Formulating likelihood functions for infectious disease dynamics for neglected tropical diseases

Reliable inference in infectious disease modelling requires careful treatment of both model structure and the relationship between latent infection dynamics and observed data. Likelihood functions, which link model parameters to empirical observations, can be formulated either to explicitly represent underlying disease transmission and reporting processes (process-based) or to summarize statistical patterns in aggregated outcomes (observation-based). Stochastic models capture inherent variability in transmission and detection, whereas deterministic models describe average system behaviour and often rely on statistical assumptions to account for residual uncertainty. Using two neglected tropical disease models, we compare parameter estimation based on complete individual-level events with inference using aggregated counts. By generating synthetic outbreak data from stochastic simulations and analyzing it under alternative modelling frameworks, we show how different combinations of model formulation and likelihood structure influence both point estimates and uncertainty quantification. Our findings indicate that, even when detailed process information is unavailable, observation-based likelihoods can produce robust parameter estimates and credible uncertainty intervals, highlighting their usefulness for practical decision-making in contexts with limited or aggregated surveillance data.