# SIR-Hawkes: Linking Epidemic Models and Hawkes Processes to Model Diffusions in Finite Populations

arXiv: https://arxiv.org/abs/1711.01679 · HTML: https://mlsanity.com/paper/1711.01679/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2017.

## Built on by (most cited first, 17 of 17)

- [Long Horizon Forecasting With Temporal Point Processes](https://mlsanity.com/paper/2101.02815/) (2021)
- [On the Predictive Accuracy of Neural Temporal Point Process Models for Continuous-time Event Data](https://mlsanity.com/paper/2306.17066/) (2023)
- [Dynamic Hawkes Processes for Discovering Time-evolving Communities' States behind Diffusion Processes](https://mlsanity.com/paper/2105.11152/) (2021)
- [Integration-free Training for Spatio-temporal Multimodal Covariate Deep Kernel Point Processes](https://mlsanity.com/paper/2310.05485/) (2023)
- [Sequential change-point detection for mutually exciting point processes over networks](https://mlsanity.com/paper/2102.05724/) (2021)
- [Maximum Likelihood Estimation for Hawkes Processes with self-excitation or inhibition](https://mlsanity.com/paper/2103.05299/) (2021)
- [Interval-censored Hawkes processes](https://mlsanity.com/paper/2104.07932/) (2021)
- [Opinion Market Model: Stemming Far-Right Opinion Spread using Positive Interventions](https://mlsanity.com/paper/2208.06620/) (2022)
- [False Information, Bots and Malicious Campaigns: Demystifying Elements of Social Media Manipulations](https://mlsanity.com/paper/2308.12497/) (2023)
- [Linking Across Data Granularity: Fitting Multivariate Hawkes Processes to Partially Interval-Censored Data](https://mlsanity.com/paper/2111.02062/) (2021)
- [AutoCas: Autoregressive Cascade Predictor in Social Networks via Large Language Models](https://mlsanity.com/paper/2502.18040/) (2025)
- [Prior Knowledge-enhanced Spatio-temporal Epidemic Forecasting](https://mlsanity.com/paper/2602.22270/) (2026)
- [Continuous-Time Reinforcement Learning for Controlled Hawkes Jump-Diffusions](https://mlsanity.com/paper/2608.19151/) (2026)
- [Fine-Grained ε-Margin Closed-Form Stabilization of Parametric Hawkes Processes](https://mlsanity.com/paper/2105.03800/) (2021)
- [Incomplete Gamma Integrals for Deep Cascade Prediction using Content, Network, and Exogenous Signals](https://mlsanity.com/paper/2106.07012/) (2021)
- [CoviHawkes: Temporal Point Process and Deep Learning based Covid-19 forecasting for India](https://mlsanity.com/paper/2109.06056/) (2021)
- [Can a latent Hawkes process be used for epidemiological modelling?](https://mlsanity.com/paper/2208.07340/) (2022)

## Abstract (arXiv)

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.