Real-time predictions of the 2018–2019 Ebola virus disease outbreak in the Democratic Republic of the Congo using Hawkes point process models

Abstract

As of June 16, 2019, an Ebola virus disease (EVD) outbreak has led to 2136 reported cases in the northeastern region of the Democratic Republic of the Congo (DRC). As this outbreak continues to threaten the lives and livelihoods of people already suffering from civil strife and armed conflict, relatively simple mathematical models and their short-term predictions have the potential to inform Ebola response efforts in real time. We applied recently developed non-parametrically estimated Hawkes point processes to model the expected cumulative case count using daily case counts from May 3, 2018, to June 16, 2019, initially reported by the Ministry of Health of DRC and later confirmed in World Health Organization situation reports. We generated probabilistic estimates of the ongoing EVD outbreak in DRC extending both before and after June 16, 2019, and evaluated their accuracy by comparing forecasted vs. actual outbreak sizes, out-of-sample log-likelihood scores and the error per day in the median forecast. The median estimated outbreak sizes for the prospective thee-, six-, and nine-week projections made using data up to June 16, 2019, were, respectively, 2317 (95% PI: 2222, 2464); 2440 (95% PI: 2250, 2790); and 2544 (95% PI: 2273, 3205). The nine-week projection experienced some degradation with a daily error in the median forecast of 6.73 cases, while the six- and three-week projections were more reliable, with corresponding errors of 4.96 and 4.85 cases per day, respectively. Our findings suggest the Hawkes point process may serve as an easily-applied statistical model to predict EVD outbreak trajectories in near real-time to better inform decision-making and resource allocation during Ebola response efforts.

Simple discrete-time self-exciting models can describe complex dynamic processes: a case study of COVID-19

“…More-over, a prediction is only realistic in the short term and generally only at times where there is no evidence of abnormal behaviour. This is consistent with other models in the literature [33,34,54–56]. Thus we consider in-sample and out-of-sample posterior predictive checks in this study as a measure of model fit only.…”

“…Hawkes processes have been successfully applied to model epidemics and infectious diseases. For example, for the Ebola outbreaks in West Africa and the Democratic Republic of Congo [33, 34], the Hawkes process is found to outperform the SEIR (Susceptible-Exposed-Infected-Recovered) mechanistic model in terms of short term prediction. Another study employs an extension of the multivariate Hawkes process to understand the transmission routes and regional connectivity for the dengue fever outbreak across regions in Australia [35].…”

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

“…We mention that branching processes of various kind, including Hawkes processes, have been proposed in various biological contexts ( Bertozzi et al, 2020 , Kelly et al, 2019 , Kim et al, 2019 , Kimmel and Axelrod, 2002 , Mei and Eisner, 2017 , Mohler et al, 2021 , Montagnon, 2019 , Park et al, 2020 , Schoenberg et al, 2019 , Xu and Zha, 2017 ). In particular ( Kelly et al, 2019 , Mohler et al, 2021 , Schoenberg et al, 2019 ) propose stationary and non-stationary Hawkes models (i.e., Hawkes processes with time-varying kernels) to model the outbreak of several epidemics, such as Ebola and COVID-19. In Bertozzi et al (2020) authors proposed a first comparison of SIR, SEIR, and Hawkes (with Gamma or Weibull kernels) to forecast the spread of COVID-19.…”

COVID-19 Outbreak Prediction with Machine Learning

“…The modeling strategy is formed around the assumption of transmitting the infectious disease through contacts, considering three different classes of well-mixed populations; susceptible to infection (class S), infected (class I), and the removed population (class R is devoted to those who have recovered, developed immunity, been isolated or passed away). It is further assumed that the class I transmits the infection to class S where the number of probable transmissions is proportional to the total number of contacts [9][10][11]. The number of individuals in the class S progresses as a time-series, often computed using a basic differential equation as follows:…”