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Jessica C. eateto clg n vltoayBooy rneo nvriy rneo,N 08544; NJ Princeton, University, Princeton Biology, Evolutionary and Ecology of Department nipratpeoeo ndsaetasiso sso-called is transmission disease in phenomenon important An nWsenArc a nrcdne,adcnrlmeasures epidemic control (EBOV) and virus unprecedented, Ebola was Africa 2014 Western the in of size outbreak he | superspreading a,1 ejmnDulsDalziel Douglas Benjamin , c eateto ahmtc,Oeo tt nvriy ovli,O 97331; OR Corvallis, University, State Oregon Mathematics, of Department | a fsrn distribution offspring n ra .Grenfell T. Bryan and , R t .Mteaial,tedis- the Mathematically, ). f pcnr,C-21Gnv ,Switzerland; 6, Geneva CH-1211 Epicentre, R | t ,wihrpeet the represents which ), aeininference Bayesian b,c a,h eata Funk Sebastian , R 0 (and d mnaMcClelland Amanda , 1073/pnas.1614595114/-/DCSupplemental. at online information supporting contains article This option. access open 1 PNAS the through online available Freely Submission. Direct PNAS a is article This interest. of conflict no declare and authors C.J.E.M., The S.R., A.T., A.M., S.F., paper. the B.D.D., M.S.Y.L., wrote B.T.G. and data; analyzed M.S.Y.L. research; to Such window Data). unique Study a houses; offer individual data of level surveillance spa- the community-based individual-level (to with dataset data a tial analyzing attacked by We problems are. superspreading these of aimed super- drivers potential how We the and super- what (i) dynamics, (ii) outbreak. transmission EBOV setting, overall the impacted spatiotemporal of have a may of role spreading in course the primarily how answer, the lack- to unclear over still EBOV is is varies how it time spreading of instance, and space For understanding over ing. systematic varied 11), events superspreading (10, EBOV of (9). measures population-level outperform mea- may control risk which targeted sures, associated of implementation identifying facilitate also, refining would for factors ; step future key a of is prediction starting superspreading Quantifying outbreaks, (8). (MERS) 2012 recent in respira- syndrome more acute the respiratory and severe East (7) the 2003 Middle in of outbreak driver (SARS) syndrome key high. tory a is events was superspreading phenomenon of has probability This the distribution small tail, offspring or right the large large When a a cases. generated secondary individual of infectious number probabil- one the also any but that infections, ity new not of describes number average distribution the offspring only The virus. the of distribution uhrcnrbtos ....dsge eerh ...... n ...performed B.T.G. and B.D.D., M.S.Y.L., research; designed M.S.Y.L. contributions: Author owo orsodnesol eadesd mi:[email protected]. Email: addressed. be should correspondence whom To osqecso uesraigfrEBOV. for and superspreading poten- causes of at of consequences understanding targeted enhance measures and control superspreaders tial of high- importance results the Our important light an superspreading. is for age predictor that demographic and outbreak the ubiq- throughout are that uitous was superspreadings epidemic by the sustained and that driven find largely We superspreading. character- EBOV core of identify to istics us allows a that introduce We framework lacking. statistical still recent are dynamics a characterizations spatiotemporal its systematic for of but outbreak, described (EBOV) population-level virus been Ebola outperform has may Superspreading measures. targeted which individually Understanding measures, phe- devising “superspreading.” control facilitate a as can others, superspreading to to than referred transmit individuals susceptibles nomenon infected more some disproportionately infections, many For Significance lhuhcnattaigdt a eeldsuperspreading revealed has data contact-tracing Although g eia eerhCuclCnr o ubekAayi and Analysis Outbreak for Centre Council Research Medical b eateto nertv ilg,Oeo tt University, State Oregon Biology, Integrative of Department PNAS d etefrteMteaia oeln fInfectious of Modelling Mathematical the for Centre e nentoa eeaino e rs n e Crescent Red and Cross Red of Federation International | eray2,2017 28, February e mnaTiffany Amanda , | h www.pnas.org/lookup/suppl/doi:10. oat nentoa Center, International Fogarty o.114 vol. f tvnRiley Steven , | o 9 no. | 2337–2342 g ,

MEDICAL SCIENCES study localized transmissions of EBOV and complement for- A 8.5 mal surveillance by detecting cases that did not interface with clinical care. In this work, we built an age-specific spatiotem- Freetown poral framework, which allowed us to explicitly infer the prob- ability distribution of the number of new cases generated by each infected individual (hereafter, offspring distribution). This framework was applied to the community-based EBOV case 8.4 dataset and deployed to infer transmission dynamics and identify superspreaders. Specifically, we used Bayesian inferential tech- niques to synthesize individual-level spatial data (i.e., GPS coor- dinates), age data, symptoms onset time, and burial time (Study Lat Data), and to impute unobserved time and transmission 8.3 network (Materials and Methods and SI Text). Study Data We analyzed a community-based dataset collected from the Safe and Dignified Burials program conducted by the International Federation of Red Cross, between October 20, 2014, and March 8.2 30, 2015, in Western Area (which comprises the capital Freetown and its surrounding area) in Sierra Leone. These data contain GPS locations (collected by mobile phones) of where the bodies −13.3 −13.2 −13.1 −13.0 of 200 dead who tested positive for Ebola were collected (typi- Lon cally at their homes). Age, sex, time of burial (which was usually Source Index Secondary performed within 24 h of death), and symptom onset time were Mean also recorded. Symptom onset time was reported retrospectively 0.0 2.5 5.0 7.5 10.0 by next of kin. Offsprings

Results BC100% 10.0 Natural History Parameters. We estimated that R0 has median value 2.39, with 95% credible interval (C.I.) of [2.05, 2.84] 7.5 75%

A 5.0 50%

150 2.5 Descendents of Mean Offsprings

Superspreaders(%) 25% 1.0 0.0 100 Index Secondary Any Secondary Count Fig. 2. (A) Spatial distribution of mean number of offspring resulting from 50 initial cases at the individual level. An infection is classified as an 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 0 sources of infection. (C) Proportion of infected individuals who are direct 2.0 2.5 3.0 3.5 and indirect descendants of the first five superspreaders (i.e., first five indi- viduals with highest number of mean offspring; note that the choice of five R0 is arbitrary here). “Any” includes superspreaders who were also the index B cases (i.e., the roots of transmission trees). 4 (Fig. 1A). We also estimated the time-varying reproductive num- 3 ber Rt (Fig. 1B). The was estimated to be 6.74 d [1.29, 16.21]. These estimates are broadly consistent with t what have been reported (3, 12). R 2 The mean of infectious period (i.e., duration from symp- toms onset to death/burial) was estimated to be 3.9 d [3.75, 1 4.0]. Because the transmission tree and times of infection were imputed (Materials and Methods), we were also able to infer the mean generation time of EBOV, which was estimated to be 0 10.9 d [9.25, 13.01]. Both estimates were lower than that esti- Nov 2014 Dec 2014 Jan 2015 March 2015 mated from cases detected within the clinical care system [e.g., Time mean infectious period 8 d estimated for patients who received clinical care (13) and mean generation time 15.3 d estimated Fig. 1. Estimates of reproductive number. (A) Posterior distribution of the by the WHO (1)]. These discrepancies potentially highlight sys- basic reproductive number, R0.(B) Posterior distribution of the weekly effec- tematic differences between community-based cases and cases tive reproductive number, Rt. Bars represent 95% C.I., and red line connects notified in clinical care systems, with terminal community-based the medians. cases progressing significantly more rapidly.

2338 | www.pnas.org/cgi/doi/10.1073/pnas.1614595114 Lau et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 hti,pro ,fo h ieo first of time the from peak 1, epidemic period of is, time corre- the periods−that to five the observation into and divided distributions is period offspring of mean estimates empirical inferred sponding and deaths weekly 3. 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(10, which of 0.16 in be study observational to an estimated from heterogene- estimate less an implies than (i.e., higher ity) and is index it and (including 0.37, distribution was secondary) offspring mean inferred our of which for distribution, and metric superspreading; and heterogeneity k transmission lower of a speaking, degree Generally (9). mean variance the the with (i.e., binomial negative superspreaders disper- few the parameter is sion a superspreading degree- and of only measure heterogeneity empirical of-transmission by common A boxplot). mostly appeared the in growth than outliers fueled epidemic less the be generated Thus, cases to average. secondary on most offspring that one observed individ- particular, In was the superspreading. it at of impact “offspring” the of quantifying level, number ual average the in asymmetry 25 m ftedsrbto.Rddte ierpeet h median the here). five represents superspreaders than are more line infectors offspring mean the dotted has which who in those Red as subdistribution (defined distribution. the of the km) (2.61 of km) (2.51 Time. and Space in Superspreading < eso h iedpnec fsuperspreading, of dependence time the show we 3A, Fig. In κ mle usata uesraig(oprdwt geo- a with (compared superspreading substantial implies 1 ugssta u siaeo h ereo superspreading of degree the of estimate our that suggests k suigta h fsrn itiuini a is distribution offspring the that assuming , PNAS IF 1 ecniudti akadsearching backward this continued We ; | eray2,2017 28, February 0 fe h pdmcpa) This peak). epidemic the after d ∼100 k > k .Fg 3B Fig. 1. ) u miia siaeof estimate empirical Our 1). = σ i.2 Fig. 2 = lhuhsuperspreading Although 1+ µ(1 | hw htms fthe of most that shows A k o.114 vol. and ersnsahigher a represents µ/k B where ), | hwaclear a show o 9 no. hw that shows 5and <15 | k µ 2339 was 1 is k )

MEDICAL SCIENCES A ing should have been even more prominent in the presence of 10.0 underreporting, compared with our estimate. Such a discrepancy suggests that our estimated degree of superspreading is poten- tially (at most moderately) conservative−for example, at a con- 7.5 stant underreporting rate of 90%, the median of k is ∼0.27 in scenario 2, moderately lower than 0.37 estimated from the base- 5.0 line analysis. Underreporting appears to have limited effect on the estimated R0, at least up to underreporting rate of 80% (Fig. 5B). Fig. 5 C and D suggest that, although we can be relatively

Mean Offsprings 2.5 confident about the most probable transmission distance, it is almost certain that we missed some long-distance transmission 0.0 events. Assuming a time-varying underreporting rate gives rise to similar results (Fig. S1). 0 5 10 15 20 Our model assumed an isotropic spatial dispersal (Materials Infectious Period (Days) and Methods). Spatial infectivity, however, may depend on the <15 15−30 30−45 population density−in particular, it may exhibit a gravity-model Age 45−60 >60 pattern that is observed in a few disease systems, including Ebola (19–21). Such gravity models scale the distance-dependent infec- B tious challenge acting on the recipients, by incorporating a “local susceptibility” as a function of the population size of the receiv- 2.0 ing area−that is, a more populated place is prone to a greater movement influx (of cases) and hence a greater effective infec- tious challenge. Based on the underlying principles of gravity 1.5 models, we also investigated the effect of population density on these estimates (Fig. S2), using two different formulations in specifying the local susceptibility. First, without taking into 1.0 account the population density, we may have missed identify- ing a few prominent superspreaders at the right tail of the off- spring distribution and, hence, underestimated superspreading 0.5 (Fig. S2A). Conversely, it was shown that population density Instantaneous Hazard has no significant effect on R0 (Fig. S2B). Finally, assuming an isotropic dispersal may have slightly biased toward the longer 0.0 transmission distance (Fig. S2C). Nevertheless, the effects were nonsignificant, mainly due to relatively homogeneous population <15 15−30 30−45 45−60 >60 density where the cases resided (Fig. S3). The parameterization Age of the incubation period and infectious period were also tested,

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 AB infectious period of an individual, rather than the assumed universal infec- 0.5 5 tious period distribution. (B) Instantaneous risk exerted by different age 0.4 groups. 4 0.3 0 R 0.2 results suggest that the combination of certain age groups (who 3 have high instantaneous hazard) with a long infectious period 0.1

(at the right tail of the infectious period distribution) constitutes k of Offspring Distribution 0.0 2 a key driver of superspreading. The discrepancy of transmissi- 10% 30% 50% 70% 90% 10% 30% 50% 70% 90% bility in age may be rooted in social contact structure (15) or CD virological linkages (e.g., potential systematic variation among 3 12.5 infected individuals) that cannot be established solely by using 10.0 epidemiological data (16). 2 7.5

Sensitivity Analysis. Underreporting is a ubiquitous feature of 5.0 epidemiological data (17, 18). In this section, we explore the 1 effect of underreporting on our analysis under two probable sce- 2.5

narios: (i) All unreported cases were circulating in the com- 0 (km) Median Transmission 0.0 Most Probable Transmission (km) Transmission Most Probable munity and not hospitalized; and (ii) all unreported cases were 10% 30% 50% 70% 90% 10% 30% 50% 70% 90% hospitalized and therefore not reported in our database. In both Under−reporting Under−reporting scenarios, we tested with constant underreporting rates, across the whole study period and region, ranging from a very low Missing Community Cases Missing Hospitalizations (10%) to a very high one (90%). Doing so allowed us to inves- tigate the probable lower and upper bound of our estimates. We Fig. 5. Effect of constant underreporting rates on estimates of transmis- sion dynamics. (A) Estimates of k. Bars represent the 95% C.I., and dots also tested with time-varying underreporting rates in both sce- represent the median values. (B) Estimates of R0.(C) Estimates of most prob- narios. Details of how to include underreported cases are pro- able distance of transmission. (D) Estimates of median transmission distance. vided in Materials and Methods. Dotted lines represent the corresponding estimates using our data. At each We focused on investigating the effect on k, R0 and trans- underreporting rate, 10 independent simulations and corresponding infer- mission distance. Fig. 5A shows that, in general, superspread- ence were performed (Materials and Methods).

2340 | www.pnas.org/cgi/doi/10.1073/pnas.1614595114 Lau et al. 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MEDICAL SCIENCES >60. K(dij; η), also known as a dispersal kernel, characterized the depen- data with those simulated from the estimated model, suggesting a good dence of the infectious challenge from infectious i to j as a function of fit (Fig. S4). Furthermore, for validating the implementation of our infer- distance dij between them. Here, we have K(dij; η) = exp(−ηdij). After the ence procedures, we generated multiple sets of pseudodata from the modal infection, it was assumed that individual j would go through an incuba- process and demonstrated that we could successfully reestimate the model tion period (i.e., time from infection to symptoms onset) and an infectious parameters (Fig. S5). period (i.e., time from onset to death). The incubation period was assumed to follow a gamma distribution Γ(a, b) distribution (where a and b are mean Testing Underreporting. We divided the observational period into many and SD, respectively), and the infectious period followed an exponential 3-d-wide intervals. Within each time interval, we had the total number of 0 distribution with mean c. We assumed the infectiousness started from the unreported cases nt = nt /(1−r)−nt , where nt and r were the observed cases symptoms onset time. It was noted that unknown contacts corresponding to in the interval and the assumed underreporting rate, respectively. Burial escaped infections were not taken into account in our framework, resulting times and symptoms-onset time of these unreported cases were drawn from 0 in a likelihood function that accounted for only successful infectious con- the empirical distribution of the observed cases. Finally, these nt cases were tacts (SI Text)−that is, our approach essentially represented a transmission distributed spatially by using the empirical distribution of (normalized) pop- network-based inference, where the focus was to construct the transmission ulation densities across the study area. We also tested an underreporting tree among infected individuals (25–28). rate that decreases with time (Fig. S1). For the scenario that considers unre- ported hospitalized cases, we drew the time from symptoms onset to hos- Data Augmentation and Model Fit and Validation. We estimated θ (i.e., the pitalization from the truncated above (at 7 d) empirical infectious period parameter ) in the Bayesian framework by sampling it from the pos- distribution of observed cases, effectively resulting in a shorter infectious terior distribution P(θ|x), where x is the observed data. Denoting the likeli- period for unreported cases. These artificially generated data were com- hood by L(θ; x), the posterior distribution of θ is P(θ|x) ∝ L(θ; x)π(θ), where bined with the observed data and fitted with our model. π(θ) is prior distribution for θ. Weak uniform priors for parameters in θ were used (Table S4). Markov chain Monte Carlo (MCMC) techniques (30) were ACKNOWLEDGMENTS. This work was supported by Bill & Melinda Gates used to obtain the posterior distribution. The unobserved infection times Foundation Grant OPP1091919; the RAPIDD program of the Science and and transmission network were imputed in the MCMC. Sampled transmis- Technology Directorate Department of Homeland Security and the Foga- sion networks were recorded and used to infer the offspring distribution rty International Center, National Institutes of Health; and the UK Medical of each case. Details of the likelihood function and the MCMC algorithm Research Council (MRC). S.F. was also supported by MRC Career Award in are given in SI Text. Model fit was assessed by comparing the observed Biostatistics MR/K021680/1.

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