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

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.