Approximation of Bayesian Hawkes process with inlabru

Hawkes process are very popular mathematical tools for modeling phenomena exhibiting a self-exciting or self-correcting behavior. Typical examples are earthquakes occurrence, wild-fires, drought, capture-recapture, crime violence, trade exchange, and social network activity. The widespread use of Hawkes process in different fields calls for fast, reproducible, reliable, easy-to-code techniques to implement such models. We offer a technique to perform approximate Bayesian inference of Hawkes process parameters based on the use of the R-package inlabru . The inlabru R-package, in turn, relies on the INLA methodology to approximate the posterior of the parameters. Our Hawkes process approximation is based on a decomposition of the log-likelihood in three parts, which are linearly approximated separately. The linear approximation is performed with respect to the mode of the parameters' posterior distribution, which is determined with an iterative gradient-based method. The approximation of the posterior parameters is therefore deterministic, ensuring full reproducibility of the results. The proposed technique only requires the user to provide the functions to calculate the different parts of the decomposed likelihood, which are internally linearly approximated by the R-package inlabru . We provide a comparison with the bayesianETAS R-package which is based on an MCMC method. The two techniques provide similar results but our approach requires two to ten times less computational time to converge, depending on the amount of data.

Intensity of COVID-19 in care homes following hospital discharge in the early stages of the UK epidemic.

BACKGROUND: defining features of the COVID-19 pandemic in many countries were the tragic extent to which care home residents were affected and the difficulty in preventing the introduction and subsequent spread of infection. Management of risk in care homes requires good evidence on the most important transmission pathways. One hypothesised route at the start of the pandemic, prior to widespread testing, was the transfer of patients from hospitals that were experiencing high levels of nosocomial events. METHODS: we tested the hypothesis that hospital discharge events increased the intensity of care home cases using a national individually linked health record cohort in Wales, UK. We monitored 186,772 hospital discharge events over the period from March to July 2020, tracking individuals to 923 care homes and recording the daily case rate in the homes populated by 15,772 residents. We estimated the risk of an increase in case rates following exposure to a hospital discharge using multi-level hierarchical logistic regression and a novel stochastic Hawkes process outbreak model. FINDINGS: in regression analysis, after adjusting for care home size, we found no significant association between hospital discharge and subsequent increases in care home case numbers (odds ratio: 0.99, 95% CI: 0.82, 1.90). Risk factors for increased cases included care home size, care home resident density and provision of nursing care. Using our outbreak model, we found a significant effect of hospital discharge on the subsequent intensity of cases. However, the effect was small and considerably less than the effect of care home size, suggesting the highest risk of introduction came from interaction with the community. We estimated that approximately 1.8% of hospital discharged patients may have been infected. INTERPRETATION: there is growing evidence in the UK that the risk of transfer of COVID-19 from the high-risk hospital setting to the high-risk care home setting during the early stages of the pandemic was relatively small. Although access to testing was limited to initial symptomatic cases in each care home at this time, our results suggest that reduced numbers of discharges, selection of patients and action taken within care homes following transfer all may have contributed to the mitigation. The precise key transmission routes from the community remain to be quantified.

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

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.