Risk stratification in compartmental epidemic models: Where to draw the line?

Predicting the Effectiveness of Endemic Infectious Disease Control Interventions: The Impact of Mass Action versus Network Model Structure

BACKGROUND

Analyses of the effectiveness of infectious disease control interventions often rely on dynamic transmission models to simulate intervention effects. We aim to understand how the choice of network or compartmental model can influence estimates of intervention effectiveness in the short and long term for an endemic disease with susceptible and infected states in which infection, once contracted, is lifelong.

METHODS

We consider 4 disease models with different permutations of socially connected network versus unstructured contact (mass-action mixing) model and heterogeneous versus homogeneous disease risk. The models have susceptible and infected populations calibrated to the same long-term equilibrium disease prevalence. We consider a simple intervention with varying levels of coverage and efficacy that reduces transmission probabilities. We measure the rate of prevalence decline over the first 365 d after the intervention, long-term equilibrium prevalence, and long-term effective reproduction ratio at equilibrium.

RESULTS

Prevalence declined up to 10% faster in homogeneous risk models than heterogeneous risk models. When the disease was not eradicated, the long-term equilibrium disease prevalence was higher in mass-action mixing models than in network models by 40% or more. This difference in long-term equilibrium prevalence between network versus mass-action mixing models was greater than that of heterogeneous versus homogeneous risk models (less than 30%); network models tended to have higher effective reproduction ratios than mass-action mixing models for given combinations of intervention coverage and efficacy.

CONCLUSIONS

For interventions with high efficacy and coverage, mass-action mixing models could provide a sufficient estimate of effectiveness, whereas for interventions with low efficacy and coverage, or interventions in which outcomes are measured over short time horizons, predictions from network and mass-action models diverge, highlighting the importance of sensitivity analyses on model structure.

HIGHLIGHTS

• We calibrate 4 models-socially connected network versus unstructured contact (mass-action mixing) model and heterogeneous versus homogeneous disease risk-to 10% preintervention disease prevalence.• We measure the short- and long-term intervention effectiveness of all models using the rate of prevalence decline, long-term equilibrium disease prevalence, and effective reproduction ratio.• Generally, in the short term, prevalence declined faster in the homogeneous risk models than in the heterogeneous risk models.• Generally, in the long term, equilibrium disease prevalence was higher in the mass-action mixing models than in the network models, and the effective reproduction ratio was higher in network models than in the mass-action mixing models.

Incorporating equity in infectious disease modeling: Case study of a distributional impact framework for measles transmission

INTRODUCTION

Deterministic compartmental models of infectious diseases like measles typically reflect biological heterogeneities in the risk of infection and severity to characterize transmission dynamics. Given the known association of socioeconomic status and increased vulnerability to infection and mortality, it is also critical that such models further incorporate social heterogeneities.

METHODS

Here, we aimed to explore the influence of integrating income-associated differences in parameters of traditional dynamic transmission models. We developed a measles SIR model, in which the Susceptible, Infected and Recovered classes were stratified by income quintile, with income-specific transmission rates, disease-induced mortality rates, and vaccination coverage levels. We further provided a stylized illustration with secondary data from Ethiopia, where we examined various scenarios demonstrating differences in transmission patterns by income and in distributional vaccination coverage, and quantified impacts on disparities in measles mortality.

RESULTS

The income-stratified SIR model exhibited similar dynamics to that of the traditional SIR model, with amplified outbreak peaks and measles mortality among the poorest income group. All vaccination coverage strategies were found to substantially curb the overall number of measles deaths, yet most considerably for the poorest, with select strategies yielding clear reductions in measles mortality disparities.

DISCUSSION

The incorporation of income-specific differences can reveal distinct outbreak patterns across income groups and important differences in the subsequent effects of preventative interventions like vaccination. Our case study highlights the need to extend traditional modeling frameworks (e.g. SIR models) to be stratified by socioeconomic factors like income and to consider ensuing income-associated differences in disease-related morbidity and mortality. In so doing, we build on existing tools and characterize ongoing challenges in achieving health equity.

Developing a dynamic HIV transmission model for 6 U.S. cities: An evidence synthesis

BACKGROUND

Dynamic HIV transmission models can provide evidence-based guidance on optimal combination implementation strategies to treat and prevent HIV/AIDS. However, these models can be extremely data intensive, and the availability of good-quality data characterizing regional microepidemics varies substantially within and across countries. We aim to provide a comprehensive and transparent description of an evidence synthesis process and reporting framework employed to populate and calibrate a dynamic, compartmental HIV transmission model for six US cities.

METHODS

We executed a mixed-method evidence synthesis strategy to populate model parameters in six categories: (i) initial HIV-negative and HIV-infected populations; (ii) parameters used to calculate the probability of HIV transmission; (iii) screening, diagnosis, treatment and HIV disease progression; (iv) HIV prevention programs; (v) the costs of medical care; and (vi) health utility weights for each stage of HIV disease progression. We identified parameters that required city-specific data and stratification by gender, risk group and race/ethnicity a priori and sought out databases for primary analysis to augment our evidence synthesis. We ranked the quality of each parameter using context- and domain-specific criteria and verified sources and assumptions with our scientific advisory committee.

FINDINGS

To inform the 1,667 parameters needed to populate our model, we synthesized evidence from 59 peer-reviewed publications and 24 public health and surveillance reports and executed primary analyses using 11 data sets. Of these 1,667 parameters, 1,517 (91%) were city-specific and 150 (9%) were common for all cities. Notably, 1,074 (64%), 201 (12%) and 312 (19%) parameters corresponded to categories (i), (ii) and (iii), respectively. Parameters ranked as best- to moderate-quality evidence comprised 39% of the common parameters and ranged from 56%-60% across cities for the city-specific parameters. We identified variation in parameter values across cities as well as within cities across risk and race/ethnic groups.

CONCLUSIONS

Better integration of modelling in decision making can be achieved by systematically reporting on the evidence synthesis process that is used to populate models, and by explicitly assessing the quality of data entered into the model. The effective communication of this process can help prioritize data collection of the most informative components of local HIV prevention and care services in order to reduce decision uncertainty and strengthen model conclusions.

Structural Sensitivity in HIV Modeling: A Case Study of Vaccination

Structural assumptions in infectious disease models, such as the choice of network or compartmental model type or the inclusion of different types of heterogeneity across individuals, might affect model predictions as much as or more than the choice of input parameters. We explore the potential implications of structural assumptions on HIV model predictions and policy conclusions. We illustrate the value of inference robustness assessment through a case study of the effects of a hypothetical HIV vaccine in multiple population subgroups over eight related transmission models, which we sequentially modify to vary over two dimensions: parameter complexity (e.g., the inclusion of age and HCV comorbidity) and contact/simulation complexity (e.g., aggregated compartmental vs. individual/disaggregated compartmental vs. network models). We find that estimates of HIV incidence reductions from network models and individual compartmental models vary, but those differences are overwhelmed by the differences in HIV incidence between such models and the aggregated compartmental models (which aggregate groups of individuals into compartments). Complexities such as age structure appear to buffer the effects of aggregation and increase the threshold of net vaccine effectiveness at which aggregated models begin to overestimate reductions. The differences introduced by parameter complexity in estimated incidence reduction also translate into substantial differences in cost-effectiveness estimates. Parameter complexity does not appear to play a consistent role in differentiating the projections of network models.