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ASSA AIDS and Demographic Models
USER GUIDE
Prepared by Debbie Budlender and Rob Dorrington of the Centre for
Actuarial Research, University of Cape Town, for the AIDS
Committee of the Actuarial Society of South Africa
This guide begins with an overview of modelling of the
HIV/AIDS epidemic in South Africa, which is presented in
section 2. Section 3 provides information on the structure
of the model. It comprises a brief description of the nature
and basis of the assumptions, the location of different
aspects of the model on the worksheets, and information
about which assumptions and values can be changed by the
user. Sections 4, 5 and 6 provide instructions on how to use
the model. Section 4 describes how to do simple runs so as
to get projections for different years. Section 5 describes
the standard output, how to interpret it, and how to obtain
additional output. Section 6 provides a brief overview of
the provincial
and urban-rural versions of the model. Finally, section 7 provides
information for the more advanced user who wants to change
parameters. This section includes a discussion of the
calibration that is necessary when making such changes.
As, structurally, the different versions of the model
are all based on the lite version this manual
describes, in the main, the
lite
version of the model. However, where appropriate, details of
to other versions of the model are discussed.
In addition there are several appendices. Appendix A details
the system requirements for running the model. Appendix B
lists all the worksheets in the main workbook of the
full
and lite versions and explains where to find particular values. Appendix
C lists all the worksheets in the workbook which pastes the
set-up assumptions into the full model to create the
provincial models and explains where to find particular
values. Appendix D is a summary list of all the worksheets,
specifying the name and nature of the worksheet, whether it
contains values that can be changed by users, and whether
its contents change when running the projection engine.
Appendix E lists all the acronyms used in the text of this
user guide.
Those seeking more information about the rationale and
evidence underlying the assumptions and methods used are
referred to a forthcoming monograph on what can be described
as the “metadata” underlying the model(s).
While reading the guide, it is useful to have the workbook
that makes up the model to hand as there are repeated
references to different parts and features of the workbook
in the text.
Although some actuarial or demographic background will be
helpful in understanding the intricacies of the model’s
construction, the model is designed to be useful to
actuaries and non-actuaries alike. Users who have no need to
make changes to the model and its assumptions, for example
those who only want to use the output, may want to skip the
detail in sections 3 and 5. Users who want to change the
assumptions underlying the model must, however, read through
this detail as their changes may otherwise have unintended
effects.
The guide assumes a basic proficiency in using Microsoft
Excel. In particular, it assumes familiarity with naming
conventions for rows and columns, understanding of concepts
such as cells, range names, and macros, and an understanding
of the difference between cells containing ordinary data and
those containing formulae.
Modelling of the AIDS epidemic in
South Africa by actuaries began with the so-called Doyle or
Metropolitan Life model, which was developed in 1989. The
model was based on a population hypothetically divided into
four groups that differed in terms of the relative ease with
which individuals belonging to each group were expected to
contract and transmit the HIV.
The code for the Metropolitan model
is proprietary. The Actuarial Society of South Africa (ASSA)
felt that it was desirable for people to have access to a
non-proprietary programme which users could alter to suit
their needs. In 1996, ASSA therefore released the ASSA500
model. This was very similar in structure to the
Metropolitan model with some simplifications to ease
programming and comprehension and to shorten run times. The
model was primarily designed to make users aware of the
likely impacts of the epidemic on mortality and morbidity.
In 1998, the AIDS Committee of ASSA
decided to develop the model further. There were several
reasons for this:
§
The ASSA500 model represented the epidemic in the black
African population, rather than the population as a whole;
§
There were concerns about the accuracy of the preliminary
results of the 1996 census and there was a need for national
estimates that attempted to correct for suspected
deficiencies;
§
Many South African demographers were continuing to ignore the
impact of AIDS in their projections of the South African
population;
§
The ASSA500 model had inherited a number of demographic
shortcomings from the Metropolitan model, particularly the
assumptions of constant fertility, non-HIV mortality over
time and the assumption of no international migration.
The result was an Excel 95 workbook
called ASSA600, released to the public in early 1999. The
model was designed to be appropriate for use as a national
population model for the Pattern II (heterosexual) HIV
epidemic found in South Africa. The base model contained a
scenario that reflected its builders’ best estimates of
values for the model parameters and was calibrated to fit
the antenatal data up to 1997. The naming convention was
also changed to allow the user to modify the parameter
values, for example for sensitivity analysis and scenario
planning. The idea was that alternative version of the model
could then be saved as ASSA601, 602, etc.
In 2000, the AIDS Committee felt
that a further revision of the model was necessary. The
update was needed because of increased knowledge about the
epidemic, the availability of new data against which to
calibrate the model, and greater awareness of the uses to
which the model was being put. It was also decided to change
the naming convention to reflect the year of the latest
antenatal data used to calibrate the model.
The resultant ASSA2000 model incorporated the following
adjustments reflecting new or updated information about the
epidemic:
Ø
1988-2000 antenatal clinic (ANC) summary results;
Ø
1998 South Africa Demographic and Health Survey (SADHS) data,
in particular, data on prevalence of STDs and condom usage;
Ø
improved estimates of the population; and
Ø
mortality data on the pattern and level of deaths that
suggested, in particular, that non-HIV mortality for adults
has not improved over time as expected.
In addition, the model was altered to:
Ø
improve the fit to ANC survey data;
Ø
allow for the possibility of making separate male and female
assumptions;
Ø
model the population groups separately;
Ø
limit the trend in mortality and fertility rates over time;
Ø
limit future in-migration;
Ø
change the HIV survival curve to be a function of a Weibull
distribution;
Ø
allow for a bimodal distribution of paediatric HIV survival;
and
Ø
disaggregate the ‘contagion matrix’ (used in ASSA600) into
more measurable and controllable parameters of heterosexual
behaviour. These include the probability that a partner
comes from a particular risk group, the number of new
partners per annum, the number of sexual contacts per
partner, the age of the partner and the probability a condom
is used.
The ASSA2000 model has been
produced as a suite of several versions. The lite
version, like the ASSA600 model before it, treats the
population of the country as one population. The full version models each of the four
population groups (Asian/Indian, black African, coloured and
white) separately at a national level, and aggregates to
produce results for the population as a whole. The provincial version is the result of
the aggregation of the application of the full
version of the model separately to each of the provinces. It
thus allows for geographic differences in the spread of the
epidemic. The ASSA AIDS Committee initially delayed the
release of the provincial
version pending the lifting of an embargo by the Department of
Health on the release (to the Committee) of the more
detailed results of the provincial antenatal surveys for
2000. When, after many months, the Department seemed no
nearer releasing the results, despite having agreed to
supply them to the Committee, the Committee decided that the
demand for the provincial
version necessitated that it be released despite the lack of
cooperation from the Department. The urban-rural version allows for
situations where there is significant migration between two
groups with significantly different prevalence levels (e.g.
urban and rural areas in some countries) in the population.
This version is currently under development but will be
released in the coming months.
This user’s guide is intended for
use with all four models. The differences between the lite and full versions will be noted in
the text at relevant places. The approaches in the provincial and urban-rural
versions are described in section 6. A fuller description of
the urban-rural version as well as a note on how to go about fitting
the model to a new country will be made available at the
time of release.
As the course of the disease
progresses and more information about it becomes available,
the model structure and base scenario will be further
updated and future versions of the model will be released.
Any feedback on the model in the
form of comments and criticisms would be appreciated and can
be sent to
aids@assa.org.za.
The model is distributed as a
flexible tool to allow researches to make their own
predictions and projections about the HIV/AIDS epidemic. No
level of accuracy is implied, nor can the Actuarial Society
of South Africa accept any responsibility for the way in
which individuals use the model or the results they obtain
from it. The model is offered free via the Internet as a
public service to anyone who has a use for it.
The ASSA2000 model as disseminated has been calibrated
to reproduce the patterns of past antenatal clinic survey
data and the number of adult deaths. As such, the model
represents the triangulation of data from the population
census, antenatal survey and registered deaths by some of
the country’s top actuaries, demographers and
epidemiologists. It is not recommended that users alter the
assumptions in the model in any way unless they have a very
good reason for doing so. If any of the assumptions are
altered in any way, the user must ensure that the model is
recalibrated to ensure that it remains consistent with the
recorded experience to date. Users who have any questions in
this regard can consult with the ASSA AIDS Committee (aids@assa.org.za).
Other sections of this guide note where the user can
change particular parameters on the worksheets to reflect a
change in assumptions. The following points should be
observed when making such changes.
One of the features of the ASSA2000 model is the large
degree of interdependence of different parameters and
assumptions. A change in one will often necessitate a change
in others. There are two broad categories of second-level
changes.
§
In some cases the first change of value will result in another change
‘automatically’, in that other values are dependent, through
a formula of the worksheet, or a macro procedure, on the
changed value. This happens, for example, where proportions
must sum to 100%. In these cases, the user does not need to
take any action. However, users should note that the
‘automatic’ changes will only take effect when the user
presses the F9 (CALC) key or runs a projection. The
automatic CALC function defaults to OFF in the ASSA2000
model to speed up the projection process.
§
In other cases the changed parameter will require a manual change to
other parameters and assumptions so as to achieve a fit with
the observed values of the ANC surveys, both overall and by
age, and the national mortality rates by age. This process
of manual changing of parameters to counterbalance previous
changes is what we refer to as ‘calibration’.
Users must be aware of the nature of the information
they are changing. Some of the parameters in the ASSA2000
workbook reflect assumptions or observed data such as
numbers in the population. These are entered as ordinary
numbers on the worksheet. Many other parameters are based on
formulae that draw on values in other cells or cell ranges
in the workbook. The contents of these cells must not be
replaced by numbers. As with ordinary Excel usage, the user
can see in the status bar whether a particular cell is the
result of a formula or range name reference. In some cases,
however, a cell will appear to contain an ‘ordinary’ number
that does not involve a reference or formula but will, in
fact, be a record of the previous year’s numbers used to
project the current year’s numbers. This is the case, for
example, with all the tables labelled as ‘before’.
In changing values on the worksheets, users must be
aware of the very different implications of changing a cell
containing a simple value and changing a cell containing a
formula or reference or a number generated in previous
projections. The
Assumptions
worksheet provides some guidance as to which values could be
changed in that calculated values are in black, while
assumptions that affect projection – and could thus
potentially be changed – are in red.
In the past, incorrect results have been attributed to
the Actuarial Society of South Africa or the models in
public documents and in the press. In order to prevent this
from happening in future, we ask that all users adhere to
the following guidelines.
§
If the results have been generated using the models without any
alternation, the user should reference them as “results
extracted from the ASSA2000 (lite if
lite
version used) AIDS and Demographic model of the Actuarial
Society of South Africa as downloaded [date] from [site
address]”.
§
If the model has been adjusted and recalibrated, the user must, in
addition to the full reference to the model, explain exactly
how and why it was adjusted. The user must also make it
clear that the resulting estimates are not those produced by
the Actuarial Society of South Africa. This must be done in
such a way that anyone reading the report is clear that the
user’s results do not represent the views of the Society.
Ideally, it should also be done in such a way that another
user can replicate the changes and check the projections.
The ASSA model projects
year-by-year changes in an initial population profile over a
period of years chosen by the user. It does so on the basis
of a number of demographic, epidemiological and behavioural
assumptions. This section of the guide provides a brief
description of the model, its key parameters and
assumptions. Any user who wants to change any of the
parameters must read this section so as to understand the
impact of any proposed changes.
The model projects on a
year-by-year basis, with each year’s projections reflecting
changes between 1 July of one calendar year and 30 June of
the following calendar year. For the sake of simplicity,
each year is referred to by a single calendar year rather
than by both of the calendar years. The ‘stock’ numbers for
each year reflect the position as at the middle of the
respective year, while the ‘flow’ numbers reflect the change
from the middle of that year to the middle of the following
year.
The model splits the population by
sex and also into three distinct age groupings: young (up to
age 13), adult (14-59) and old (60 and above). The full
version of the model also splits the population by population
group. The adult group is divided into four risk groups,
which are differentiated by their level of exposure to the
risk of contracting the HI virus through heterosexual
activity. These risk groups are:
PRO
Individuals whose level of sexual activity is such that
it is similar to that of commercial sex workers, and the
level of condom usage and infection with STDs is similar to
that of the STD group.
STD
Individuals whose level of sexual activity is such that
their HIV prevalence is similar to someone regularly
infected with STDs.
RSK
Individuals with a lower level of sexual activity, but
who are still at risk from HIV in that they have, on
average, one new partner per annum and sometimes engage in
unprotected sex.
NOT
Individuals who are not at risk of HIV infection.
By definition, someone from the RSK group will not have sex
with someone from the PRO group. Further, those in the NOT
group have sex only with others in that group or, if they
have sex with individuals from other groups, always take
effective precautions.
The numbers in these risk groups are determined initially
according to the proportions appearing on the Assumptions
sheet. These proportions are applied to all adult ages
equally. The assumptions have been determined, where
possible, on the basis of empirical evidence. Where this was
not possible, either educated guesses were made or the
assumptions were determined so that modelled results fit
observed data such as the antenatal prevalence figures for
past years. The latter method of determining values is part
of the ‘calibration’ process discussed later.
The age and risk classifications divide the population
into the following groups, with each group’s calculation
done on a separate worksheet within the workbook. In the full version of the model, there is a set of these worksheets for
each population group. In the aggregate of the provinces,
there is a workbook for each province and a set of
worksheets for each population group within each province:
Young:
All individuals aged 0 to 13. The only infections
assumed are those arising at birth or from breastfeeding. On
their 14th birthday, individuals are allocated to the risk
groups according to the assumed proportions on the Assumptions
sheet. The model assumes that a proportion of those born to
HIV+ mothers are HIV+ at birth. Further, the model assumes
that a further proportion of non-HIV babies contract the
virus from their HIV+ mothers through breast-feeding. It is
assumed that none of the babies with perinatal infection
survive to age 14 and that there are no other sources of
infection before this age. The Young age group is shaded
yellow on the worksheets.
FemPRO:
Female members of the PRO risk group up to age 59,
subdivided by duration since infection.
FemSTD:
Female members of the STD risk group up to age 59,
subdivided by duration since infection
FemRSK:
Female members of the RSK risk group up to age 59,
subdivided by duration since infection
FemNOT:
Female members of the NOT group up to age 59
FemOLD:
On their 60th birthdays all individuals are allocated
to the OLD class. The duration since infection
classification still applies, but no further infections or
fertility occur beyond this age. The OLD worksheets are a
run-off of the population. No one is assumed to survive
beyond age 90. The OLD group is shaded in grey on the
worksheets.
Male***:
The same structure as the Fem*** worksheets but with no
births.
The total population is allocated between male and female
and over the age range according to the distributions given
in the Population
worksheet. While it is possible to measure, to some extent,
the size of the STD group and, to a lesser extent, the PRO
group, the RSK and hence NOT groups are hypothetical
constructs whose size is set to reproduce past patterns of
prevalence through the calibration process.
Diagram 1 displays how individuals move from state to state
under the action of the model. Certain transitions are
assumed to be impossible e.g. moving from HIV+ to HIV-; and
becoming infected after age 60. The model allows for the
inclusion of migrants in all risk groups and at all ages.
Migrants are assumed to have the same duration since
infection profile and prevalence rate as non-migrants of the
equivalent risk group.
The heterosexual interaction and hence spreading of the
virus is modelled taking into account the following, given
the person is from a particular risk group: the chance that the partner is from a particular risk group, the number
of new partners per year, the number of contacts per partner
and the probability of transmission if no condom used (given
the risk group of the partner), and the probability that a
condom was used.
The number of new partners per year and the number of
contacts per partner for females at a particular age are a
function of a ‘sexual activity’ curve. This curve was chosen
such that the pattern of HIV infections of pregnant women
assumed by the model to be attending antenatal clinics is
more or less the same as the results of the ANC surveys.
Infection is introduced into the
PRO risk group via 300 male and 300 female infected
‘imports’ in the lite model. Smaller numbers are used for each of the population
groups in the full version of the model to allow for
both the smaller size of the populations as well as possible
lags in the start of the epidemic. These imports are not
added to the population, but rather used to create HIV
prevalence of partners in the initial years and hence start
the epidemic. The number of imported HIV need not be a whole
number or even greater than one. This feature allows the
model to cater for situations where the starting date of the
epidemic is before or after 1985, by simply changing the
size of this number.
The epidemic spreads through the
population at risk by assumed infection of non-infected
individuals within and between groups. The rate of spread of
the infection is controlled by assumptions about two key
factors, namely the amount of
sexual activity, and a range of factors determining the probability of infection.
The distribution of female sexual
activity by age is represented in the model by the sexual
activity curve, which is found on the SexActivity sheet. The curve involves
an assumption about the relative sexual activity by age for
females. The curve is bell-shaped with the following form:
where
a
(the position factor) is determined by the average age of
first sexual intercourse
b (the shape factor) is set, in part, to reproduce the shape
of prevalence by age from the antenatal results as well as
the age distribution of AIDS cases and AIDS deaths
c (the scale factor) is set so that the average of S is 1.
The activity of males is a function of that of females and
the age of their partners.
By varying the shape of the curve, the distribution of the
new HIV infections by age is adjusted (separately for
different population groups and province in the two other
models). The user can manipulate both a
(position) and b (shape) factors, but must run the ‘Goal seek’ macro after any changes
to restandardise the curves i.e. reset the scale factor. The
macro is run by clicking the ‘Goal seek’ button on the chart
on the SexActivity worksheet. The shape and position factors are
recorded at the top of the leftmost table on the worksheet,
in column C.
The default values for a and b for the female curve have been set to reproduce the age
distribution of ANC HIV prevalence age distributions over
time. The reasonableness of the male curve can be checked
against the age distribution of reported male AIDS cases
circa 1995. When changing the shape of the curves and the
age distribution of partners of females, the user should
ensure that the this consistency between the number of
deaths and number of AIDS cases still holds. This can be
checked by looking at the ANC Age
Profile and AIDS Age Profile
worksheets and ensuring that the dotted curves (actual
figures) are reasonably close to the solid ones (modelled
figures).
ASSA2000 models sexual behaviour,
and thus the probability of infection, on the basis of a
combination of several components, as follows:
-
a matrix showing the probability that a partner is from a
particular risk group;
-
a matrix of male-to-female transmission probabilities per
sexual contact for various combinations of risk group
encounters;
-
a matrix of the ratio of male-to-female to female-to-male
transmission probabilities for various combinations of risk
group encounters;
-
a matrix showing the number of new partners per year and the
number of contacts per new partner per year;
-
a matrix showing the probability that a female partner is
from a particular risk group;
-
a matrix of condom usage for each risk group by age; and
-
the effectiveness of condoms.
These components are all recorded
on the Assumptions worksheet.
All the above information is then brought together in the
following formula:
The probability of someone in risk group i,
aged x becoming infected in a year
where
represents the probability that the partner is from
risk group j
represents the sex activity weighted prevalence of a
partner from risk group j
represents probability of transmission from partner in
risk group j to partner in risk group i
with sex g
represents the probability of a condom being used
e
represents the effectiveness of
condoms
represents the number of contacts per new partner
represents the sex activity (i.e. the proportion of sex
at that age)
represents the number of new partners per annum
The combination of components allows the model to be
used to test the impact of interventions that attempt to
change one or more of these variables.
3.2.4 Perinatal infections
Twenty five percent of babies born to infected mothers are
assumed to be infected. This is consistent with the
0,25-0,30 range often quoted. The lower end of the range was
chosen since the infant mortality rate (IMR) produced by the
model appears to be on the high side in comparison with
various demographic estimates
and because the model
allows for later infection via breastfeeding. As explained
below, infection via breastfeeding is assumed to have a
bimodal distribution, with those contracting HIV three
months or more after birth having a much higher median time
to death than those who are infected at birth. The ASSA2000
model allows for this by assuming a mortality rate of 30%
per annum for those born infected, but a Weibull
distribution and median time to death of six years for those
who contract the disease via mother’s milk.
The user can modify the proportion of births assumed to be
infected and the proportion assumed to be infected by
mother’s milk on the
Assumptions
worksheet. The relevant table is fourth from the top on the
left of the worksheet.
3.3
Starting population
The starting population reflects
the actual population as at 1 July 1985.
This was derived by a process of reconstruction linking
estimates of the population in 1970 to those of the census
population in 1996, ensuring consistency with estimates of
fertility and mortality rates derived independently and
between the numbers of males and females in various age
groups.
The current provinces did not exist
in 1985. For the provincial
version of the model, it was therefore necessary to
reconstruct the base population that could be expected to
have been within these boundaries in that year. This was
done by taking into account a remapping of the 1991 census
into the new boundaries and the patterns of interprovincial
migration between 1985 and 1996.
3.4
Mortality
The mortality data is found in the
MortTable
worksheet. The initial rates of mortality apply on average at
1 January 1986, to be consistent with a starting population
six months earlier at 1 July the previous year.
The non-HIV probability of death and probability of becoming
infected are used in a multiple decrement life table that
applies to individuals not infected by HIV.
The model uses a table of estimated mortality rates at
each age for each of the years 1985 to 1999. After 1999,
mortality rates are projected to trend logistically to
ultimate rates at a rate determined by a ‘mortality
improvement factor’ using the following formula:
where
a
= the mortality rate in 1999
b
= the ultimate mortality rate
c
= the mortality improvement factor
This is contained in the lookup formula which can be
found in the table of current year non-AIDS mortality in the
MortTable
worksheet.
The user can alter the tables of
mortality rates for the years to 1999, the ultimate rates of
mortality, the mortality improvement factor, and the
formulae for interpolating future rates of mortality for all
ages on the MortTable
worksheet. The relevant formulae are found in the tables
headed ‘Mortality Improvement factor for Non-AIDS Mortality’
and ‘Current Year=X Non-AIDS Mortality Rates’ respectively.
In the full
version of the model, these changes need to be made to the
population group specific MortTable sheets.
3.4.2
Mortality of those born with HIV
A mortality rate of 30% per annum
is assumed for babies born infected with the virus. The
value can be changed on the Assumptions sheet or, if more sophistication
is required, the user can change the assumption of a
constant annual rate of mortality for these babies on the Male/Female
HIVTable worksheets. The relevant table on the Assumptions sheet is fourth from the top on the left-hand side.
It is headed ‘Other Assumptions’ and the relevant values are
those for male and female ‘Infant AIDS mortality’. The
relevant table on the Male/Female HIVTable worksheets is second from the right. It records
survival rates by duration in one-year intervals from 0 to
14 years.
These parameters are recorded in
the Male HIVTable and Female HIVTable worksheets.
For those aged 14 plus and for those born with HIV, the
proportions (lt) are calculated using a Weibull distribution with
parameters reflecting median time to death and shape.
The median time to death is set on
the Assumptions worksheet. The relevant table on
the Assumptions worksheet is fourth from the top
on the left-hand side, and is headed ‘Other Assumptions’.
The table provides for the possibility of different median
times in respect of three different age groups of males and
females, namely 14-24 years, 25-34 years, and 35 years and
above. If more sophistication is required, the formula for
defining lx, the proportion alive at age x, can be changed on the Male HIVTable and Female HIVTable
worksheets. For
simplicity, the shape parameter has been set as a function
of the median time to death. This can be replaced with
another value if the user has a better estimate.
A different approach is adopted in
respect of babies infected via mother’s milk. It is becoming
increasingly apparent that paediatic HIV has a bimodal
distribution. Babies who contract HIV three months or more
after birth can be expected to survive much longer than
those who are infected at birth. The ASSA2000 model thus
assumes a Weibull distribution and median time to death of
six years and a shape parameter of 0,8 for those who
contract the disease via mother’s milk.
Although the available evidence suggests that a median time
to death of around nine years would be appropriate for
Africa and that it becomes shorter with increasing age at
sero-conversion, such short median times to death in the
model produce a pattern of deaths by age that is
inconsistent with that observed. The model thus assumes a
median time to death of 11 years for those under 25 and 10
years for those age 25 years and older when infected.
The parameters relating to
fertility of those not infected are found on the Non-HIV
Fertility worksheet. Overall age-specific fertility rates are
determined in a similar way to the mortality rates, with a
table of estimated age-specific fertility rates for the
period to 1996, after which rates are determined by
interpolating between the rates in 1996 and the ultimate
rates. The first table in this worksheet provides non-HIV
fertility rates for each of the four risk groups for the
current year by taking into account the relative fertility
of women in each age group and the proportion of women in
the various risk groups at that age.
The relative fertility factors can be found in the second
table from the top left of the Assumptions worksheet. The results are shown in columns B, C, D
and E in the non-HIV fertility
sheet. The relative fertility factors can be changed on the Assumptions sheet.
The model assumes that PROs have a
lower fertility rate than STDs, who have a lower rate than
RSKs, who, in turn, have a lower rate than NOTs. Although
this may seem counter-intuitive, the argument for the
assumption is that, in order to maintain a highly sexually
active life-style, PROs would probably use contraception or
abort foetuses. In addition, there is evidence suggesting
that STDs may lead to lower fertility. On the other hand, if
awareness of contraception is high, then individuals
choosing to have children are more likely to be in stable
relationships and therefore at reduced risk of contracting
HIV. It is unlikely that the relative fertility rate
assumptions have a great impact on the results, with the
possible exception of the number of infants born
HIV-positive.
These parameters are found in the HIV+ Fertility
worksheet.
The model allows for the impact of the duration of infection
on fertility by multiplying the non-HIV fertility rates by a
factor determined as follows:
where
a
= factor allowing for the bias, particularly at the younger
ages, arising from the fact that those falling pregnant are
those having sex and not using condoms
b
= factor allowing for an initial impact of the virus on
fertility
c
= factor allowing for the impact of the virus on fertility
over time
d
= duration of
infection in years
The first three factors can be
changed in the columns entitled ‘Start Ratio’, ‘Initial
Impact’ and ‘Reduction Factor’ towards the right of the
worksh | 
