Dynamic Survival Analysis for non-Markovian Epidemic Models

TL;DR

This paper introduces DSA, a novel method for analyzing non-Markovian epidemic models that leverages PDE-based mean-field trajectories to approximate individual infection and recovery times, enabling likelihood-based inference.

Contribution

The paper presents DSA, a new approach that connects population-level PDE models with individual-level epidemic data, extending analysis capabilities to non-Markovian models.

Findings

DSA accurately estimates parameters from synthetic data.

DSA effectively analyzes real epidemic data from FMD and COVID-19.

The software implementation facilitates practical epidemic data analysis.

Abstract

We present a new method for analyzing stochastic epidemic models under minimal assumptions. The method, dubbed DSA, is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of PDE 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 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.