UCLA

The self-exciting Hawkes point process model (Hawkes, 1971) has been used to describe and forecast communicable diseases. In this dissertation, there are two parts. First, we introduce the non-parametric version of the recursive model (Schoenberg, 2019), an adaptation of the Hawkes model which allows for variable productivity, or disease reproduction rate. Here, we extend the data-driven non-parametric EM method of Marsan & Lenglin� (2008) in order to fit the recursive model without assuming a particular functional form for the productivity. We then evaluate the ability of the non-parametric recursive model to fit and forecast cases of mumps in Pennsylvania compared to that of other point process models and a variation of the commonly used SIR (Susceptible, Infected, Recovered) compartmental model. Second, we examine increasing surges of the COVID-19 pandemic using the HawkesN model with an exponential kernel (Rizoiu et. al., 2018), which assumes a finite susceptible population, is considered stationary when the reproduction number K is greater than one, and has interpretable terms similar to that of the SIR model (Kresin et. al., 2021). The HawkesN model is fit using a least squares method introduced in Schoenberg (2021), which is an effective method when an epidemiologic dataset only provides a daily case count rather than a specific time of infection. We first examine doubling time of COVID-19 in California during three notable surges using the HawkesN model and compare its predictive ability to that of an adaptation of the SIR compartmental model. Secondly, we compare HawkesN to the same compartmental model in forecasting cases of SARS-COV-2 for all fifty states nationwide. This larger study is to guide further work in improving the predictive ability of HawkesN.