Multiphasic stochastic epidemic models

Abstract At the onset of the COVID-19 pandemic, various non-pharmaceutical interventions aimed to reduce infection levels, leading to multiple phases of transmission. The disease reproduction number, Rt, quantifies transmissibility and is central to evaluating these interventions. This article discusses hierarchical stochastic epidemic models with piece-wise constant Rt, suitable for capturing distinct epidemic phases and estimating disease magnitude. The timing and scale of Rt changes are inferred from data, while the number of phases is allowed to vary. The model uses Poisson point processes and Dirichlet process components to learn the number of phases, providing insight into epidemic dynamics. We test the models on synthetic data and apply them to freely available data from the UK, Greece, California, and New York. We estimate the true number of infections and Rt and independently validate this approach via a large seroprevalence study. The results show that key disease characteristics can be derived from publicly available data without imposing strong assumptions.