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Dynamic Demographic Analysis pp 91–114Cite as

Modeling the Dynamics of an HIV Epidemic

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Part of the book series: The Springer Series on Demographic Methods and Population Analysis ((PSDE,volume 39))

Abstract

The evolution of an HIV epidemic involves many population dynamics that are closely linked with age. Understanding these dynamics can help policy makers and program planners design interventions, measure progress in the fight against HIV, and prepare for the future impact of the disease. To this end, we propose a model for sex- and age-specific projections of HIV prevalence that uses B-splines to model changes in HIV incidence. We are able to combine HIV prevalence data from antenatal clinics with prevalence data from nationally representative surveys to estimate the model parameters. Several approaches are also proposed for generating forecasts from our relatively parsimonious B-spline model. We apply these techniques to investigate the dynamics of HIV incidence in Tanzania. The results support a rapid increase in HIV incidence from the early 1980s to the early 1990s, followed by a decline up through 2003. We also generate forecasts of HIV prevalence for 2007 and 2011, and compare them to nationally representative data from these years. Our assessment of the predictive performance of the approaches suggests that additional information is needed to produce accurate forecasts of sex- and age-specific prevalence, but that B-splines provide a potentially useful approach for achieving this goal.

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Notes

  1. 1.

    Wawer et al. (2005) estimate the average probability of heterosexual HIV transmission per coital act using data from HIV-discordant, monogamous couples. They find that probability of transmission depends on the stage of infection in the index partner, who first became HIV+. The risk of transmission peaks at 0.008 (per coital act) during the first few months after the index partner’s infection, then declines and stabilizes around 0.001 over the next several years, and subsequently increases to 0.004 several months before the index partner’s death. Hollingsworth et al. (2008) report similar findings.

  2. 2.

    This dynamic relies on the assumption that the susceptible sub-population is not replenished with new, uninfected individuals at a rate faster than the exit of uninfected members.

  3. 3.

    In Eastern and Southern Africa, the median survival time from seroconversion is roughly 11 years in the absence of antiretroviral therapy (Todd et al. 2007).

  4. 4.

    Using data from Rakai, Uganda, Hollingsworth et al. (2008) estimate that HIV-positive individuals spend about 8 years (80 %) of their remaining life in the asymptomatic stage of HIV, when infectiousness is relatively low. This result applies to a context without antiretroviral therapy that prolongs survival.

  5. 5.

    Brookmeyer and Konikoff (2011) discuss techniques for estimating HIV incidence from data on HIV prevalence at two points in time.

  6. 6.

    The importance of this point is emphasized by the work of Eyawo et al. (2010), who estimate that the percentage of HIV+ individuals who are in stable heterosexual serodiscordant relationships may exceed 40 %.

  7. 7.

    The HIV/AIDS Indicator Survey from 2003–2004 only tested for HIV on the mainland, while subsequent surveys also included the island of Zanzibar. In 2007–2008 and 2011–2012, estimates of adult HIV prevalence at the national level (including Zanzibar) stand at 5.7 % and 5.1 %, respectively.

  8. 8.

    The DHS/AIS from 1999 and 2003–2004 only include information collected from the mainland, and thus we exclude respondents from Zanzibar when calculating the estimates from the 2011–2012 DHS/AIS.

  9. 9.

    Data from urban ANCs are deflated by a factor of 0.973, and rural ANC data are deflated by a factor of 0.964 (see Table 1, Gouws et al. 2008).

  10. 10.

    The \(\varGamma _{t-t_{0}}\) specification is adopted from an earlier model (Chin and Lwanga 1991), and was chosen because it provided a close fit to the data available at that time.

  11. 11.

    Uniform prior distributions with a domain from 0 to 2 are used for the sex- and age-specific incidence parameters, j a (in Heuveline (2003), the upper bounds of the confidence intervals for j a are all below 1.5). Similarly, the scale parameters, H, have a uniform(0,1) prior, and the B-spline coefficients α 1 and α 2 follow uniform(0,5) distributions. Finally, the error term for the B-spline coefficients follows a normal distribution, \(\varepsilon \sim \) N(0, τ 2), and τ 2 is assumed to follow an inverse gamma distribution with shape and scale parameters set equal to 1. We assume these priors are independent and take their product to form the joint prior distribution.

  12. 12.

    The B-spline model produces the annual estimates of HIV incidence, shown in Fig. 6.5, which are then averaged across 5-year periods and used as inputs to the population projection model.

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Acknowledgements

This research was supported by grants from the NICHD (R24HD041025) and the NIA (P30AG17266). The authors thank Robert Schoen and an anonymous reviewer for helpful comments on this manuscript.

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  1. Department of Sociology and Criminology, Penn State University, University Park, PA, 16802, USA

    Jason R. Thomas

  2. Department of Statistics, Penn State University, University Park, PA, 16802, USA

    Le Bao

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  1. Population Research Institute, Pennsylvania State University Population Research Institute, University Park, Pennsylvania, USA

    Robert Schoen

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Thomas, J.R., Bao, L. (2016). Modeling the Dynamics of an HIV Epidemic. In: Schoen, R. (eds) Dynamic Demographic Analysis. The Springer Series on Demographic Methods and Population Analysis, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-319-26603-9_6

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