r0  c
dxr c r 0
c r c
 xr r 0

xr r 0   c r y c r 0  yr c r 0     r  
dt

N r 0 


dyr c r 0 c r
y h r0

xr c r 0   c r yr c r 0    r  
dt

N r0

 c
 x r 0

Equation 4,
 c
 yr r 0

with all parameters defined as before except for Ct if there is a superscript 'c',  which is the
proportion of individuals that become partially resistant to Ct re-infection once recovered from
infection, and  which is the factor decrease in the Ct force of infection for individuals that are
partially resistant to re-infection. For FSWs reached by the intervention, the model equations are:

y h 11
dx c 11
  1  N 11  N 12   c 1 x c 11   c 1 1    y c 11  x c 11    1  
dt
N 11  N 12


 c
dy c 11
y h 11
 y 11
 c 1 x c 11   c 1 y c 11  y c 11    1  
dt
N

N
11
12 


y h 11
dxr c 11
c 1 c

xr 11   c 1 y c 11  yr c 11  xr c 11    1  
dt

N 11  N 12


 c
dyr c 11 c 1
y h 11
 yr 11

xr c 11   c 1 yr c 11  yr c 11    1  
dt

N

N
11
12 



 c
 xr 11


dp c
y h 11
  x c 11  1    y c 11  p   x c 12  1    y c 12    1  
dt
N 11  N 12


 c
y h 11
dx c 12
 x 12
 c 1 x c 12   c 1 1    y c 12  x c 12  p c    1  
dt
N

N
11
12 





 c
 x 11

 c
 p


dy c 12
y h 11
 c 1 x c 12   c 1 y c 12  y c 12    1  
dt
N 11  N 12

dxr c 12
dt
dyr c 12
dt
 c
 y 12

c

y h 11
1 c

xr 12   c 1 y c 12  yr c 12  xr c 12  pr c    1  

N 11  N 12


 c
y h 11
c 1 c
 yr 12

xr 12   c 1 yr c 12  yr c 12    1  

N

N
11
12 



 c
 xr 12


dpr c
y h 11
  xr c 11  yr c 11  y c 11  pr   xr c 12  yr c 12  y c 12    1  
dt
N 11  N 12





 c
 pr

Equation 5
with all parameters defined as before except for Ct if there is a 'c' superscript, and the force of
infection estimated as follows:

c

c
0
  y c 10  y c 11  y c 12  yr c 10  yr c 11  yr c 12
 1  1  
N1
 
1


y c 00  yr c 00 c
 1  1 
 0 1  ef 
N0


n0

 c
  1 1  ef  and



Equation 6
n1
where  c r is now the per act transmission probability for Ct from an infected individual of sex r.
The HIV model is defined in equations 7 and 8 with the state variables xhri, hhri and yhri denoting
the number of individuals susceptible, acutely HIV infected, and chronically HIV infected,
respectively and the subscript r denoting the sex and i=0 denoting those not in contact with the
PPT intervention and i=1 denoting those reached by the PPT intervention. For all clients and for
the FSWs that are not reached by the intervention, the model equations are:
dx h r 0
  r N r 0  y h r 0  h r 0 x h r 0   r x h r 0
dt
dh h r 0
 h r 0 x r 0     r h h r 0
dt
dy h r 0
 h h r 0     r  y h r 0
dt
Equation 7,
where hri is the HIV force of infection from FSWs (r=1) or clients (r=0) in intervention class i.
For FSWs reached by the intervention, the model equations are:
dx h11
 1  N11  N12   y h11  h11 x h11  1 x h11
dt
dh h11
 h11 x11    1 h h11
dt
dy h11
 h h11    1  y h11
dt
Equation 8
Where the parameters are defined as before and the force of infection hri is estmated as follows
for the model that includes just Ct and Ng:



1h 1  ef 

 1  ef 

N0
h 00  1  1 
h1i  1  1 
N1
h
0
 y
h
1i
all i
y
h
00
n0

 h1hi Y n i 1  Y c i n  Y n i Y c i n  c  Y c i 1  Y n i c  1  Y n i 1  Y c i  and


 









h
 h00
Y n i 1  Y c i n  Y n i Y c i n  c  Y c i 1  Y n i c  1  Y n i 1  Y c i 

 








n1
Equation 9
where Yni and Yci are the probabilities that either the male client or their FSW partner in
intervention category i has Ng (n superscript) or Ct (c superscript), and n and c are the
respective Ng and Ct cofactors for increasing HIV transmission. The Hd cofactor hd is included
in the same way by adding all Hd, Ng and Ct co-infection combinations.
Supplementary material 2: Model fitting methods.
The model was first fit to HIV/STI prevalence data from Johannesburg and then to the other
settings. The fitting process involved different steps. Firstly, the model was fit to Ng data from
before and after the PPT intervention in Johannesburg[1] by varying the Ng biological
parameters, and the number of FSWs seen per client per month. Following this, the model was fit
to Ct data by varying its biological parameters. There was no Hd prevalence data in
Johannesburg, and so the model did not simulate it in this setting. Lastly, to fit the model to the
HIV prevalence amongst FSWs and clients (approximated by male STI clinic client data) in
Johannesburg, the HIV transmission probability per sex act for males-to-females and vice versa
were increased from 0.002 and 0.001 respectively until a fit was obtained. This was done to take
into account the effect of other STIs not included in the model while assuming that Ct and Ng
increased HIV susceptibility/infectivity by a factor of 2 and 3 respectively[2].
To fit the model to HIV/STI data from the other settings, behavioural and epidemiological inputs
from that setting were used, whereas most biological parameters were kept fixed to the values
used for Johannesburg. The only exceptions to this were the duration of Ng/Ct infection, which
were allowed to vary between settings because of differences in the underlying level of STI
treatment, and the HIV transmission probabilities which were allowed to vary by +/-50% of the
values used in Johannesburg because of its large variability in different settings/populations[3]
and its likely dependence on the prevalence of other STIs. In addition, the female-to-male HIV
transmission probability in Cotonou was decreased by 60% because of the high prevalence of
circumcision in Cotonou[4]. Hd was only modelled in Free State because the other settings had
low or undocumented Hd prevalences.
In general, the fitting procedures used for each setting were similar to those used for
Johannesburg. However, the impact of other intervention activities had to be included for Free
State and Cotonou. In Free State, condom use amongst high-risk women increased from 3% to
~30% over the first 9 months of the intervention, whereas in Cotonou condom use increased after
the start of the SIDA intervention from 68% of last sex acts in 1993 to 79.5% in 1998[5].
References
1.
2.
3.
4.
5.
World Health Organisation. Periodic presumptive treatment fr sexually
transmitted infections - programmatic and research guidelines. Geneva; 2006.
Rottingen J, Cameron DW, Garnett GP. A systematic review of the epidemiologic
interactions between classic sexually transmitted diseases and HIV. Sexually
Transmitted Diseases 2001, 28:579-595.
Boily MC, Baggaley RF, Wang L, Masse B, White R, Hayes R, et al.
Heterosexual risk of HIV-1 infection per sexual act: a systematic review and
meta-analysis of observational studies. Lancet Infectious Diseases 2009, 9:118129.
Vickerman P, Watts CH, Delany S, Alary M, Rees H, Heise L. The importance of
context: model projections on how microbicide impact could be affected by the
underlying epidemiological and behavioural situation in two African settings. Sex
Transm Dis 2006, 33:397-405.
Alary M, Mukenge Tshibaka L, Bernier F, Geraldo N, Lowndes CM, Meda H, et
al. Decline in the prevalence of HIV and sexually transmitted diseases among
female sex workers in Cotonou, Benin, 1993-1999. AIDS 2002, 16:463-470.
Supplementary material 3: Percentage deviation in Johannesburg PPT impact projections (after 2 years) at different coverage levels and
frequencies of PPT for +/-10% change in model parameters. Figure only shows those parameters that resulted in less than 5% deviation in impact
projections.
% deviation in Ng prevalence impact projection
relative to baseline projections
a. % deviation from baseline Ng prevalence impact projection
5%
4%
3%
2%
1%
0%
-1%
-2%
-3%
-4%
-5%
+10%
-10%
% become ‘resistant’
after Ct
+10%
-10%
Degree of protection
when 'resistant'
+10%
-10%
Duration of
azithromycin effect
STI parameters
Coverage=10%, 0.5 per month
Coverage=20%, 0.5 per month
+10%
-10%
HIV acute phase
cofactor
+10%
-10%
+10%
-10%
+10%
-10%
Duration of HIV acute Duration men buy sex Duration of sex work
phase
HIV parameters
Coverage=20%, 1 per month
Risk behaviour parameters
Coverage=40%, 1 per month
Coverage=80%, 1 per month
% deviation in Ct prevalence impact projection
relative to baseline projections
b. % deviation from baseline Ct prevalence impact projection
5%
4%
3%
2%
1%
0%
-1%
-2%
-3%
-4%
-5%
+10%
-10%
% become ‘resistant’
after Ct
+10%
-10%
Degree of protection
when 'resistant'
+10%
-10%
Duration of
azithromycin effect
STI parameters
Coverage=10%, 0.5 per month
Coverage=20%, 0.5 per month
+10%
-10%
HIV acute phase
cofactor
+10%
-10%
+10%
-10%
+10%
-10%
Duration of HIV acute Duration men buy sex Duration of sex work
phase
HIV parameters
Coverage=20%, 1 per month
Risk behaviour parameters
Coverage=40%, 1 per month
Coverage=80%, 1 per month
% deviation in HIV incidence impact projection
relative to baseline projections
c. % deviation from baseline HIV incidence impact projection
5%
4%
3%
2%
1%
0%
-1%
-2%
-3%
-4%
-5%
+10%
-10%
% become ‘resistant’
after Ct
+10%
-10%
Degree of protection
when 'resistant'
+10%
Duration of
azithromycin effect
STI parameters
Coverage=10%, 0.5 per month
-10%
Coverage=20%, 0.5 per month
+10%
-10%
HIV acute phase
cofactor
+10%
-10%
+10%
-10%
+10%
-10%
Duration of HIV acute Duration men buy sex Duration of sex work
phase
HIV parameters
Coverage=20%, 1 per month
Risk behaviour parameters
Coverage=40%, 1 per month
Coverage=80%, 1 per month
Supplementary material 4: Comparison of the Cotonou, Laos and Free State model fits with
epidemiological data. For Cotonou and Free State the projected Ng and Ct trends are for those
FSWs reached by the PPT intervention whereas they are for all SWs for Laos. The black dashed
vertical lines show when the interventions in these settings stopped, although the interventions are
assumed to continue in these projections.
a. Cotonou, Benin
60%
HIV or STI prevalence (%)
50%
40%
30%
20%
10%
0%
-15
-10
-5
0
5
Time pre and post PPT intervention in years
Data estimates Model projections -
b. Laos
FSW HIV
CL HIV
FSW Ng
FSW Ct
FSW HIV
CL HIV
PPT FSWs Ng
PPT FSWs Ct
30%
HIV or STI prevalence (%)
25%
20%
15%
10%
5%
0%
-1
0
1
2
Time pre and post PPT intervention in years
Data estimates Model projections -
FSW HIV
CL HIV
FSW Ng
CL Ng
FSW Ct
CL Ct
FSW HIV
CL HIV
FSW Ng
CL Ng
FSW Ct
CL Ct
c. Free State, South Africa
25%
STI prevalence (%)
20%
15%
10%
5%
0%
-1
0
1
2
Time pre and post PPT intervention in years
Data estimates Model projections -
Women Ng
Miner Ng
Women Ct
Miner Ct
Women Hd
Miner Hd
Women Ng
Miner Ng
Women Ct
Miner Ct
Women Hd
Miner Hd