Can a latent Hawkes process be used for epidemiological modelling?

TL;DR

This paper introduces a novel epidemic modeling approach using a latent Hawkes process with covariates, enabling infection source estimation and future case prediction, demonstrated on synthetic and real COVID-19 data.

Contribution

The paper presents a new epidemic model based on a latent Hawkes process with a Kernel Density Particle Filter for inference and prediction.

Findings

Effective on synthetic data

Accurate COVID-19 case predictions

Benchmark outperforming alternative models

Abstract

Understanding the spread of COVID-19 has been the subject of numerous studies, highlighting the significance of reliable epidemic models. Here, we introduce a novel epidemic model using a latent Hawkes process with temporal covariates for modelling the infections. Unlike other models, we model the reported cases via a probability distribution driven by the underlying Hawkes process. Modelling the infections via a Hawkes process allows us to estimate by whom an infected individual was infected. We propose a Kernel Density Particle Filter (KDPF) for inference of both latent cases and reproduction number and for predicting the new cases in the near future. The computational effort is proportional to the number of infections making it possible to use particle filter type algorithms, such as the KDPF. We demonstrate the performance of the proposed algorithm on synthetic data sets and COVID-19 reported cases in various local authorities in the UK, and benchmark our model to alternative approaches.