A time-modulated Hawkes process to model the spread of COVID-19 and the impact of countermeasures

Abstract

Motivated by the recent outbreak of coronavirus (COVID-19), we propose a stochastic model of epidemic temporal growth and mitigation based on a time-modulated Hawkes process. The model is sufficiently rich to incorporate specific characteristics of the novel coronavirus, to capture the impact of undetected, asymptomatic and super-diffusive individuals, and especially to take into account time-varying counter-measures and detection efforts. Yet, it is simple enough to allow scalable and efficient computation of the temporal evolution of the epidemic, and exploration of what-if scenarios. Compared to traditional compartmental models, our approach allows a more faithful description of virus specific features, such as distributions for the time spent in stages, which is crucial when the time-scale of control (e.g., mobility restrictions) is comparable to the lifetime of a single infection. We apply the model to the first and second wave of COVID-19 in Italy, shedding light onto several effects related to mobility restrictions introduced by the government, and to the effectiveness of contact tracing and mass testing performed by the national health service.

Infinite-server systems with Hawkes arrivals and Hawkes services

“…This is essentially observed, during periods of suffering, for instance, earthquakes, crime and riots and social media trend (Daw and Pender [8] and Rizoiu et al [20]) and in the financial market, incorporating some kind of contagion effect (Aït-Sahalia et al [1]). Recently, the same phenomenon is observed to describe the temporal growth and migration of COVID-19 (see Chiang et al [6], Escobar [12], Garetto et al [13]). The work by Eick et al [9], and recent works by Daw and Pender [8] and Koops et al [16], motivated us to consider the service process as a state-dependent Hawkes (sdHawkes) process.…”

Spatiotemporal Clustering with Neyman-Scott Processes via Connections to Bayesian Nonparametric Mixture Models

“…For example, Hawkes processes [Hawkes, 1971] produce clusters via a self-excitatory model: each event increases the probability of subsequent events. There has been a resurgence of interest in these models, and recent work has generalized the basic Hawkes process [Wang et al, 2012, Zhou et al, 2013, Linderman and Adams, 2014, Wu et al, 2019, Dutta et al, 2020, established new theory [Chen et al, 2017a], incorporated neural networks into the model [Mei and Eisner, 2016, Zuo et al, 2020, Zhang et al, 2020a, developed new inference and estimation algorithms [Simma and Jordan, 2010, Halpin, 2012, Rasmussen, 2013, Wheatley et al, 2016, Chen et al, 2017b, Shelton et al, 2018, Kirchner and Bercher, 2018, Zhang et al, 2020b, and specialized them to new domains like email and social media exchanges [Gomez-Rodriguez et al, 2010, Blundell et al, 2012, Farajtabar et al, 2015, Guo et al, 2015, He et al, 2015, Kobayashi and Lambiotte, 2016, Li et al, 2017, Mohler et al, 2018, online education [Jiang et al, 2021], crime modeling [Mohler et al, 2011], biology [Carstensen et al, 2010, Verma et al, 2021, healthcare , and epidemiology [Choi et al, 2015, Garetto et al, 2021, Chiang et al, 2021. One advantage of Hawkes processes is that parameters can often be inferred by simple maximum likelihood estimation.…”

COVID-19 epidemic control using short-term lockdowns for collective gain

“…Our analysis provides important insights as how to implement lockdowns of brief duration to control SARS-CoV-2 dynamics, a problem also discussed e.g. in (Sadeghi et al, 2021;Borri et al, 2021;Garetto et al, 2021), leading to further insights on their merits and possible limitations. The health system's target should be to maintain the number of people infected or in intensive care below a certain level, see also recent works on control of SARS-CoV-2 like (Gondim and Machado, 2020;Tsay et al, 2020;Kohler et al, 2021;Berger, 2020).…”