More on the cohort-component model of population projection in the context of HIV/AIDS: A Leslie matrix representation and new estimates

Abstract

This article presents an extension of the cohort-component model of population projection (CCMPP) first formulated by Heuveline (2003) that is capable of modeling a population affected by HIV. Heuveline proposes a maximum likelihood approach to estimate the age profile of HIV incidence that produced the HIV epidemics in East Africa during the 1990s. We extend this work by developing the Leslie matrix representation of the CCMPP, which greatly facilitates the implementation of the model for parameter estimation and projection. The Leslie matrix also contains information about the stable tendencies of the corresponding population, such as the stable age distribution and time to stability. Another contribution of this work is that we update the sources of data used to estimate the parameters, and use these data to estimate a modified version of the CCMPP that includes (estimated) parameters governing the survival experience of the infected population. A further application of the model to a small population with high HIV prevalence in rural South Africa is presented as an additional demonstration. This work lays the foundation for development of more robust and flexible Bayesian estimation methods that will greatly enhance the utility of this and similar models.

Figure 1

Age-specific HIV incidence rates, i_a,t, for different values of the population-specific scale parameter, H, over time

Figure 2

Estimated mortality rates for Uganda based on CCMPP parameter estimates for survivorship model (method 1) and the Weibull model (method 2), and model age-specific mortality patterns estimated from Żaba et al. (2007) Note: See text for more details. Żaba1 – HIV prevalence is not declining, ratio of HIV prevalence among the dead to prevalence among the living < 4; Żaba2 – HIV prevalence is declining, ratio < 4; Żaba3 – HIV prevalence is not declining, ratio > 4; Żaba4 – HIV prevalence is declining, ratio > 4.

Figure 3

A comparison of age patterns of annual HIV incidence rates in East Africa estimated CCMPP estimates (grey lines) to those estimated by Żaba et al. (2008) (black lines)

Figure 4

Projected prevalence over time for women aged 15-50 Note: The horizontal and vertical dashed lines indicate the prevalence and year, respectively, from the observed data.

Figure 5

Projected prevalence over time for men aged 15-54 Note: The horizontal and vertical dashed lines indicate the prevalence and year, respectively, from the observed data.

Figure 6

Projected population pyramids at 25 year intervals for KwaZulu-Natal South Africa Note: The white bars indicate the proportion of the population in each age group (HIV− and HIV+ combined), while the black bars indicate the proportion of the total population who are HIV+ in each age group. 95% confidence intervals are depicted by the dots.