Dynamic survival analysis for non-Markovian epidemic models

We present a new method for analyzing stochastic epidemic models under minimal assumptions. The method, dubbed Dynamic Survival Analysis (DSA), is based on a simple yet powerful observation, namely that populationlevel mean-field trajectories described by a system of Partial Differential Equations (PDEs) may also approximate individual-level times of infection and recovery. This idea gives rise to a certain non-Markovian agent-based model and provides an agent-level likelihood function for a random sample of infection and/or recovery times. Extensive numerical analyses on both synthetic and real epidemic data from the Foot-and-Mouth Disease (FMD) in the United Kingdom and the COVID-19 in India show good accuracy and confirm method’s versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modeling, analyzing and interpreting epidemic data with the help of the DSA approach.