Temporal variations in the effective reproduction number of the 2014 west Africa ebola outbreak

Abstract

Background The rapidly evolving 2014 Ebola virus disease (EVD) outbreak in West Africa is the largest documented in history, both in terms of the number of people infected and in the geographic spread. The high morbidity and mortality have inspired response strategies to the outbreak at the individual, regional, and national levels. Methods to provide real-time assessment of changing transmission dynamics are critical to the understanding of how these adaptive intervention measures have affected the spread of the outbreak. Methods In this analysis, we use the time series of EVD cases in Guinea, Sierra Leone, and Liberia up to September 8, 2014, and employ novel methodology to estimate how the rate of exponential rise of new cases has changed over the outbreak using piecewise fits of exponential curves to the outbreak data. Results We find that for Liberia and Guinea, the effective reproduction number rose, rather than fell, around the time that the outbreak spread to densely populated cities, and enforced quarantine was imposed on several regions in the countries; this may indicate that enforced quarantine may not be an effective control measure. Conclusions If effective control measures are not put in place, and the current rate of exponential rise of new cases continues, we predict 4400 new Ebola cases in West Africa during the last half of the month of September, with an upper 95% confidence level of 6800 new cases.

Time series of iIncidence of EVD cases in West Africa

Time series of recorded average number of new EVD cases per day during the initial phase of the 2014 West African outbreak, for Guinea, Sierra Leone, and Liberia (dots). The green lines show a selection of the piecewise exponential fits to the data (not all fits are shown to clarify the presentation); a moving window of groups of 10 contiguous points are taken at a time, and the rate of exponential rise estimated for those 10 points. The results for the estimations of the exponential rise for the full set of piecewise fits are shown in Figure 2. Shown in red is the fitted exponential rise from July 1st onwards.

Estimated rates of exponential rise from piecewise exponential fits

Estimated rates of exponential rise from piecewise exponential fits to the average daily EVD incidence data, as shown in Figure 1; a moving window of groups of 10 contiguous incidence data time series points are taken at a time, and the rate of exponential rise estimated for those 10 points. The dates shown on the x axis are last date in each contiguous set of 10 points, and the vertical error bars denote the 95% confidence interval. The horizontal black line shows the estimated rate of rise of an exponential fit to the incidence time series from July 1st to Sep 8th, with the black dotted lines indicating the 95% confidence interval.