Assessment of epidemic projections using recent HIV survey data in South Africa: a validation analysis of ten mathematical models of HIV epidemiology in the antiretroviral therapy era

Background Mathematical models are widely used to simulate the eff ects of interventions to control HIV and to project future epidemiological trends and resource needs. We aimed to validate past model projections against data from a large household survey done in South Africa in 2012. Methods We compared ten model projections of HIV prevalence, HIV incidence, and antiretroviral therapy (ART) coverage for South Africa with estimates from national household survey data from 2012. Model projections for 2012 were made before the publication of the 2012 household survey. We compared adult (age 15–49 years) HIV prevalence in 2012, the change in prevalence between 2008 and 2012, and prevalence, incidence, and ART coverage by sex and by age groups between model projections and the 2012 household survey. Findings All models projected lower prevalence estimates for 2012 than the survey estimate (18·8%), with eight models’ central projections being below the survey 95% CI (17·5–20·3). Eight models projected that HIV prevalence would remain unchanged (n=5) or decline (n=3) between 2008 and 2012, whereas prevalence estimates from the household surveys increased from 16·9% in 2008 to 18·8% in 2012 (diff erence 1·9, 95% CI –0·1 to 3·9). Model projections accurately predicted the 1·6 percentage point prevalence decline (95% CI –0·3 to 3·5) in young adults aged 15–24 years, and the 2·2 percentage point (0·5 to 3·9) increase in those aged 50 years and older. Models accurately represented the number of adults on ART in 2012; six of ten models were within the survey 95% CI of 1·54–2·12 million. However, the diff erential ART coverage between women and men was not fully captured; all model projections of the sex ratio of women to men on ART were lower than the survey estimate of 2·22 (95% CI 1·73–2·71). Interpretation Projections for overall declines in HIV epidemics during the ART era might have been optimistic. Future treatment and HIV prevention needs might be greater than previously forecasted. Additional data about service provision for HIV care could help inform more accurate projections

Assessment of epidemic projections using recent HIV survey data in South Africa: A validation analysis of ten mathematical models of HIV epidemiology in the antiretroviral therapy era

Background: Mathematical models are widely used to simulate the effects of interventions to control HIV and to project future epidemiological trends and resource needs. We aimed to validate past model projections against data from a large household survey done in South Africa in 2012. Methods: We compared ten model projections of HIV prevalence, HIV incidence, and antiretroviral therapy (ART) coverage for South Africa with estimates from national household survey data from 2012. Model projections for 2012 were made before the publication of the 2012 household survey. We compared adult (age 15-49 years) HIV prevalence in 2012, the change in prevalence between 2008 and 2012, and prevalence, incidence, and ART coverage by sex and by age groups between model projections and the 2012 household survey. Findings: All models projected lower prevalence estimates for 2012 than the survey estimate (18·8%), with eight models' central projections being below the survey 95% CI (17·5-20·3). Eight models projected that HIV prevalence would remain unchanged (n=5) or decline (n=3) between 2008 and 2012, whereas prevalence estimates from the household surveys increased from 16·9% in 2008 to 18·8% in 2012 (difference 1·9, 95% CI -0·1 to 3·9). Model projections accurately predicted the 1·6 percentage point prevalence decline (95% CI -0·3 to 3·5) in young adults aged 15-24 years, and the 2·2 percentage point (0·5 to 3·9) increase in those aged 50 years and older. Models accurately represented the number of adults on ART in 2012; six of ten models were within the survey 95% CI of 1·54-2·12 million. However, the differential ART coverage between women and men was not fully captured; all model projections of the sex ratio of women to men on ART were lower than the survey estimate of 2·22 (95% CI 1·73-2·71). Interpretation: Projections for overall declines in HIV epidemics during the ART era might have been optimistic. Future treatment and HIV prevention needs might be greater than previously forecasted. Additional data about service provision for HIV care could help inform more accurate projections. Funding: Bill & Melinda Gates Foundation

Assessment of epidemic projections using recent HIV survey data in South Africa: a validation analysis of ten mathematical models of HIV epidemiology in the antiretroviral therapy era

Background: Mathematical models are widely used to simulate the effects of interventions to control HIV and to project future epidemiological trends and resource needs. We aimed to validate past model projections against data from a large household survey done in South Africa in 2012. Methods: We compared ten model projections of HIV prevalence, HIV incidence, and antiretroviral therapy (ART) coverage for South Africa with estimates from national household survey data from 2012. Model projections for 2012 were made before the publication of the 2012 household survey. We compared adult (age 15–49 years) HIV prevalence in 2012, the change in prevalence between 2008 and 2012, and prevalence, incidence, and ART coverage by sex and by age groups between model projections and the 2012 household survey. Findings: All models projected lower prevalence estimates for 2012 than the survey estimate (18·8%), with eight models' central projections being below the survey 95% CI (17·5–20·3). Eight models projected that HIV prevalence would remain unchanged (n=5) or decline (n=3) between 2008 and 2012, whereas prevalence estimates from the household surveys increased from 16·9% in 2008 to 18·8% in 2012 (difference 1·9, 95% CI −0·1 to 3·9). Model projections accurately predicted the 1·6 percentage point prevalence decline (95% CI −0·3 to 3·5) in young adults aged 15–24 years, and the 2·2 percentage point (0·5 to 3·9) increase in those aged 50 years and older. Models accurately represented the number of adults on ART in 2012; six of ten models were within the survey 95% CI of 1·54–2·12 million. However, the differential ART coverage between women and men was not fully captured; all model projections of the sex ratio of women to men on ART were lower than the survey estimate of 2·22 (95% CI 1·73–2·71). Interpretation: Projections for overall declines in HIV epidemics during the ART era might have been optimistic. Future treatment and HIV prevention needs might be greater than previously forecasted. Additional data about service provision for HIV care could help inform more accurate projections. Funding: Bill & Melinda Gates Foundation

Set-Based Analysis for Biological Modeling

International audienceThe understanding of biological systems and processes requires the development of dynamical models characterized by nonlinear laws and often intricate regulation architectures. Differential and difference equations are common formalisms to characterize such systems. Hybrid dynamical systems come in handy when the modeled system combines continuous and discrete evolutions or different evolution modes such as where slow evolution phases are interrupted by fast ones. Biological data with kinetic content are often scarce, thus it can be appropriate to reason in terms of sets of (parametrized) models and sets of trajectories. In doing so, uncertainties and lack of knowledge are explicitly taken into account and more reliable predictions can be made. A crucial problem in Systems Biology is thus to identify regions of parameter space for which model behavior is consistent with experimental observations. In this chapter, we investigate the use of set-based analysis techniques, designed to compute on sets of behaviors, for the validation of biological models under uncertainties and perturbations. In addition, these techniques can be used for the synthesis of model parameter sets, so that the execution of the considered biological model under the influence of the synthesized parameters is guaranteed to satisfy a given constraint or property. The proposed approach is illustrated by several case studies, namely a model of iron homeostasis in mammalian cells and some epidemic models

Set-Based Analysis for Biological Modeling

The understanding of biological systems and processes requires the development of dynamical models characterized by nonlinear laws and often intricate regulation architectures. Differential and difference equations are common formalisms to characterize such systems. Hybrid dynamical systems come in handy when the modeled system combines continuous and discrete evolutions or different evolution modes such as where slow evolution phases are interrupted by fast ones. Biological data with kinetic content are often scarce, thus it can be appropriate to reason in terms of sets of (parametrized) models and sets of trajectories. In doing so, uncertainties and lack of knowledge are explicitly taken into account and more reliable predictions can be made. A crucial problem in Systems Biology is thus to identify regions of parameter space for which model behavior is consistent with experimental observations. In this chapter, we investigate the use of set-based analysis techniques, designed to compute on sets of behaviors, for the validation of biological models under uncertainties and perturbations. In addition, these techniques can be used for the synthesis of model parameter sets, so that the execution of the considered biological model under the influence of the synthesized parameters is guaranteed to satisfy a given constraint or property. The proposed approach is illustrated by several case studies, namely a model of iron homeostasis in mammalian cells and some epidemic models