A Novel Point Process Model for COVID-19: Multivariate Recursive Hawkes Process

Jan 1, 2022·
Bohan Chen
,
Pujan Shrestha
,
Andrea L. Bertozzi
,
George Mohler
,
Frederic Schoenberg
· 1 min read
Abstract
This chapter presents a novel point process model for COVID-19 transmission—the multivariate recursive Hawkes process, which is an extension of the recursive Hawkes model to the multivariate case. Equivalently the model can be viewed as an extension of the multivariate Hawkes model to allow for varying productivity as in the recursive model. Several theoretical properties of this process are stated and proved, including the existence of the multivariate recursive counting process and formulas for the mean and variance. EM-based algorithms are explored for estimating parameters of parametric and semi-parametric forms of the model. Additionally, an algorithm is presented to reconstruct the process from imprecise event times. The performance of the algorithms on both synthetic and real COVID-19 data sets is illustrated through several experiments.
Type
Publication
Predicting Pandemics in a Globally Connected World, Volume 1: Toward a Multiscale, Multidisciplinary Framework through Modeling and Simulation

The multivariate recursive Hawkes process extends self-exciting point-process models in two directions needed for epidemic data: transmission can interact across multiple populations, and the productivity of events can vary recursively rather than remaining fixed. This gives the model enough flexibility to represent heterogeneous and evolving COVID-19 transmission patterns.

The chapter establishes existence of the counting process and derives its first two moments. It also develops expectation-maximization procedures for parametric and semiparametric specifications, together with a reconstruction algorithm for observations whose event times are reported only coarsely.

Synthetic experiments validate the estimators, and applications to real COVID-19 data illustrate how the model recovers cross-population excitation and time-varying transmission effects from imperfect public-health records.

COVID-19 Expectation-Maximization Hawkes Processes Infectious Disease Modeling Point Processes Spatiotemporal Statistics