Biased epidemic analysis due to heterogenous and partial surveillance: a study on deterministic and stochastic multi-class models for epidemic dynamics

This thesis investigates the impact of partial and heterogeneous detection on epidemic indicators in the context of outbreak analysis. Beginning with a deterministic SIR model, structured heterogeneity is introduced through contact-based risk classes, enabling a reformulation of key epidemiological quantities. The analysis is then extended to a stochastic network-based model, providing a more realistic account of variability, both in transmission dynamics and detection process. We examine how class-dependent detection probabilities distort observable trends, leading to significant bias in growth-based estimates. Correction strategies based on the spectral structure of the transmission process are developed and illustrated through deterministic simulations, and further explored within a stochastic setting to assess their qualitative robustness under realistic variability. The results support a robust and interpretable methodology for incorporating observational heterogeneity in epidemic assessment.