Simulation based-inference of epidemiological and phylodynamic models via Neural Posterior Estimation

Mathematical models are essential for understanding and forecasting infectious disease dynamics, yet parameter inference remains challenging when likelihoods are intractable or unknown. Simulation-based inference (SBI) offers a powerful alternative by leveraging model simulations in place of explicit likelihood evaluations. However, traditional SBI approaches such as Approximate Bayesian Computation often rely on ad-hoc summary statistics and suffer from reduced efficiency in high-dimensional settings. Recent advances in SBI address these limitations by employing flexible statistical or machine-learning surrogates to approximate likelihoods or posterior distributions, improving scalability and accuracy. Neural Posterior Estimation (NPE), in particular, employs neural density estimators to learn the posterior directly from simulated data, automatically extracting informative representations without requiring handcrafted statistics. Despite its promise, NPE has seen limited application in infectious disease epidemiology and phylodynamics. In this study, we assess the ability of NPE to infer parameters in mechanistic models of infectious disease dynamics. Using data from the 2014 Ebola virus outbreak in Sierra Leone, we present two case studies reflecting common outbreak-analysis scenarios. First, we fit a compartmental Susceptible-Exposed-Infectious-Recovered transmission model to time series of reported cases and deaths. Second, we fit a Birth & Death phylodynamic model with exposed and infectious hosts to an early Ebola virus phylogeny. In both applications, NPE produces accurate and reliable posterior estimates. We further show that the amortized nature of NPE facilitates model calibration and criticism, enabling rapid assessment of model fit across multiple datasets. Our results highlight the potential of NPE as a flexible, scalable, and statistically principled tool for epidemiological and phylodynamic inference. Finally, we provide detailed online tutorials illustrating the NPE workflow in both applications.