A Sensitivity-Based Framework for Infectious Disease Transmission Dynamics. Towards Multi-Objective Decision Support for Epidemic Management

Abstract

Population heterogeneity in social contact patterns, susceptibility, and disease progression strongly shapes infectious disease transmission, but its influence is often difficult to interpret in high-dimensional structured models. This thesis develops a sensitivity-based framework centred on the next-generation matrix (NGM) to clarify how changes in these mechanisms affect transmission potential and to explore how this understanding can support epidemic decision-making.

First, sensitivity and elasticity methods from matrix population theory are adapted to age-structured infectious disease models. The resulting indices exploit the eigenstructure of the NGM to quantify how perturbations in specific transmission pathways, contact patterns, epidemiological parameters, and population characteristics affect the reproduction number. This extends the use of the NGM beyond epidemic-threshold calculations towards an interpretable decomposition of structured transmission.

Second, the framework is applied longitudinally to SARS-CoV-2 transmission in Belgium. Time-indexed NGMs are constructed by combining social contact data with reconstructed age-specific susceptibility profiles. The analysis shows that the relative contributions of age groups changed substantially across pandemic phases as behaviour, immunity, interventions, and viral variants evolved. These findings caution against static interpretations of which population groups drive transmission and demonstrate the value of repeatedly applying local sensitivity analysis over time.

Finally, an age-structured stochastic transmission model is embedded within a multi-objective optimisation framework that simultaneously considers hospitalisation burden and educational loss. Applied retrospectively to Belgium, the framework identifies an estimated Pareto front and model-implied non-dominated contact-reduction schedules, including candidate alternatives that improve upon benchmark outcomes under the specified objectives and assumptions.

Together, these contributions provide a coherent progression from mechanistic interpretation to longitudinal epidemiological attribution and multi-objective decision support. The thesis demonstrates how structured modelling can make transmission mechanisms and intervention trade-offs more transparent, while emphasising that resulting conclusions remain conditional on model structure, data quality, reconstructed latent quantities, and uncertainty.