Age Group Sensitivity Analysis of Epidemic Models: Investigating the Impact of Contact Matrix Structure

TL;DR

The paper addresses the challenge of epistemic uncertainty in age-structured contact matrices by introducing AGSA, a framework that couples age-stratified transmission dynamics with Latin Hypercube Sampling and Partial Rank Correlation Coefficient analysis. It collects 136 independent contact-pattern parameters, propagates them through two representative epidemic frameworks, and aggregates sensitivity by age to identify which groups most influence key outcomes such as $\mathcal{R}_0$, peak burden, and fatalities. A novel aggregation method weights age-group sensitivities by their statistical reliability, producing robust age-specific guidance. The work demonstrates how sensitivity patterns shift with outbreak severity and offers a data-collection blueprint to reduce uncertainty, enhancing forecasting and informing targeted public health interventions.

Abstract

Understanding the role of different age groups in disease transmission is crucial for designing effective intervention strategies. A key parameter in age-structured epidemic models is the contact matrix, which defines the interaction structure between age groups. However, accurately estimating contact matrices is challenging, as different age groups respond differently to surveys and are accessible through different channels. This variability introduces significant epistemic uncertainty in epidemic models. In this study, we introduce the Age Group Sensitivity Analysis (AGSA) method, a novel framework for assessing the impact of age-structured contact patterns on epidemic outcomes. Our approach integrates age-stratified epidemic models with Latin Hypercube Sampling (LHS) and the Partial Rank Correlation Coefficient (PRCC) method, enabling a systematic sensitivity analysis of age-specific interactions. Additionally, we propose a new sensitivity aggregation technique that quantifies the contribution of each age group to key epidemic parameters. By identifying the age groups to which the model is most sensitive, AGSA helps pinpoint those that introduce the greatest epistemic uncertainty. This allows for targeted data collection efforts, focusing surveys and empirical studies on the most influential age groups to improve model accuracy. As a result, AGSA can enhance epidemic forecasting and inform the design of more effective and efficient public health interventions.

Figures (5)

• Figure 1: Workflow of the AGSA framework. The input parameters include the contact matrix (CM) describing the interaction structure of the population and additional model parameters. Using Latin Hypercube Sampling (LHS), an ensemble of sampled contact matrices is generated and used with the epidemic model to calculate target variable values. Partial Rank Correlation Coefficient (PRCC) analysis is performed on these results to derive sensitivity measures, which are then aggregated by age group to determine group-specific sensitivities. Outputs include sensitivity data and visualizations.
• Figure 2: Contact matrices representing the social contact patterns in Hungary, estimated in prem2021projecting. The full contact matrix is the sum of the available, environment-specific matrices showing the distribution of all contacts among the age groups.
• Figure 3: Demonstrations of the AGSA framework in the Influenza model by Pitman et al. Target parameter: number of infected individuals at the epidemic's peak. Top row: mild influenza outbreak with $\mathcal{R}_0=1.2$, bottom row: severe outbreak with $\mathcal{R}_0=2.5$. In both cases, the target variable is the number of infected individuals at the epidemic's peak. Left panels: pairwise PRCC values and associated p-values for the sensitivity analysis of contact matrix elements. Notice that both the diagonal of the PRCC matrix and the p-value matrix (Eq. \ref{['eq:PRC_mtx']} and \ref{['eq:p-val_mtx']}) are shown on these panels. Right panels: aggregated PRCC values by age group.
• Figure 4: Aggregated sensitivity values ($P$) and corresponding confidence intervals (CI) across age groups for different target variables in mild ($\mathcal{R}_0 = 1.2$, top row) and severe ($\mathcal{R}_0 = 2.5$, bottom row) epidemic scenarios. The target variables include the basic reproduction number ($\mathcal{R}_0$), ICU peak occupancy, and cumulative fatalities. The legend on the bottom right figure applies to all.
• Figure B.5: Diagram of the transmission model from rost2020early utilized to illustrate the proposed framework. Solid black arrows represent the movement of patients between compartments, whereas dashed arrows show potential pathways for the spread of infection.