Nonparametric estimation of recursive point processes with application to mumps in Pennsylvania

The self-exciting Hawkes point process model (Hawkes, 1971) has been used to describe and forecast communicable diseases. A variant of the Hawkes model, called the recursive model, was proposed by Schoenberg et al. (2019) and has been shown to fit well to various epidemic disease datasets. Unlike the Hawkes model, the recursive model allows the productivity to vary as the overall rate of incidence of the disease varies. Here, we extend the data-driven nonparametric expectation-maximization method of Marsan and Lengliné (2008) in order to fit the recursive model without assuming a particular functional form for the productivity. The nonparametric recursive model is trained to fit to weekly reported cases of mumps in Pennsylvania during the January 1970-September 1990 time frame and then assessed using one week forecasts for the October 1990-December 2001 time period. Both its training and predictive ability are evaluated compared to that of other candidate models, such as Hawkes and SVEILR (susceptible, vaccinated, exposed, infected, lightly infected, recovered) compartmental models.