An Environmentally-Adaptive Hawkes Process with An Application to COVID-19

TL;DR

This paper introduces an environmentally-adaptive Hawkes (EAH) model that incorporates environmental factors and dynamic branching to better model complex temporal processes like COVID-19 spread.

Contribution

The paper presents a generalized Hawkes process with environmental multipliers and demonstrates its application to COVID-19 data, outperforming classical models.

Findings

EAH model is more flexible than classical Hawkes process.

The model effectively captures environmental influences on event dynamics.

It outperforms traditional Hawkes models in modeling COVID-19 data.

Abstract

We proposed a new generalized model based on the classical Hawkes process with environmental multipliers, which is called an environmentally-adaptive Hawkes (EAH) model. Compared to the classical self-exciting Hawkes process, the EAH model exhibits more flexibility in a macro environmentally temporal sense, and can model more complex processes by using dynamic branching matrix. We demonstrate the well-definedness of this EAH model. A more specified version of this new model is applied to model COVID-19 pandemic data through an efficient EM-like algorithm. Consequently, the proposed model consistently outperforms the classical Hawkes process.