Among the statistical tools for online information diffusion modeling, both
epidemic models and Hawkes point processes are popular choices. The former
originate from epidemiology, and consider information as a viral contagion
which spreads into a population of online users. The latter have roots in
geophysics and finance, view individual actions as discrete events in
continuous time, and modulate the rate of events according to the self-exciting
nature of event sequences. Here, we establish a novel connection between these
two frameworks. Namely, the rate of events in an extended Hawkes model is
identical to the rate of new infections in the Susceptible-Infected-Recovered
(SIR) model after marginalizing out recovery events -- which are unobserved in
a Hawkes process. This result paves the way to apply tools developed for SIR to
Hawkes, and vice versa. It also leads to HawkesN, a generalization of the
Hawkes model which accounts for a finite population size. Finally, we derive
the distribution of cascade sizes for HawkesN, inspired by methods in
stochastic SIR. Such distributions provide nuanced explanations to the general
unpredictability of popularity: the distribution for diffusion cascade sizes
tends to have two modes, one corresponding to large cascade sizes and another
one around zero.

研究了在线信息传播建模的统计工具，发现在 Hawkes 模型中，扩展事件的频率与 SIR 模型中的新感染率相同，并导出了 HawkesN 的级联大小分布。