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.

Disclaimer

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.

3.1  Division Into subgroups

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.

3.2  Process of infection

3.2.1  Introduction

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.

Diagram 1: A schematic diagram of the lite model

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.

  3.2.2  Starting the epidemic

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.

3.2.3  Infection assumptions

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.

3.4.1  Non-HIV mortality

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.

3.4.3  Mortality of those contracting HIV after birth

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 (l_t) 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 l_x, 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.

3.4.4  Median time to death

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.

3.5  Fertility

3.5.1  Non-HIV

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.

3.5.2  HIV and fertility

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 worksheet.

3.5.3  Overall

The births resulting from this fertility are split into males and females according to the assumed proportion of births that are male. This proportion is found on the Assumptions worksheet. The relevant table is second from the top and second from the left side of the worksheet. The births populate the age zero cells in the next step of the projection via the Young sheet. The proportion of births that are boys can be changed by the user but will have minimal effects on the workings of the model.

3.6  Migration

The migration-related variables are found on the Male Migration and Female Migration worksheets. For ease of computation, the model assumes that all migration takes place at the end of the relevant year. ‘Migrant’ can refer to both immigrants and emigrants. The figures in the Male Migration and Female Migration worksheets represent net immigration (i.e. in-migrants less out-migrants).

The starting population was constructed to include all migrants received up to 1985.

Migrants are apportioned to the four risk groups according to the proportions in the Assumptions sheet. These are found in the table third from the top on the left side of the worksheet. Currently these proportions are set to be the same as those of the receiving population but the values can be changed by the user.

Migration after 1996 is assumed to fall from its 1996 level, logistically, towards close to zero over a 30-year period.

3.7 Population groups

The ASSA2000 lite model does not distinguish between the different population groups defined during the apartheid era, namely black African, coloured, Asian and white. The full version of the model allows for separate modelling of the epidemic in the four population groups. This feature of the model was developed in response to user demand. This demand was motivated, in part, by the observation that the impact of the epidemic is very different in the different groups. These differences constitute one of the reasons for differences between the prevalence in the Western and Northern Cape on the one hand and the other provinces on the other. Further, some users wanted to extrapolate the results of the model to socio-economic groups, and population group is thought to be a useful proxy for this in South Africa. There were thus both demographic and economic reasons for modelling the epidemic in terms of population groups.

Developing this aspect required a number of demographic assumptions. The disaggregation presents significant challenges during calibration of the model. Unfortunately, very limited data exist about the impact of the epidemic in the different population groups. Mortality data has not been available on a population group basis since 1990, and the ANC data has not been published in disaggregated form since 1995. The mortality data has, since 1998, again been collected on the basis of population group but has not yet been published. The ANC survey continues to collect information on population group. This information is not publicly available, but ASSA’s AIDS Committee has been given access to data for 1997 to 1999.

The model has been fitted to these data and to data from private sector company and insurance testing by taking into account differing levels of STDs and condom usage

3.8 Behaviour change and interventions

The update of the model released in April 2002 allow the user the choice as to whether to give effect to a pattern of preset changes in mother-to-child-transmission (MTCT), transmission probabilities (to simulated an STD intervention), number of new partners per annum, and condom usage. These changes reflect possible changes in individual behaviour and government interventions. Lookup tables of the preset changes are found to the lower right of the Assumptions worksheets for each of the population groups. The user indicates whether the change scenario is wanted by selecting a ‘1’ for change, and ‘0’ for no change on the Assumptions worksheet before activating the projections. The user can choose the start year and rate of roll out of each intervention by altering the values in the lookup table.

With the exception of the Western Cape, the tables reflect the change scenario reflected on the ASSA website. This scenario has the following assumptions:

§                no antriretroviral therapy (ART);

§                MTCT intervention phased in from 40% of births in the year starting 1 July 2001, to 90% five years later. The intervention is assumed to be 50% effective in preventing infection of babies;

§                treatment of sexually transmitted diseases such that they are reduced by 15%. This intervention is also phased in over the five years starting 1 July 2001;

§                a doubling in condom usage over the five year period starting 1 July 2001;

§                a decrease in the number of new sexual partners by 15% over the five year period starting 1 July 2001.

The change scenario for the Western Cape allows for a more accelerated roll out of MTCT and STD interventions, reflecting the provinces clear and early commitment to these interventions.

For the provincial version of the model, the workbook pastes in a zero for all provinces except the Western Cape, i.e. the default is no change.

4.1  Starting the epidemic

The model has a start date of 1 July 1985. At this date, each risk group is assumed to be free of HIV. An initial level of prevalence is then introduced by setting the number of ‘imported HIV’ on the Assumptions sheet to start the epidemic. HIV levels and patterns in later years are generated by the assumptions built into the model.

To run the model, open the appropriate ASSA2000 workbook. When prompted, click on the ‘Enable Macros’ button. If you click on ‘Disable Macros’, the workbook will open, but you will not be able to run any projections.

The copyright notice will appear automatically after you click ‘Enable Macros’. Click on the ‘Accept’ button (provided you accept the copyright conditions). If you are using the lite version,the workbook will open with the Assumptions worksheet on the screen. If you are using the full version, the workbook will open with the Assumptions – All worksheet on the screen. Clicking on the ‘Decline’ button will close the workbook.

Before running the model, click the ‘Reset Projection to Zero’ button on the Assumptions or Assumptions – All worksheet. This runs the ‘ResetProj’ macro, which allocates the initial population into age bands and the four risk groups according to the proportions on the Population worksheet and the Assumptions worksheet.

4.2  Projecting

The model allows the user to project in two different ways. The first is by making use of buttons which run the model for periods of one, five, ten or forty years at a time. Clicking more than one button one after the other produces a projection for the sum of the years.

For example, to estimate the situation as at July 1998, 13 years after the start date, perform the following actions after having reset the model as described above:

§         Click the ‘Project 10 years’ button on the Assumptions worksheet;

§         Click the ‘Project One year’ on the Assumptions worksheet three times, allowing time for the programme to run each year between clicks.

After each click, the bottom left-hand corner of the screen will report on the year-by-year progress of the projection. After the four clicks described above, the sheets, in particular the Results and Population worksheets, will reflect the picture 13 years after the start date of July 1985.

An alternative method of obtaining the same output is to specify the end year. To do this, perform the following actions after having reset the model:

§          Type in the end year required in the cell to the right of the ‘To specific year’ button on the Assumptions worksheet and <ENTER>;

§          Click the ‘To specific year’ button.

Again, the bottom left-hand corner of the screen will record the progress of the projection.

For simple runs, it makes little difference which method of running the projection is chosen. For some users, however, one way may serve the purpose better than others. For example, a user who wants to change a particular assumption as from a certain date, will want to use the first method. Similarly, a user who wants to record results at particular points, for example, every five years, should use the first approach.

By default, the model projects forward from July 1985. Some users will be more interested in projections into the future than in what has happened to date. The model will project the epidemic to July of the current year if you click the ‘To current date’ button on the Assumptions worksheet. The current year for the projection is derived from the system date on the computer on which the projection is performed. As before, progress is recorded at the bottom left-hand corner of the screen. The end point of this projection can then be used for projections into the future.

To run repeated projections from the current date, or from any other specified date, the user should perform the following actions:

§          Run the projection to the desired starting date by one of the methods described above;

§          Click the ‘Store Population’ button to store the results for the last year of the projection;

§          Click the ‘Reset Projection from Store’ button to establish the position in the last year of the previous projection as the new starting point;

§          Run the new projections by one of the methods described above.

As is the case with all projections, the further into the future one projects, the less reliability one can place on the results. This is especially true when projecting the impact of an epidemic about which there is still much uncertainty. For this reason it is not recommended to use the ASSA model to project beyond 40 years. However, some users will want longer projections, for example, to estimate cohort life expectancies. Such users will find that the program tends to become very large and slow on longer projections irrespective of which of the above methods are adopted to run the model.

The user can circumvent the problem by storing the population after 40 years, resetting the base situation to what has been stored, and projecting forward from there, as follows:

§          Click the ‘Store Population’ button after projecting for 40 years.

§          Click on the ‘Reset Projection from Store’ button to get ready for further projections.

These steps need to be repeated if the projection is longer than 80 years. Unless the user is only interested in the end point, he or she should save the output they are interested in (say mortality rates over time) before resetting.

5.1  Standard outputs

Key statistics for each year of the projection can be placed in the Results worksheet to record their passage over time. Currently the recorded statistics include:

§         numbers of people as at 1 July in each sex/risk group/HIV classification and in total;

§         number of deaths in each year (July-June) due to AIDS or other reasons;

§         HIV prevalence rates for different groups;

§         fertility and birth rates;

§         male and female mortality rates by age; and

§         crude extra mortality i.e. additional mortality resulting from AIDS.

The Results worksheet contains results for each year of the projection.

Further population results, such as numbers alive and dead by HIV status for each age, can be found in the Population worksheet. The Population worksheet contains information only on the start and end dates of the projection. Where several projections are performed one after the other, the start date is the original start date i.e. July 1985 unless the ‘Store Population’ and ‘Reset Population from Store’ functions have been used.

To view the Results or Population worksheets, simply click on the appropriate tabs at the bottom of the screen.

Other worksheets contain charts of some of the generated information.

§          The AIDS Age Profile worksheet shows the distribution of AIDS cases by age;

§          The HIV prevalence worksheet shows prevalence by risk group and sex for each year from the first year of the projection to the final year;

§          The ANC Age Profile worksheet shows the projected distribution of ANC AIDS cases by five-year age groups for the projected year, as well as the observed distributions for 1995, 1999 and 2000.

§          The Cumulative Deaths worksheet contains a chart of the cumulative number of people who have died from AIDS in each year from the start of the projection to the end;

§          The (non-cumulative) Deaths worksheets contains a chart of the number of people becoming infected with HIV, dying from AIDS and dying from other causes in each year from the start of the projection to the end;

§          The Pyramid worksheet contains a chart of the population pyramid for each sex in the last year of projection in five-year age groups;

§          The Mortality worksheet contains a chart of the projected mortality curves for each sex in the last year of projection with and without AIDS (‘No AIDS’);

§          The Reported deaths – Female/Male worksheets compare the number of total adult deaths by age for females and males separately with those estimated to have actually occurred in South Africa in selected years.

The user can obtain a full-screen picture of any of these charts (except the reported deaths) by clicking the appropriate button on the Assumptions worksheet after running a projection. The chart can by printed in the normal way, by choosing ‘File’ and then ‘Print’ through the Excel menu system. To copy the chart to another document, for example in MSWord, the user can use the ‘Edit’ menu and ‘Copy’ function of Excel. By then using the ‘Paste Special’ and ‘Picture’ options in the MSWord, the chart will take up less disk space and memory.

To return to the Assumptions worksheet from any of the charts, click the ‘Return’ button at the bottom right of the worksheet.

5.2  Adding output statistics

Although the results of the projection are recorded in each of the worksheets, in most worksheets this is only done for one year at a time. The Results worksheet allows the user to record desired output over time.

The user can erase items not of interest from the Results worksheet. In doing so, however, the user should note that some items are used to produce the charts described above, so if these are needed, then those specific rows must not be erased. The user can also add statistics that have not been included on the standard Results worksheet. References or formulae for desired statistics should be inserted in the column headed ‘LATEST’ (column B).  However, the user must ensure that all rows are inserted above the line marked ‘NB: Any additions must be inserted above this line!’

In the simple case, the user can add statistics computed directly from data already included in the model. In the more complicated case, the user can add data from other sources and calculate additional output data from this and existing data.

A very simple example would be adding as output the population in the age group used for calculations of the economically active population in each year. In South Africa, the age group 15-65 is usually used for this purpose. To include the output on the Population worksheet, the user would perform the following actions:

§          Insert a row in the Results worksheet anywhere above line marked ‘NB: Any additions must be inserted above this line!’;

§          Label the row in the column headed ‘STATISTIC’ (column A), for example give it the label ‘15-65’;

§          Insert in the ‘LATEST’ column the formula for calculating this number in  a year, i.e. ‘=SUM(Population!L19:L67)’

When the projection is run, the number of economically active people in each year of the projection will be recorded in the Results sheet.

An alternative way of achieving the same result is to perform the calculation on the Population worksheet, and then refer to the calculated cell on the Results spreadsheet. The detailed steps for doing this are as follows:

§          Insert the formula to calculate the population aged 15-65 years on the Population worksheet at the bottom of the ‘Total Population’ column. For this example, we assume this is done in cell C97;

§          On the Results worksheet, insert and label a new row ‘15-65’ as described above;

§          On the Results worksheet, in the ‘LATEST’ column, type the reference ‘=Population!C97’.

When inserting the above and other formulae, remember that the cells will not necessarily be updated until after you run a projection, as ASSA2000 sets the default of the CALCulation function from Automatic to Manual. To see the updated calculation without running a projection, press the F9 key on the keyboard.

Another simple example would be to calculate the death rate of male and female PROs. To do this, the user would perform the following actions:

§          Insert four rows in the Results worksheet, for example in the ‘Deaths’ section;

§          Label the rows in the column headed ‘STATISTIC’, with the labels ‘AIDS Male PRO deaths’, ‘Normal Male PRO deaths’, ‘AIDS Female PRO deaths’ and ‘Normal Female PRO deaths’;

§          Insert in the ‘LATEST’ column of these rows the appropriate references for these statistics, namely ‘MalePRO!AO51’, ‘MalePRO!AL51’, ‘FemPRO!AO51’ and ‘FemPRO!AL51’;

§          Insert two rows in the Results worksheet, for example in the ‘Fertility and Growth’ section;

§          Label the rows in the column headed ‘STATISTIC’, with the labels ‘Male PRO Death Rate’ and ‘Female PRO Death Rate’

§          Insert in the ‘LATEST’ column of these rows the appropriate formulae for calculating the death rates, namely ‘=(B39+B40)/(B10+B11)’ AND ‘=(B41+B24)/(B12+B13)’;

When the projection is run, the death rates for male and female PROs in each year of the projection will be recorded in the Results sheet.

A more complicated example would be adding as output the number of workdays lost to AIDS-related disease. To obtain this output, the user would need to perform the following actions:

§          On the HIVTable worksheet, create a table setting out the estimated number of workdays lost per annum. This could be indexed by any or all of age, sex, duration since infection and risk group. These data would have to be obtained from elsewhere.

§          On the Results worksheet, insert a new row, for example above the mortality tables.

§          In the new row, in the column labelled ‘LATEST’, type in the formula that will calculate the new statistic based on the table and the population worksheet.

The new statistics will be recorded on the Results sheet for each step of the projection. Charts using any of the new statistics can also be produced.

6.1 The provincial version

The provincial version of the ASSA2000 model consists of an aggregation of the application of the full ASSA2000 model to each of the provinces. By projecting and calibrating each province separately, the provincial model has the potential to allow for differences between the provinces in respect of particular characteristics, such as different demographic composition of the population, different levels of STDs and different starting times for the epidemic.

The provincial version of the ASSA model utilises two workbooks – the workbook for the full version of the model, together with a workbook that contains the initial assumptions relating to each province. The user creates the workbook for a particular provincial model by first loading the full model and the AssumptionsProv workbook and then running a macro on the AssumptionsProv workbook which pastes in the province-specific starting assumptions into the full version of the model. The full version can then be operated in the usual manner, as described above, to give results pertaining to a particular province and can be save as the provincial version of the model.

The workbook of provincial assumptions consists of an Initializer worksheet where the user specifies the province, destination file, and whether the model allows for a change scenario. There are a further nine Prov – Common worksheets, and 36 Prov – Population Group worksheets containing initial assumptions which are pasted into different worksheets of the full version worksheet once the user has specified the province and asked that the paste operation take place. The cells of the workbook consist of a mix of absolute values and formulae. Some of the latter appear to give invalid or incorrect values when viewed in the workbook of provincial assumptions. However, once the formulae are pasted into the full version worksheet, the cells referred to in the formula take effect and the values become valid.

6.2 The urban-rural version

The urban-rural version also allows for the case where available data on HIV prevalence consists of inconsistent and irregular samples surveys from urban and rural clinics. The user can input data from all the sites, specify each site as either urban or rural, and indicate how the data should be aggregated to produce average urban, rural and national figures.

Calibrating the urban-rural model is somewhat more difficult than calibrating the full version of the model.  Not only does one have to calibrate are three levels (urban, rural and national) but in many situations one has no data for setting the size of the risk groups (STD in particular) (or a number of the other parameters) and these have to be set by trial and error to produce the best fit.

As far as possible, the parameters of the ASSA2000 model have been set by reference to studies of empirical evidence. This was possible, for example, in respect of the size of the STD group, the probability of transmitting the virus, age of the partners, and condom usage. Where it was not possible, parameters are set within bounds of reasonableness to produce output comparable with observations of antenatal seroprevalence levels and estimates of the actual number of deaths based on the registered deaths.

Calibration involves adjustments of parameters that have not been estimated independently so that the ‘results’ of the model more or less match observed reality. In particular, the model results should match the results of the annual ANC surveys both in terms of overall level and by age. The model results should also match the number of adult deaths estimated on the basis of those recorded by the Department of Home Affairs on the population register after adjusting for an estimate of under-recording.

Calibration can be done visually, using the charts on the Calibration, ANC Age Profile and Reported deaths worksheets.

The Calibration worksheet looks at the fit with ANC survey data. In judging the fit, it must be borne in mind that the ANC points before 1997 are probably biased upwards, perhaps as a result of an urban bias in the location of data collection sites over a period when prevalence levels were higher in the urban areas. The ‘target’ points are therefore the ones that should be used when calibrating the model. Further, the 1998 ANC survey value is incorrect as the Department of Health made an error in weighting the provincial results to get the national estimate. The correct value should be some 2% lower than the published value.

The user can obtain a full-screen calibration graph of the antenatal clinic prevalence each year by clicking the ‘Calibration data’ button on the Assumptions worksheet after running a projection. The aim is to get the solid curves to follow the points marked by the data as closely as possible. These points correspond to HIV prevalence among:

§         ANC attendees;

§         Commercial sex workers (CSWs); and

§         STD clinics;

in respect of each:

§         actual surveyed prevalence; and

§         ‘target’ expected prevalence.

The ‘target’ prevalence is based on the patterns found in other African countries where the epidemic has been experienced for longer than in South Africa.

The variables for HIV prevalence among women aged 15-49 are found on the HIVTable worksheet.

The procedure used in the original calibration of the model was first to fit the prevalence figures for the PRO group. This group is roughly equivalent to CSWs but not identical in that some CSWs will be at less risk than PROs as defined in the model because, for example, they use condoms and have STDs treated. The next step after fitting the PRO group, was to fit the STDs and finally the ANC attendees. It was assumed that most sexual activity occurs between partners in the same risk group. Further, by definition, members of the RSK group do not have sexual contact with members of the PRO group, and members of the NOT group do not have unprotected sexual contact with members of any of the other groups.

Based on evidence that suggests that women only visit a clinic late in their second trimester, the projection intervals run from the middle of one year to the middle of the next year. This assumes that women are, on average, six months pregnant when they first visit the clinic.

In order to model the prevalence of women attending public antenatal clinics rather than that of all pregnant women, the ASSA2000 model increases the age-specific rates of all pregnant women in the population by a multiple to allow for the fact that the prevalence of women attending public antenatal clinics is likely to be higher than that of pregnant women in general.

Adopting this approach, it is impossible to get anything but a crude fit to the PRO and STD target points. Modelled prevalence plateaus at a far higher level than the observed and ‘target’ points suggest. One possible explanation for this mismatch is that the survey and target CSW prevalences may include people from the (lower risk) RSK and STD risk groups, while the model definition of the PRO group is narrower, including only people at higher risk.

The ANC Age Profile sheet compares the prevalence by age from the antenatal survey with that generated by the model. It can be accessed by clicking the ‘ANC Age profile’ button on the Assumptions sheet. Calibration should aim to ensure as close a fit to the age profile of the antenatal prevalence data as possible by changing such factors as the female curve of sex activity and the age distribution of partners.

The Reported deaths worksheets contain charts which look at the fit with deaths recorded by the Department of Home Affairs. There are two such worksheets, one for male deaths and one for females. The user can view these worksheets by selecting the appropriate tabs on the workbook after running a projection. A full screen view is obtained by choosing the ‘Full screen’ option on Excel’s View menu.

The charts show the estimated number of deaths in the country based on the registered deaths by age for each of the years 1996 (calendar), 1997/98, 1998/99 and 1999/2000, as well as deaths projected by the model for the last year of the projection. The aim in calibration is to match as closely as possible the estimates of the number of deaths based on the registered deaths.

  7.3 Calibration tips

Theoretically the user can change a wide range of parameters on the worksheet. In practice, however, there are only a limited number of combinations of parameters for which changes could provide a potentially realistic picture of the AIDS epidemic in South Africa. Further, because of the interdependence of different parts of the model, it is sometimes not easy to predict the effects of a particular change. This sub-section therefore provides some tips as to type and extent of changes in output that are likely to result from changing particular parameters.

The following pointers suggest the effect of changing some of the key parameters on the outcome:

§          The size of the NOT group determines to a large extent the level at which the antenatal prevalence is expected to plateau in the long run.

§          Provided it remains fairly small (around 1% of the population), the PRO group does not impact much on the long-term course of the epidemic.

§          The STD group is conceptually defined to be those infected with STDs to such an extent that the average transmission probability is expected to be that recorded on the Assumptions sheet. In constructing the model, the proportions were set equal to those recorded in the 1998 Demographic and Health Survey, which implied that this proportion were infected with STDs about 25% of the time.

§          The age profile of prevalence is determined largely by the sex activity, age of partner and age distribution of condom usage assumptions.

Appendix A: System requirements

Pentium III 500Mhz (or better from a speed perspective)

Windows 98 or later

Microsoft Excel 98 or later

64MB Ram

Appendix B: Description of worksheets

Assumptions

This is the worksheet that appears on the screen when the user opens the model. At the centre it contains a number of buttons that allow the user to run projections, jump to worksheets containing output graphs and calibration checks, and reset the model.

§          The ‘Project One Year’, ‘5’, ‘10’ and ‘40’ buttons allow the user to run the model for that number of years cumulatively, in other words, in addition to the point to which the model has already been run.

§          The ‘To Date’ button runs the model to the current year as determined by the clock on the machine running the model.

§          The user can specify the year to which he or she wants to project, by entering the year and clicking on the ‘To specific year’ button.

§          The ‘Reset Projection to zero’ button returns the workbook to the start year.

§          The ‘Store Population’ and ‘Reset Projection from Store’ allow the user to run the projection to a point in time, store the population details at this point, and then to use this as a new starting point for projections, resetting from the stored population each time.

Around the central buttons, the worksheet contains a number of tables and matrices containing key parameters.

Several of the matrices reflect assumptions underlying the modelling of sexual behaviour. These include:

§          a matrix showing the probability that a partner is from a particular risk group. The relevant table is the topmost table second from the left;

§          matrices of male-to-female and female-to-male transmission probabilities per sexual contact for various combinations of risk group encounters. The relevant tables are the topmost tables third and fourth from the left;

§          a matrix showing the number of new partners per year and the number of contacts per new partner per year. The table is the topmost table fifth from the left;

§          a matrix showing the number of contacts per male partner from different risk groups of females of the different risk groups, as well as the averages. The table is the rightmost table on the worksheet;

§          a matrix of condom usage for each risk group by age. This is the long thin table in the middle of the worksheet; and

§          the effectiveness of condoms. This is a single value shown on the worksheet just above the condom usage table.

Other tables reflect further basic assumptions, as follows:

§          a table, at top left, showing the total of the starting population;

§          a table, second down from the top left, showing the percentage distribution of the male and female adult populations across the four risk groups, as well as relative fertility of females in each risk group;

§          a table, third down from the top left, showing the percentage distribution of the male and female immigrant adult population across the four risk groups;

§          a table, fourth down from the top left, reflecting assumptions about infant AIDS mortality and median time to death and imported infection for male and female;

§          a table, fifth down from the top left, showing assumed proportions of perinatal and breastfeeding infection and AIDS median time to death;

§          a table, second from the left and second from top, giving proportion of male births. (This table is not utilised in the current version of the model.)

The full version of the model contains a separate Assumptions worksheet for each population group, as well as an Assumptions – All worksheet. In respect of this and other worksheets, the sheets are labelled with the standard name followed by the name of the population group, namely ‘Asian’, ‘Black’, ‘Coloured’ and ‘White’. The group-specific Assumptions worksheets contain all the tables described above in respect of that particular population group. They also contain four additional behaviour change lookup tables, to the far right, as follows:

§                a table giving mother to child transmission rates under the change scenario for each of the years 2001 through 2005 in respect of births and mother’s milk, the rates for the no change scenario, and the rate of effectiveness of the intervention strategy;

§                a table giving rate of reduction in male-to-female and female-to-male STD transmission under the change scenario for each of the years 2001 through 2005, and the rates for the no change scenario;

§                a table giving the number of new partners per annum under the change scenario for PRO, STD and RSK females for each of the years 2001 through 2005, and the numbers for the no change scenario; and

§                a table showing condom usage for the RSK group under the change scenario for each year of age between 14 and 59, and for each of the years 2001 through 2005, as well as condom usage for the no change scenario.

The Assumptions – All worksheet contains all the buttons to drive the model. These include the buttons contained in the Assumptions worksheet on the lite version, as well as a number of additional buttons which allow the user to access group-specific information. When the model is first opened, only the aggregate worksheets are seen. These worksheets contain the summary results from the four component population groups. The additional buttons on the Assumptions – All worksheet are as follows:

§          The ‘Change Assumptions for Asian Group’ reveals all the worksheets specific to the Asian group and places the Assumptions – Asian worksheet on the screen. The corresponding Black, Coloured and White buttons reveal all the worksheets for that specific group. Pressing any of these buttons hides all worksheets relating to population groups other than the chosen one.

§          The ‘Show All Population Groups’ button reveals all worksheets for all population groups.

§          The ‘Hide All Population Groups’ button hides all worksheets except the aggregate ones.

The Assumptions – All worksheet of the full version of the model also allows the user to choose whether to run the model with the change or no-change scenario in terms of behaviour change. A message under the additional buttons described above instructs the user to ‘Enter 1 for change scenario, 0 otherwise’ in the cell to the right of the message.

Results

This worksheet is used to store output over time. It thus summarises the results for each year from the start to end date of a projection. From top to bottom it records information on the clear and infected populations, deaths, accumulated AIDS deaths, HIV prevalence rates, fertility and growth, advocacy output, male and female mortality by age, and force of infection. None of this information is used in the running of the model although some of it is used to produce the graphs. Much of it could be removed if the user had no use for it.  However, there is no need to remove or replace any of it in order for the user to produce his or her own output. To add their own output, users can insert rows above the line marked ‘NB:  Any additions must be inserted above this line!’ and enter the required extraction formula in column B.

The full version of the model contains a separate Results worksheet for each population group in addition to the one which is used for aggregate results.

Population

This worksheet summarises population statistics for the start and end date of a projection. Where several projections are done one after the other, the start date is the original start date. Working from left to right on the worksheet, we have:

§          Details of starting population by age and sex;

§          Infected and non-infected population by age and sex as at 1 July of the current year;

§          Deaths by age and sex projected for the twelve months beginning 1 July of the current year. In this table, age ‘B’ represents deaths of babies born during the projected year. Deaths marked ‘0’ represent deaths of those who were under 1 year of age at the start of the projected year;

§          Numbers used to construct the population pyramid as at 1 July of the current year;

§          A summary table of male and female deaths in the twelve months beginning 1 July of the current year in five-year age groups;

§          A summary table used for calculating the number of people sick with AIDS.

Below these tables, we find:

§          A table showing numbers and proportions of new adult infections;

§          A table summarising numbers and proportions of AIDS deaths in five year age groups.

The full version of the model contains a separate Population worksheet for each population group, as well as an aggregate worksheet for the population as a whole. The group-specific Population worksheets do not have the second set of tables contained in the Population worksheet of the lite model, namely the table showing the numbers and proportions of new adult infections, and the table summarising numbers and proportions of AIDS deaths in five year age groups.

MortTable

This sheet produces the non-HIV mortality rates for each year, by looking up the rates up to 1999 and interpolating between the 1999 rates and ultimate rates for years after 1999. Working from left to right, the worksheet reflects:

§          1-(Non-AIDS survival) (i.e. non-AIDS mortality), by one-year age group for age last birthday and sex, for the current year;

§          Mortality improvement factors, by one-year age group and sex;

§          Non-AIDS mortality rates by sex and one year age group for exact ages, for the current year;

§          Ultimate non-AIDS mortality rates for one-year age group and sex;

§          Mortality to date in respect of non-AIDS mortality rates by one-year age group and year, with separate tables for male and female;

§          Projected vs recorded deaths for five-year age groups, for each of the years 1996 to 1999, and for male and female separately. These are used to produce the graphs for calibrating the model against the recorded deaths.

The full version of the model contains a separate MortTable worksheet for each population group, as well as an aggregate worksheet for the population as a whole. The group-specific MortTable worksheets do not contain a table of projected vs recorded deaths as described above. The aggregate MortTable worksheet contains a table of weights by population group and age for ages 0 to 12 years which is used to compute the aggregate mortality rates.

SexActivity

This sheet calculates the relative amount of sex at each age for males and females. The distribution of male sex activity by age is derived from the distribution for females and the age and risk group mix of the partners of the women.  The leftmost table on this sheet contains separate indices for male and female sex activity in one-year age groups. (The values for male sexual activity at ages 14 to 59 do not sum exactly to 100% because it is assumed that there is some male sexual activity after age 59.) The next table from the left contains f(x), representing the percentage of total female sexual activity occurring at age x. The third table contains the parameters used to generate f(y|x), the percentage of partners of females aged x who are aged y. The next table is the table of  f(y|x) values. The table below that contains the values for g(x|y), the distribution of female partners of men aged y. The SexActivity worksheet includes a chart that displays the male and female sexual activity curves, and one, on the far right, that displays the age distribution of male partners of women at selected ages.

The full version of the model contains a separate SexActivity worksheet for each population group, but no aggregate SexActivity worksheet for the population as a whole.

Male HIVTable and Female HIVTable

This sheet records the survival curves (i.e. the proportion of people surviving by duration since becoming infected) for adults, those born with the virus and those becoming infected through mother’s milk.  Reading from left to right, the worksheets contain the following tables:

§          HIV survival rates by broad age group (14-24, 25-34 and 35 plus) of adults, and duration of infection in one-year intervals;

§          Survival of HIV births by duration of infection in one-year intervals;

§          Survival of babies infected by mother’s milk by duration of infection in one-year intervals.

The columns marked ‘Surviving’ refer to the proportion of infected people still alive t years after infection.

From the proportions surviving, the model works out death rates, which are recorded in the top set of tables alongside the relevant survival rates. The model also interpolates from these rates to produce a further table of mortality rates by age of the individual and duration of infection in one-year intervals for those aged 14 years and above. This table is found below the chart.

The mortality curves are displayed in a chart below the topmost set of tables.

The full version of the model contains separate Male and Female HIVTable worksheets for each population group, as well as aggregate Male and Female worksheets for the population as a whole. While most of the other aggregate worksheets are constructed through simple summation of the values in the group-specific worksheets, the values in the aggregate HIVTable worksheet have two differences.  First the estimated prevalence levels of those attending antenatal clinics in the top table are derived as a weighted average of the same figures in the each of the population groups, weighted by the proportions of pregnant women from each group attending public antenatal clinics.  Secondly, the second table down contains the national prevalence figures as published or estimated elsewhere and is not derived from the population-group specific sheets.

HIVTable

This sheet is used to produce the estimates from the model of the prevalence of women attending antenatal clinics by five-year age group and in total. It also contains a table of observed values against which the estimates can be compared for calibration purposes. The top table of this worksheet contains data in five-year age groups. Two columns for pregnant women show the numbers who are HIV positive and negative. A series of columns represents the prevalence of women attending ANC clinics. Finally, there is an adjustment factor which adjusts the prevalence in the population as a whole to allow for the fact that it includes women who attend private clinics, in order to arrive at an estimate of the prevalence of those who attend public antenatal clinics.

The second set of tables when moving from top to bottom contains three sets of data – for ANC, STD clinics and commercial sex workers. The ANC columns record survey and target data. The columns for STD clinics and CSWs record South African and target data for each year.

The full version of the model contains a separate HIVTable worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

Non-HIV Fertility

This sheet produces age specific fertility rates for HIV negative women in each of the risk groups.  Reading from left to right, this contains the following tables:

§          Non-HIV fertility rates by the four risk groups and age of the woman in one-year age-groups, from age 14 to 59, for the current year;

§          Non-HIV fertility rates by year for the period 1985 to 1996 by one-year age-groups, from age 15 to 49 for all HIV positive women irrespective of risk group;

§          A fertility improvement factor and ultimate rates by one-year age groups, from age 15 to 49;

§          The ratio of HIV+ fertility to non-HIV fertility by one-year age groups, from age 15 to 49, for the current year (produced by the HIV+ Fertility sheet);

§          The proportion of women in each risk group in one-year age groups, from age 15 to 49.

The full version of the model contains a separate Non-HIV Fertility worksheet for each population group. There is a single aggregate Fertility worksheet which combines information from the group-specific Non-HIV Fertility and HIV+ Fertility worksheets. The Fertility worksheet contains the following tables:

§          Population group female weights for each age from age 14 to 49 years;

§          Percentage change in fertility attributable to HIV, which among others, records HIV prevalence and aggregates the HIV+ and HIV- fertility rates from the group-specific worksheets for each age from 14 to 49 years.

HIV+ Fertility

This sheet calculates the adjustment ratio for converting the fertility rates of HIV negative women to fertility rates for women infected with the virus. The worksheet contains a single table. The rows record the age of the individual, from 14 to 59 years. A first set of columns records the duration of infection, from one to 29 years. The third last column records the start ratio – the ratio of HIV positive to HIV negative ruling immediately before becoming infected. The second last column records the initial impact on the fertility ratio of becoming infected. The final column records the reduction factor, which is equal to 1 minus the rate at which fertility drops per year infected.

The full version of the model contains a separate HIV+ Fertility worksheet for each population group.

Male Migration and Female Migration

These sheets contain the net numbers of migrants into the population at each age for each year.  Each of these worksheets contains a single table. The rows of the table reflect the age of the individual in one-year age groups. The columns of the table reflect the year, from 1985 to 2025.  The model assumes that beyond 2025 the number of migrants remains the same as those in 2025.

The full version of the model contains separate Male and Female Migration worksheets for each population group, as well as aggregate Male and Female worksheets for the population as a whole.

FemPRO

This sheet calculates the numbers of females in the PRO risk group at each duration since becoming infected, the number of new infections and the number of infected and uninfected births at each age. The worksheet has a BEFORE table at the top, with an AFTER table below it. The BEFORE position consists of data reflecting the population at the start of the year. The first set of columns contain, for each year of age and each year of duration of being infected, the number of people in that group. The columns to the right of this series contain a range of other parameters that affect the change in position over the projection period. The AFTER table again provides a value for each year of age and each year of duration. The AFTER position is calculated from the BEFORE position during projections using the formulas in the cells of the AFTER table to provide the BEFORE table for the next year. The final columns of the AFTER table provide for calculation of necessary adjustments to account for migration.

Below these tables is a STORE table. This is used for storing the population profile when the ‘Store Population’ button on the Assumptions sheet is clicked, so that one can revert to the stored population using the ‘Reset Population from store’ button.

The full version of the model contains a separate FemPRO worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

FemSTD

As for FemPRO.

The full version of the model contains a separate FemSTD worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

FemRSK

As for FemPRO.

The full version of the model contains a separate FemRSK worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

FemNOT

This sheet is analogous to the above sheets but without the complication of having to allow for infected people. The worksheet has a BEFORE table at the top, with an AFTER table alongside. The BEFORE position consists of data reflecting the population at the start of the year. The columns contain, for each year of age, the starting position, the number of deaths during the year, and net immigration. The AFTER table provides a value for each year of age reflecting the position at the end of the year. The AFTER position is calculated from the BEFORE position during projections to provide the BEFORE table for the next year. The small NEW table below the AFTER table reflects the number of male YOUNG people joining the FemNOT category over the year.

The full version of the model contains a separate FemNOT worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

MalePRO

As for FemPRO.

The full version of the model contains a separate MalePRO worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

MaleSTD

As for FemPRO.

The full version of the model contains a separate MaleSTD worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

MaleRSK

As for FemPRO.

The full version of the model contains a separate MaleRSK worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

MaleNOT

As for FemNOT.

The full version of the model contains a separate MaleNOT worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

MaleOLD

This sheet is analogous to the above sheets without sexual intercourse, i.e. there are no newly infected and no births. The worksheet has a BEFORE table at the top, with an AFTER table below it. The BEFORE position consists of data reflecting the population at the start of the year. The first set of columns contain, for each year of age and each year of duration, the number of people in that group. The columns to the right of this reflect total infected, total clear and infected, and number of AIDS and non-AIDS deaths. The AFTER table again provides a value for each year of age and each year of duration. The final columns of the AFTER table provide for calculation of necessary adjustments to account for migration. The AFTER position is calculated from the BEFORE position during projections using the formulas in the cells of the AFTER table to provide the BEFORE table for the next year.

The full version of the model contains a separate MaleNOT worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

FemOLD

As for MaleOLD.

The full version of the model contains a separate FemOLD worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

Young

This sheet calculates the number of survivors from birth at each age up to age 14. The worksheet has a BEFORE table at the top, with an AFTER table below it, and several calculation tables and a STORE table below that. The BEFORE position consists of data reflecting the population at the start of the year. The first set of columns contain, for each year of age and sex, the number of people in that group who are clear, who were born HIV+, and who have become infected through mother’s milk. The table includes a row for babies born during the year. The columns to the right of this series reflect the number of female and male deaths predicted for each of the three HIV categories, and estimated female and male net migration. The AFTER table again provides a value for each year of age and sex in respect of each of the three HIV categories. The AFTER position is calculated from the BEFORE position during projections using the formulas in the cells of the AFTER table to provide the BEFORE table for the next year. The tables between the AFTER and STORE table contain the formulae for calculation of the number of infected and non-infected babies born during the year, and surviving to the end of the year, as well as the number infected through mother’s milk.

The full version of the model contains a separate Young worksheet for each population group, as well as an aggregate worksheet for the population as a whole.

AIDS Age Profile

The worksheet contains a chart showing the distribution of AIDS cases by age. The data refer to to cases up until 1995, as data have not been collected since this date.

HIV Prevalence

The worksheet contains a chart showing HIV prevalence by risk group and sex for each year from the first year of the projection to the final year. The risk groups charted are female PRO, female STD, male STD, female POP and male POP. The POP lines represent the prevalence for the total female and male populations aged 15-49 years.

ANC Age Profile

The worksheet contains a chart showing the projected distribution of ANC AIDS cases by five-year age groups for the end-year of the projection, as well as the observed distributions for 1995, 1999 and 2000.

Calibration

The worksheet charts actual, ‘target’ and modelled prevalence among ANC attenders and STD clinic attenders as well as modelled CSW and RSK prevalence and CSW ‘target’ prevalence from the first year of projection to the end year. The ‘target’ data reflect patterns found in other African countries that have more experience of the epidemic than South Africa.

Cumulative Deaths

The worksheet contains a chart showing the cumulative number of people who have died from AIDS in each year from the start of the projection to the last year of the projection.

Deaths

The worksheet contains a chart showing the numbers of people becoming infected with HIV, dying from AIDS, and dying from other causes in each year.

Pyramid

The worksheet contains a chart of the population pyramid for each sex in the last year of projection in five-year age groups.

Mortality

The worksheet contains a chart of the projected mortality curves for each sex in the last year of projection with and without AIDS. The label qx on the Y-axis refers to the probability of a male or female individual aged exactly x dying within the next year of age.

Reported deaths – Female and Male

These worksheets chart reported deaths, after adjustment for under-recording, by five-year age group for 1996 (calendar year) and 1997/98, 1998/99 and 1999/2000 against total projected deaths for the last year of the projection.

Copyright

The copyright worksheet opens automatically when the user opens the model workbook with macros enabled. (If macros are not enabled, the user will be unable to run any projections.)

Appendix C: Description of worksheets in provincial version workbook

This workbook is used to paste starting assumptions into the ASSA2000 full model to create a model of a chosen province.  In order to run it the user must first ensure that the ASSA2000 full version of the model is open.

Initializer

This worksheet allows the user to specify:

§                whether the ASSA2000 file being used contains behaviour change;

§                the province for which the data should be copied; and

§                the name of the file into which the assumptions are to be pasted (the source or destination file).

By clicking the square buttons under the specification table, the user causes data to be copied from this workbook to the specified destination file.

EC – Common

This worksheet contains the following tables:

§                a table giving the formulae used to calculate the modelled ANC prevalence, as well as the observed prevalence for 1995, 1999 and 2000 in five-year age groups;

§                a table giving observed and target rates of infection for ANC, STD clinics and CSW for each of the years from 1985 to 2005.

The values in these tables are copied into the corresponding cells of the HIVTable worksheet of the destination workbook.

EC – Asian

This worksheet contains the following tables:

§                a single-row table giving the initial population. This is copied to the Assumptions – Asian worksheet;

§                a table showing the percentage distribution of the male and female adult populations across the PRO, RSK and STD risk groups, as well as relative fertility of females in each risk group. The values are copied to the Assumptions – Asian worksheet, where the percentage in the NOT group is derived;

§                a table showing the percentage distribution of the male and female immigrant adult population across the PRO, RSK and STD risk groups. The values are copied to the Assumptions – Asian worksheet, where the percentage in the NOT group is derived;

§                a table showing infant AIDS mortality, median term to death of HIV+ in three age groups, and the equation used to compute imported infectivity of PROs for male and female. The values are copied to the Assumptions – Asians worksheet;

§                a table showing the equation for determining the proportion of  babies infected perinatally, proportion infected via breastfeeding, and AIDS median time to death. The values are copied to the Assumptions – Asians worksheet.

§                a table showing, for each year of age, condom usage for the RSK group, age distribution of the starting population, the mortality improvement index and ultimate mortality for male and female, non-AIDS mortality to date for each year for male and female, the fertility improvement factor and ultimate rate, the start ratio, initial factor and reduction factor for the impact of HIV duration on fertility, and net male and female migration for each year from 1985 to 1996. The RSK condom usage data is copied to the Assumptions – Asians  worksheet. The age distribution is copied to the Population - Asians worksheet. The mortality data is copied to the MortTable – Asians worksheet. The fertility data is copied to the Non-HIV Fertility – Asians worksheet. The migration data is copied to the Male Migration – Asians and Female Migration – Asians worksheets.

§                a set of four tables relating to MTCT, PRO-PRO transmission probability, the number of new partners of females, and condom usage under the change scenario. These data are copied to the relevant tables on the Assumptions – Asians worksheet.

Other worksheets

The remaining worksheets names take the form Prov – Common or Prov – Population Group and contain the same tables as the EC – Common and EC – Asian worksheets respectively.

Appendix D: Summary of worksheets

In theory, the user can change virtually any value or formula in the workbook. In practice, there are a limited number of values and formulae which can usefully and sensibly be changed. The third column of the table below indicates which worksheets contain cells with assumptions that can sensibly be changed. The fourth column indicates which worksheets are altered by the model during each projection.

Appendix E: Acronyms

ANC                      Antenatal clinic

ART                      Anti-retroviral therapy

ASSA                   Actuarial Association of South Africa

CSW                     Commercial sex worker

HIV                       Human immuno-deficiency virus

IMR                       Infant mortality rate

MRC                     Medical Research Council

MTCT                    Mother-to-child-transmission

SADHS                 South African demographic and health survey

SALT                    South African Life Tables

STD                      Sexually transmitted disease