Spatial and temporal dynamics of superspreading events in the 2014-2015 West Africa Ebola epidemic

Abstract

The unprecedented scale of the Ebola outbreak in Western Africa (2014-2015) has prompted an explosion of efforts to understand the transmission dynamics of the virus and to analyze the performance of possible containment strategies. Models have focused primarily on the reproductive numbers of the disease that represent the average number of secondary infections produced by a random infectious individual. However, these population-level estimates may conflate important systematic variation in the number of cases generated by infected individuals, particularly found in spatially localized transmission and superspreading events. Although superspreading features prominently in first-hand narratives of Ebola transmission, its dynamics have not been systematically characterized, hindering refinements of future epidemic predictions and explorations of targeted interventions. We used Bayesian model inference to integrate individual-level spatial information with other epidemiological data of community-based (undetected within clinical-care systems) cases and to explicitly infer distribution of the cases generated by each infected individual. Our results show that superspreaders play a key role in sustaining onward transmission of the epidemic, and they are responsible for a significant proportion ([Formula: see text]61%) of the infections. Our results also suggest age as a key demographic predictor for superspreading. We also show that community-based cases may have progressed more rapidly than those notified within clinical-care systems, and most transmission events occurred in a relatively short distance (with median value of 2.51 km). Our results stress the importance of characterizing superspreading of Ebola, enhance our current understanding of its spatiotemporal dynamics, and highlight the potential importance of targeted control measures.

Keywords: Bayesian inference; Ebola; offspring distribution; superspreading.

Fig. 1.

Estimates of reproductive number. (A) Posterior distribution of the basic reproductive number, $R_0$. (B) Posterior distribution of the weekly effective reproductive number, $R_{\mathrm{t}}$. Bars represent 95% C.I., and red line connects the medians.

Fig. 2.

(A) Spatial distribution of mean number of offspring resulting from initial cases at the individual level. An infection is classified as an index case if it has a posterior probability of importation (i.e., not infected by any cases in the data) >0.5; otherwise, it is classified as a secondary case. Lat, latitude; Lon, longitude. (B) Distribution of mean number of offspring by different sources of infection. (C) Proportion of infected individuals who are direct and indirect descendants of the first five superspreaders (i.e., first five individuals with highest number of mean offspring; note that the choice of five is arbitrary here). “Any” includes superspreaders who were also the index cases (i.e., the roots of transmission trees).

Fig. 3.

Spatial and temporal dependence of superspreading. (A) Reported weekly deaths and inferred mean offspring distributions and the corresponding empirical estimates of $k$ at different time periods. The whole time period is divided into five periods$-$that is, period 1, from the time of first observation to the time of epidemic peak $t_{\mathrm{peak}}$; period 2, ($t_{\mathrm{peak}}$, $t_{\mathrm{peak}}+20\text{d}$); period 3, ($t_{\mathrm{peak}}+20$, $t_{\mathrm{peak}}+50$); period 4, ($t_{\mathrm{peak}}+50$, $t_{\mathrm{peak}}+100$); and period 5, from $t_{\mathrm{peak}}+100$ to the time of last observation. Such a dividing was used so that we could use the peak time as a reference point and ensure a similar number of cases in most intervals. (B) Distribution of distance of transmission for all infector–infected pairs. Black dotted line represents the median (2.51 km) of the distribution. Red dotted line represents the median (2.61 km) of the subdistribution in which the infectors are superspreaders (defined as those who has mean offspring more than five here).

Fig. 4.

Heterogeneity of infectiousness in age. (A) Relation between mean offspring and infectious period. It is worth noting that here an infectious period is strictly referred to the mean of the posterior samples of imputed infectious period of an individual, rather than the assumed universal infectious period distribution. (B) Instantaneous risk exerted by different age groups.

Fig. 5.

Effect of constant underreporting rates on estimates of transmission dynamics. (A) Estimates of $k$. Bars represent the 95% C.I., and dots represent the median values. (B) Estimates of $R_0$. (C) Estimates of most probable distance of transmission. (D) Estimates of median transmission distance. Dotted lines represent the corresponding estimates using our data. At each underreporting rate, 10 independent simulations and corresponding inference were performed (Materials and Methods).

Fig. S1.

Effect of time-varying underreporting on estimates of transmission dynamics. (A) Estimates of $k$. Bars represent the 95% C.I., and dots represent the median values. (B) Estimates of $R_0$. (C) Estimates of most probable distance of transmission. (D) Estimates of median transmission distance. Dotted lines represent the corresponding estimates using our data. The underreporting rate is assumed to decrease with a step size 10%, from 90 to 10%, in the course of the epidemic: The study period is divided into nine equal intervals, and each interval takes an underreporting rate that is 10% lower than the previous one.

Fig. S2.

Testing the assumption of an isotropic spatial dispersal. (A) The distribution of mean offsprings under different scenarios. (B) The distribution of R₀ under different scenarios. (C) The distribution of transmission distance under different scenarios. Here we considered three scenarios. In scenario 1 (base scenario), we assumed an isotropic dispersal and did not take into account the potential effect of population density. We considered in scenarios 2 and 3 that the dispersal kernel value was “moderated” by the relative population density of the $100m\times 100m$ grid that a case resides in. Scenarios 2 and 3 differ in how the population density was normalized (to between $[\mathrm{0,1}]$) to obtain the discounting factor: In scenario 2, we normalized according to $log$(1 + population density), and in scenario 3, we normalized according to the absolute scale of population density.

Fig. S3.

Population density and spatial distribution of the cases in the study area. Other than the smaller clusters near the center of the study area, most cases were found in more populated regions. It was noted that the raw grid resolution is $100m\times 100m$ (which is too fine to display), and here it is binned into $30\times 30$ grids for better visualization. Lat, latitude; Lon, longitude.

Fig. S4.

Assessing the model fit. We used the estimated model to simulate (500 times) forward the transmission path and timings of events (i.e., infection time, onset time, and death time). (A) Comparison of the observed weekly temporal distribution of the cases with that summarized from the simulated data. Gray area represents the 95% C.I., and the black dots and line are the observed data, with 5 of 500 random realizations (colored lines) of the simulated epidemics imposed. We compared the temporal autocorrelations (at lag = 1 and lag = 2) of the observed and simulated epidemics. We also compared the peak height, the growth rate before peak, and decay rate after peak between the observed and simulated (the growth and decay rates correspond to the slopes of best-fitted linear lines to the observed or simulated data). Dotted lines represent the values of the summary statistics corresponding to the observed data. (B) Comparison of the observed spatial autocorrelation and the simulated. Here we used two common measures, Moran’s I and Geary’s C indices (33, 34), which range from −1 to 1 (a value close 1 indicates strong clustering and close to −1 indicates strong dispersion). Dotted lines represent the values of the summary statistics corresponding to the observed data.

Fig. S5.

Checking of the implementation of the inference procedures. We simulated 10 independent pseudodata from the model, with the model parameter values close to the posterior means obtained from fitting with the real dataset. The model is then fitted to each of the simulated datasets, and the resultant posterior distributions of the model parameters are shown. The true values of the model parameters are indicated by the red lines.