Likelihood-based Inference for Dynamical Survival Analysis Epidemic Models

Abstract: Stochastic compartmental models are fundamental tools in epidemic modeling. A recent idea termed Dynamical Survival Analysis (DSA) replaces a stochastic population-level hazard in these models by its large population limit, yielding a more tractable approximation. We consider inferential considerations under this model framework, including marginal likelihoods that enable model fitting to partially observed surveillance data, and variance corrections to correct biased uncertainty estimates due to the deterministic approximation. We derive a remarkably simple expression for a likelihood given only case count data, and show that a Gaussian Process variation can reintroduce the missing variance component in a hierarchical model. These contributions allow for straightforward inference using generic statistical software such as STAN, and are applied to several case studies and simulated experiments.