Modelling the human immunodeficiency virus (HIV) epidemic: A review of the substance and role of models in South Africa.

We review key mathematical models of the South African human immunodeficiency virus (HIV) epidemic from the early 1990s onwards. In our descriptions, we sometimes differentiate between the concepts of a model world and its mathematical or computational implementation. The model world is the conceptual realm in which we explicitly declare the rules - usually some simplification of 'real world' processes as we understand them. Computing details of informative scenarios in these model worlds is a task requiring specialist knowledge, but all other aspects of the modelling process, from describing the model world to identifying the scenarios and interpreting model outputs, should be understandable to anyone with an interest in the epidemic.

Introduction

No epidemic has received the attention of the ongoing human immunodeficiency virus (HIV) and acquired immune deficiency syndrome (AIDS) pandemic, and no matter of public health concern has been the subject of so much controversy and policy debate. Scenario modelling has been widely employed in attempts to better understand the demographic, health and economic impacts of the epidemic under various interventions, for example, antiretroviral treatment, pre-exposure prophylaxis and condom use.

Despite modelling being ubiquitous and some models generating intense public debate, with consequences, for example, on World Health Organization (WHO) treatment and prevention guidelines, it remains poorly understood by non-specialists. Even modellers themselves hold differing views about the principal uses and limitations of models.

This article reviews the evolution of models, and their applications, in the context of the South African HIV epidemic. We describe, in terms aimed at a wider audience than just modellers, the basic structure of the modelling process, challenges that modellers face and how this has affected policy debate. In Appendix 1, we explore in more detail the social complexities of the particular issues and controversies.

Basic modelling concepts

Books, tutorials and reviews of epidemiological modelling are plentiful, including guidance for working with models in the context of policy debate.[1,2,3,4] Nevertheless, it is useful to review some essential aspects of all scenario modelling. The aim of mathematical modelling is to first identify the key rules that govern the behaviour of a natural world phenomenon, and then to implement those rules in mathematical relations, so that we can learn more about the phenomenon.

For models of the HIV epidemic, this may mean understanding how gender, age, location and other sociological factors influence fertility, exposure to ‘infectious contacts’, access to healthcare and mortality. What determines whether and what kind of model is feasible or useful are the questions we want to answer about the ‘real world’ epidemic, coupled with the data available to justify assumptions about precisely stated rules driving critical processes (dynamical rules). Mathematical and computational challenges may be substantial and sometimes curtail the ambitions of modellers.

It is important to differentiate the specialised technical aspects of model construction and analysis, carried out by mathematical modellers, from the conceptual aspects, which are accessible to anyone with basic insights into the situation being modelled, including doctors, politicians, health system administrators, biologists and activists. This conceptual and technical distinction helps clarify thinking and reminds us that model building should be an inclusive multidisciplinary process rather than the protected domain of specialists.

For example, in the early 2000s, members of the activist organisation the Treatment Action Campaign approached the developers of the Actuarial Society of South Africa (ASSA) models and asked them to incorporate antiretroviral treatment into their model, which they did. An analysis of the cost of rolling out antiretroviral treatment in the public health system, based on the outputs of the ASSA model, was featured on the front page of the Mail & Guardian. The ASSA models were explained by demographers in affidavits in litigation by activists advocating for treatment. The scenarios, assumptions and outputs of the model were debated and understood by a broad range of people: politicians, activists, lawyers, etc. The actual equations in the model spreadsheet were likely of interest to, and understood by, only a handful of specialists.[5,6,7,8]

To maintain the distinction between concepts and techniques, we use concepts popularised by ecological modeller Tony Starfield: model world versus model implementation.[9] A Model World is the conceptual realm in which we explicitly declare the rules – usually some simplification of ‘real world’ processes as we understand them. Model Implementation then refers to the mathematical and computational details.

For example, a model world may be conceptually inhabited by genderless people between the ages of 15 and 49 who all have exactly the same behaviours and mortality. We may declare that in our model world each day brings the same risk of infection or death as the day before, without any notion of individual age, the mechanisms of infection or death. A related model implementation of such a world may consist of some mathematical equations or computer programme.

Model worlds capture the essential ideas which we then formally analyse and explore in technical investigations, using mathematical and computational tools. A model world has abstracted entities and rules, but no particular history. When we set up initial conditions in a model world, like winding up a clock set to midnight, and then let it run, we produce scenarios – particular realisations of processes and events consistent with the assumptions of the model world. A full-fledged investigation may involve many scenarios located in several model worlds.

There are typically two kinds of variables in a model: (1) state variables, that is, scenario-specific accounting indicators, such as the size of population, number of infections and number of deaths, and (2) parameters, that is, model world defining metrics such as, most critically, rates of infection, rates of death and other state transition rules. When the model executes (e.g. as a stand-alone piece of software or as a spreadsheet), state variables evolve over time from given initial conditions, but for this to happen, parameter values must actively be chosen. Sometimes parameters are chosen based on pre-existing knowledge or estimates. Sometimes they are chosen entirely heuristically, just to see what is implied by their values lying here or there within some plausible range. Another option is model calibration, by which parameters are chosen in such a way that the emergent behaviour of the model is consistent with some data. For example, we can try different values of an infectious ‘contact rate’ (how frequently people become infected), and then see whether a suitably narrow range of this parameter produces a time-varying prevalence that is consistent with survey data.

For sexually transmitted infections, a key aspect of model worlds is how infections occur. Infection can happen for a population group at some rate, without any concern for sexual interactions. There can be a single rate across the population or it could be differentiated by age, risk group and gender. Alternately, infection can be conceptualised at a very fine level of detail: a model world could track sexual relationships – or even sexual acts – per individual, with each individual having their own risk of contracting or transmitting the infection.

In model worlds, there are no grey areas of the kind we find in the real world, no hidden unknown rules, factors and entities – although the interplay of components may be complex and may require some sophistication to implement, or conceptually untangle. Modelling then might be seen as teasing out the implications of hypothetical claims about how the world is composed and governed. If done skilfully, this helps explain some aspect of the real world. It informs real world choices that need to be made, even if the full underlying truth in the real world is much more elusive and ambiguous than in any model world we may have constructed. Table 1 highlights key features of the model worlds implemented in the models we review here.

TABLE 1

Examples of models of the South African HIV epidemic.

Model	Model world				Scenarios	Implementation
	Population	Transmission	Mortality	Interventions
Padayachee and Schall 1990	Black people aged 15 to 49	HIV incidence and prevalence estimated from blood transfusion, antenatal and clinic infection numbers.	Not applicable	None	Used data sources to estimate number of black people aged 15 to 49 with HIV from 1989 to 1991	Three simple models using straightforward calculations
Doyle 1990	Population divided by sex, 5-year age intervals and four HIV risk groups.	Mainly a function of risk group and the proportion of infected people, but ‘some allowance’ for ‘sexual activity according to age and sex’.	Age-related non-HIV mortality. Additional risk of mortality for people with HIV	None	Many. Doyle used it to estimate South African population, while Lee et al. used it to estimate infections in Soweto. The initial HIV-positive population is ‘imported’ into the model.	Macro
Padayachee 1992	Individuals have age and sex.	Each person, adjusted for age and sex, has a probable number of sexual partners with whom they have sex a probable number times, each of whom has HIV with a specified probability.	Mortality not explicitly discussed, but number of AIDS cases calculated based on infection period	None	From 1985 a prespecified number of immigrants with HIV ‘seed’ the model. Number of HIV and AIDS cases estimated until 2000	Micro
ASSA (various)	Population divided by sex, province, 5-year age intervals and four HIV risk groups. Infants enter the population annually. People with HIV at various clinical stages of progression.	Function of risk group, proportion of infected people, age and sex. Mother-to-child transmission also modelled.	Age and sex-related non-HIV mortality. Additional risk of mortality for people with HIV	From ASSA2002, antiretrovirals, mother-to-child transmission prevention, condoms, etc.	Calibrated to available data sources up to the year of the model suffix, and then projected forward.	Macro (originally as spreadsheets, then as C++ code)
Granich deterministic 2009	People of no sex or specific age, except that they are 15 to 49 years. People with HIV are assigned to a WHO stage.	Homogenous: no risk groups, single incidence rate for the whole population.	Single mortality rate for people without HIV. Additional risk of mortality for people with HIV	Scaled-up universal test-and-treat versus treating at CD4 count of 350 versus no treatment	Calibrated to South African adult HIV epidemic.	Macro (the authors also did a stochastic model)
Hontelez 2015	In the most complex model of their nine models, people are differentiated by age and sex.	Heterogeneous sexual behaviour. People are part of sexual networks and people at different stages of HIV infection have different degrees of infectiousness.	Age and sex-related non-HIV mortality. Additional risk of mortality for people with HIV	Similar to Granich et al.	Calibrated to South African adult HIV epidemic.	Micro
THEMBISA 2014–2016	Population divided by sex, province, 5-year age intervals and HIV risk groups. Infants enter the population annually. People with HIV at various CD4 count based stages of progression.	Function of risk group, proportion of infected people, age and sex. Mother-to-child transmission also modelled.	Age and sex-related non-HIV mortality. Additional risk of mortality for people with HIV	Antiretrovirals, PMTCT Option B+, condoms, etc.	Calibrated similarly to ASSA but also includes additional data on marriages and partnerships.	Macro

The crucial point is as follows: everyone with a legitimate interest in the situation being modelled is entitled to a comprehensible description of the model world. They should expect to be part of the model world construction, critique and interpretation processes. Modellers need to talk in conceptual terms about this model world, without resorting to jargon or specialised techniques.

The core demographic models

Padayachee and Schall, working for Johannesburg’s City Health Department, published the first serious model of the whole South African HIV epidemic in April 1990.[10] They cited two earlier models that estimated the number of gay men and antenatal care attendees in what was then southern Transvaal with HIV. They also mentioned a WHO model that estimated the number of AIDS cases in South Africa but noted that the model was based on ‘very little, if any, supporting evidence from South Africa’ (p. 330).

Padayachee and Schall actually implemented three simple models, which used antenatal clinic, blood transfusion, sexually transmitted infection and family planning clinic data and population estimates by province to estimate infections for the whole country up to 1992. Their model worlds consist of adult (aged 15 to 49 years) black people, possibly living in a particular province or urban or rural area, but with no other identifiable characteristics. Their first model fitted clinic and blood transfusion data to estimate a rate at which the epidemic was growing. They extrapolated this to calculate national prevalence and the rate at which it was growing up to 1992. Their second model, whose method they called ‘direct’, used various data sets to estimate the number of people with HIV in each province, which they then aggregated for the whole country. Their third model, whose method they called back calculation, used the number of known AIDS cases and an assumption about the time from HIV infection to AIDS to back-calculate the number of HIV cases, derive an incidence rate and then use this to project the number of HIV cases in the future.

They estimated the number of black South Africans, aged 15 to 49 years, with HIV for the end of 1989, 1990 and 1991. Their model calculated between 45 000 and 63 000 infections by end of 1989, rising to between 317 000 and 446 000 at the end of 1991. Clearly there were problems with their methodology: for one thing blood donor HIV prevalence rates were not representative. However, their models provided some idea of the extent of the epidemic using the limited data available then. They wrote: ‘Because of the lack of basic data, these forecasts are tentative, but they nevertheless indicate the great seriousness of the HIV epidemic in South Africa’ (p. 329).

In October 1990, Doyle and Millar, working for the Metropolitan Life Insurance Company, published one of the most influential models of the epidemic.[11] They constructed a model world with an adult population comprising four risk groups: (1) people having no sexual contact, or in long-term monogamous relationships, who are not at risk of HIV, (2) people at some risk, conceived as being in stable relationships but with one or the other partner having more than one sexual relationship, (3) people with higher levels of risk, such as those with other sexually transmitted infections, and (4) sex workers and people with large numbers of sexual partners. These four risk groups remained a part of highly cited models derived from or based on the Doyle model (as it came to be known) until the late 2000s.

Model world inhabitants were assigned rates for forming new relationships, within and across risk groups, and rates of transmission within relationships. It allowed for 5-year age groups to be defined, with different levels of HIV prevalence at the beginning of a scenario. It also had parameters for fertility, mother-to-child transmission rate and HIV and non-HIV mortality rates. It could be used for heterosexual or homosexual populations, adapted as needed to populations of interest. Doyle applied the model to South Africa, leading to prescient predictions that were not obvious in the early 1990s, for example, that the epidemic would kill many young adults, but that the population would not decline (although the growth rate would slow).[12] Lee et al. applied the model to Soweto, estimating that by 2010 it would account for 28% – 52% of all deaths there.[13]

The model implementation of Doyle and Millar’s model world was in the form of population counts at discrete time steps, deterministically updated according to the expected values emerging from statistical rules (like probability of infection or death). Doyle cites other models developed by the Institute of Actuaries and Society of Actuaries at the time but points out that these ‘considered one small homogeneous risk group’ and were inappropriate for modelling the South African epidemic.[12]

These model implementations are often called deterministic compartmental, frequency-dependent or macro. By contrast, a microsimulation, network or agent-based implementation, possibly of the same underlying model world, proceeds by explicitly tracking a large number of identifiable individual model world inhabitants and subjecting them, usually stochastically, to the different events to which they are exposed. The first microsimulation of the South African epidemic that we can find is a Medical Research Council lecture cited in Doyle and Millar’s 1990 paper. Unfortunately, we can find no further references to this particular one in the literature.

Doyle’s model was a proprietary one used by Metropolitan Life, primarily for the purpose of making decisions about employee benefits (pers comm. Stephen Kramer). It was the progenitor of other models, including those of the ASSA. Given the computing power at the time, the level of detail is impressive, in most respects exceeding the complexity of a widely cited and highly impactful model, published as late as 2009[14] that stimulated the debate on early treatment as a means of reducing new transmissions.

Groeneveld and Padayachee used a microsimulation implementation of a model world in which each person, based on their age and gender, has an expected number of sexual partners per year, with a specified proportion of ‘short’ relationships, and an estimate of the frequency of sexual contacts with partners who are infected with HIV with a probability dependent on age and gender. The authors also estimated the annual number of immigrants with HIV who entered South Africa annually. Their goal was to ‘to estimate the extent of HIV infection among black heterosexual South Africans’. They attempted to predict new HIV infections for the period 1985–2000 and concluded that there would be 5.7 million people with HIV in South Africa by 2000. By comparison, the most comprehensive up-to-date current model of the epidemic, THEMBISA, estimates that there were 3.3 million people infected in 2000.[15]

Brophy adapted a World Bank model for the South African epidemic and investigated demographic effects on the black population under various scenarios.[16] The model world divided the population by sex and 5-year age groups. There were also partially overlapping groups: blood transfusion recipients, heterosexual females, heterosexual males and bisexual males. It considered fertility rates, the age pattern of fertility and mortality levels by male and female. The model population was matched to the sex and age structure of the 1985 census. Various data sources were used to estimate fertility and life expectancy. Some parameters, such as the number of sexual partners, coital frequency, condom use, as well as fertility and life expectancy from 2005 to 2010, were essentially guessed (and various scenarios were tried). They calibrated the model so that it estimated the middle estimate of the number of infections in 1990 of the model by Padayachee and Schall (described above). Brophy predicted substantial reductions in the population and life expectancy in 2000, 2005 and 2010 under three AIDS scenarios of increasing severity versus a no-AIDS scenario. In the bleakest scenario, the model estimated that there would be just about 1.9 million people with HIV in the adult black population in 2000 (the actual number was about 3 million).

Dorrington described the origins of the ASSA models.[17] The first ASSA model was developed on a spreadsheet by a team led by Alan Whitelock-Jones. It was titled ASSA500 and was similar to the Doyle model with some simplifications. Dorrington explains that the motivation for ASSA to develop a model when the Doyle model already existed was that the latter was proprietary and there was a need for a ‘program which the user could alter to his or her needs’ (p. 99). Consequently, the model was placed on ASSA’s website and Dorrington wrote: ‘the reader is encouraged to download and play with it’ (p. 101).

Dorrington also wished to improve the model world of Doyle, specifically because it assumed constant fertility and non-HIV mortality over time; the ASSA model world would include decreasing fertility rates and improving non-HIV mortality. Using the same risk groups as the Doyle model, it additionally accounted for ‘net national in-migration’ (p. 100). While users of the Doyle model needed to set the parameters for the community they were modelling, the ASSA models are explicitly aimed at modelling the South African epidemic, with later models disaggregating the outputs by province.

The starting point of the ASSA600 model was the 1985 South African population, known from a census conducted that year. The model was calibrated to reported AIDS cases in 1995 and antenatal HIV prevalence, derived from annual surveys by the Department of Health for 1994–1997. Dorrington described the calibration of the model as ‘perhaps inevitably a little more art than science’. The ASSA modellers aimed to produce a population estimate for 1996, national mortality rates for 1998, a projection of antenatal clinic HIV prevalence rates and a projection of national fertility rates.

Over the next decade, ASSA600 had several successors: ASSA2000, ASSA2002 and ASSA2008. From 2000, the suffix indicates the latest year of the empirical, primarily antenatal survey, data against which the models were calibrated (i.e. not the year they were published). The goal was to fit the known empirical data, estimate past unknown and project future, demographic and HIV outputs, such as population size, non-HIV and HIV mortality, HIV prevalence and incidence. From ASSA2002, the effects of antiretroviral treatment were incorporated.[5,6]

The ASSA models are widely cited. Besides being comprehensive, they have also been open and easily accessible. As Johnson explains, the ‘Excel interface of the publicly-available model is appealing to many non-modellers’.[18]

The latest ASSA model has been calibrated with data only as far as 2008. In recent years, the ASSA models too have been superseded, most notably by the THEMBISA model.[18] This combines the features of three other models, besides the ASSA model. The model world complexity is substantial, including more realistic sexual behaviour ‘calibrated to marriage data and cross-sectional data on numbers of partners’, ‘more determinants of mother-to-child transmission’ and ‘most of the new strategies for preventing and treating paediatric HIV’. For example, it features CD4 count staging instead of clinical staging as in the ASSA models and allows for earlier antiretroviral initiation. It includes newer prevention interventions such as male medical circumcision, pre-exposure prophylaxis and ‘WHO options B and B+ for prevention of mother-to-child transmission’. In contrast to the ASSA models, it takes into account change in risk behaviour by people over time.

The Joint United Nations Programme on HIV and AIDS (UNAIDS) has also produced widely used models. In the 1990s, UNAIDS used Epimodel – developed in 1987 by the Global Programme on AIDS – for its global, regional and country HIV projections.[19] This was eventually replaced by Spectrum, developed by the erstwhile Futures Group (now Avenir Health), and the Estimation and Projection Package (EPP), since combined into one programme.[20,21,22]

The model provides a user interface that takes a range of inputs, for example, base year population by age and sex, fertility rates, life expectancy (AIDS and non-AIDS), migration rates, number of people on antiretrovirals, number of people on cotrimoxazole and about a dozen or so more (see Table 1).[22] It then aggregates all cases in the population aged 15 to 49 years and fits a non-age-structured population model to the historical aggregates, thereby inferring incidence and projecting outputs such as HIV infections and deaths.

Johnson[18] writes:

The Spectrum/EPP model is used … in producing estimates of the global distribution of HIV, and therefore has the advantage of benefiting from a substantial body of international expertise in HIV epidemiology. However, the separation of the modelling of HIV incidence and demographic impact in this model does limit the ability of the model to make use of age-specific data in model calibration. [p. 6]

Spectrum/EPP is used to estimate official estimates for every country in the world every two years for the United Nations Population Division; it serves an important purpose, providing rough estimates of HIV prevalence and mortality where none would otherwise be available. The model is also used to analyse the long-term impact and cost of interventions, though as Johnson says, it is ‘limited in its ability to evaluate the impact of HIV prevention strategies and make long-term projections’. Where countries have developed high-quality specialised models, such as the THEMBISA model for South Africa, it makes more sense to use these.

Modelling when to start treatment

In 2009, Granich et al. at the WHO presented two models.[14] The first model is a population-level transmission model (implemented deterministically) that calculated the long-term dynamics of the HIV epidemic based on different treatment strategies. The second model (implemented stochastically) investigated the effect on R0 – ‘the number of secondary infections resulting from one primary infection in an otherwise susceptible population’ – of different treatment strategies applied to an hypothetical person.

The paper argued that, in South Africa, a policy of universal testing coupled with immediate treatment for adults found to be HIV-positive would effectively eliminate the epidemic. In particular, they estimated that HIV incidence could drop to less than 0.1% per year by 2016. They also costed the strategy.

The paper caused great excitement and controversy. It has been cited, according to Google Scholar, 1640 times (as of 11 March 2017). We know of no other HIV model that has been cited as often, which is extraordinary considering the simplicity of the models: there is no gender or age structure. Perhaps this simplicity, coupled with the strongly stated message the authors conveyed, engaged readers across multiple disciplines and accounted for much of the interest taken in the paper. The paper also encouraged a flurry of other models that looked at the same question.[23]

Even 4 years later, a detailed set of microsimulation models by Hontelez et al. was published, trying to answer the same question as Granich et al.[14] The modellers developed ‘nine structurally different mathematical models of the South African HIV epidemic in a stepwise approach of increasing complexity and realism’.

The simplest resembled the Granich model. The most complex included ‘sexual networks and HIV stages with different degrees of infectiousness’. Hontelez et al.[24] defined ‘universal test-and-treat’ as annual screening and immediate treatment for all HIV-positive adults, starting at 13% in January 2012 and scaling up to 90% coverage by January 2019. Elimination of the HIV epidemic was defined as incidence below 1 per 1000 person-years.

It is controversial whether addition of complexity to models improves them. For example, one of the authors of the Granich et al. paper, Brian Williams, has written:

Hontelez et al. suggest that the [then] current scale-up of ART at CD4 cell counts less than 350 [cells/mm3] will lead to elimination of HIV in 30 years. I disagree … and believe that their more complex models rely on unwarranted and unsubstantiated assumptions.[25]

The Granich model and the ensuing attempts by other modellers to verify, refute or improve upon it raise important questions about what we are trying to achieve with modelling. The original paper is the one that was widely debated. Even though it could be improved, it answered the question of whether a test-and-treat policy had the potential to massively reduce incidence. Most subsequent models agreed with that of Granich et al. that universal test-and-treat would substantially reduce new infections but not as quickly as they proposed. The assumption of rapid scale-up of treatment coverage and significant viral suppression in those failing treatment were, perhaps, too optimistic.

Models targeting particular policy conundrums

Interventions other than antiretroviral treatments have also been modelled. There are numerous such models, and here we briefly note some without describing their model worlds.

The results of a randomised controlled trial that compared infection rates in circumcised versus uncircumcised men in Orange Farm[26] were used to calculate that this intervention could prevent between 1.1 and 3.8 million infections as well as 0.1 to 0.5 million deaths over a 10-year period in sub-Saharan Africa.[27] A comparison of the cost-effectiveness of treatment as prevention, treatment (solely for the benefit of the patient) and circumcision concluded that although treatment as prevention was cost-effective, it was less so than treatment or circumcision.[28,29]

Modelling the introduction of pre-exposure prophylaxis (PrEP), researchers found that it could avert 30% of new infections in ‘targeted age groups of women at highest risk of infection’. However, they also found that the cost-effectiveness of PrEP relative to treatment would decrease rapidly as treatment coverage increased.[30] Another group had more optimistic results modelling PrEP in serodiscordant couples (although it is unclear how a model can address whether antiretrovirals should be given to the HIV-negative or HIV-positive partner in a relationship).[31] They concluded:

Although the cost of PrEP is high, the cost per infection averted is significantly offset by future savings in lifelong treatment, especially among couples with multiple partners, low condom use, and a high risk of transmission. [p. 1]

Another model found that treatment plus PrEP was more effective than either strategy alone but would also produce high prevalence of drug resistance.[32] Hallett et al. investigated the use of PrEP for seronegative partners in stable serodiscordant partnerships, as an alternative or adjunct to treatment for the HIV-positive partner.[31]

Sexual behaviour – such as condom use, number of partners, concurrency, and transactional sex – has been widely modelled.[33,34,35,36,37,38] Models developed by the ASSA researchers, for example, estimated that HIV incidence in South Africa dropped during the period from 2000 to 2008 and that increased condom use was the ‘most significant factor explaining’ this decline.[39] The role of concurrency has however been contentious, with conflicting findings.[33,34,40]

Experimental interventions such as microbicides[41] and vaccines have also been considered,[42] and so has the role of treating sexually transmitted infections.[43] For further references, see Johnson.[18]

Currently, models such as THEMBISA and Spectrum are being used to track progress towards national and global objectives, such as the UNAIDS 90-90-90 targets (90% of people with HIV diagnosed, 90% of people diagnosed on treatment and 90% of people on treatment virally undetectable),[44] as well as elimination of mother-to-child transmission.[45]

Discussion

The distinction between model worlds and the technical implementation of models is useful for demystifying modelling and perhaps allows more people to participate in model construction and critique, and hence reach better informed decisions on the policy implications of models. While models, with their complex equations and computer code, might be impenetrable to all but specialists, the conceptual ingredients – the model world – should be accessible to a wide audience.

The earliest models of the South African HIV epidemic projected prevalence and mortality over time, a task that remains useful today. New models were subsequently developed to estimate the effects of interventions, for example, how antiretroviral treatment would reduce mortality (ASSA2002 interventions model) or how it would reduce new infections (the Granich model).

The challenge facing modellers was summarised by Dorrington[5]:

Estimating the exact impact of HIV/AIDS on mortality is not a simple task since there are many uncertainties surrounding the dynamics of the spread of the virus and subsequent passage to death. In addition there are difficulties in deciding on the level of overall mortality in South Africa since not all deaths are registered. However, determining an order of magnitude of the impact is well within the capabilities of a trained demographer. (our emphasis) (para. 7)

Models, even simple ones, can shed light on ‘big picture’ questions. They cannot be used to provide precise predictions of the long-term future. Models can also provide plausible estimates of unobserved epidemic indicators and assist with planning for the short-term future. These benefits and limitations of models should be kept in mind before deciding to add complexity to model worlds, and consequently model implementations.

Modelling is still an evolving component of biomedical science. Perhaps, as we argue in Appendix 1, a key factor in advancing consensus in how models are assessed, especially with societal implications, is a more inclusive interdisciplinary approach to defining and debating ‘model worlds’, and ‘model world scenarios’, the conceptual aspects of modelling that should be accessible to everyone with an interest in the HIV epidemic. This should lead to improved models that contribute more robustly to policy discussions.