Optimizing the timing of an end-of-outbreak declaration: Ebola virus disease in the Democratic Republic of the Congo

Abstract

Following the apparent final case in an Ebola virus disease (EVD) outbreak, the decision to declare the outbreak over must balance societal benefits of relaxing interventions against the risk of resurgence. Estimates of the end-of-outbreak probability (the probability that no future cases will occur) provide quantitative evidence that can inform the timing of an end-of-outbreak declaration. An existing modeling approach for estimating the end-of-outbreak probability requires comprehensive contact tracing data describing who infected whom to be available, but such data are often unavailable or incomplete during outbreaks. Here, we develop a Markov chain Monte Carlo-based approach that extends the previous method and does not require contact tracing data. Considering data from two EVD outbreaks in the Democratic Republic of the Congo, we find that data describing who infected whom are not required to resolve uncertainty about when to declare an outbreak over.

Fig. 1.. Schematic illustrating our MCMC-based approach for estimating the end-of-outbreak probability.

(A) The MCMC method for calculating the end-of-outbreak probability requires three inputs: disease incidence time series data [input (i)], the offspring distribution [input (ii)], and the serial interval distribution [input (iii)]. The offspring and serial interval distributions shown are the actual distributions for EVD used in our analyses (see Materials and Methods). (B) The likelihoods of different possible transmission trees being the true transmission tree given the disease incidence data (up to the current time) are derived here, and the end-of-outbreak probability conditioned on a particular transmission tree can be calculated using the traced method introduced in (5). The end-of-outbreak probability given inputs (i) to (iii) can be calculated either by combining the end-of-outbreak probabilities under every possible transmission tree, weighted by the likelihood of each tree (enumerate method), or, equivalently, by using MCMC to sample possible transmission trees from the likelihood (MCMC method). (C) End-of-outbreak probability estimates on each day during and following the outbreak can be obtained by applying this process using data up to and including the current day.

Fig. 2.. End-of-outbreak probability estimates for simulated datasets with weekly data.

(A) Disease incidence data (gray bars; values are shown on the left y axis) and end-of-outbreak probability estimates obtained using the MCMC, traced, Nishiura, enumerate, and simulation methods (values are shown on the right y axis) for the first simulated dataset. The blue shaded region indicates 95% credible intervals of end-of-outbreak probability estimates obtained in individual MCMC iterations. (B) Equivalent results for the second simulated dataset.

Fig. 3.. End-of-outbreak probability estimates for historical EVD outbreaks in the DRC.

(A) Disease incidence data (gray bars; values are shown on the left y axis) and end-of-outbreak probability estimates obtained using the MCMC and traced methods (values are shown on the right y axis) for the 2017 EVD outbreak in Likati health zone, DRC. The blue shaded region indicates 95% credible intervals of end-of-outbreak probability estimates obtained in individual MCMC iterations. (B) Equivalent panel to (A) for the 2020 EVD outbreak in Équateur province, DRC (end-of-outbreak probabilities are only shown for the MCMC method, because the transmission tree was unavailable for this outbreak). (C) The earliest day following the day the final recorded case developed symptoms on which the 2017 Likati health zone outbreak could have been declared over, based on the percentage risk of further cases calculated using the MCMC or traced method falling below each of a range of threshold values. The error bars indicate 95% credible intervals of theoretical declaration dates obtained in individual MCMC iterations. (D) Equivalent panel to (C) for the 2020 Équateur province outbreak. In all panels, the actual day on which the outbreak was declared over (for both outbreaks, this was 42 days after the final case recovered) is indicated by an orange dotted line [vertical in (A) and (B) and horizontal in (C) and (D)]. Example MCMC trace plots for end-of-outbreak probability calculations using the MCMC method are shown in figs. S6 and S7.