Supplementary webappendix

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Supplementary webappendix

This webappendix formed part of the original submission and has been peer reviewed.

We post it as supplied by the authors.

Supplement to: Merler S, Ajelli M, Fumanelli L, et al. Spatiotemporal spread of the 2014

outbreak of Ebola virus disease in Liberia and the effectiveness of non-pharmaceutical

interventions: a computational modelling analysis. Lancet Infect Dis 2014; published

online Jan 7. http://dx.doi.org/10.1016/S1473-3099(14)71074-6.

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Spatio-temporal spread of the Ebola 2014 outbreak in Liberia

and the effectiveness of non-pharmaceutical interventions: a

computational modelling analysis

Stefano Merler

1

, Marco Ajelli

1

, Laura Fumanelli

1

,

Marcelo F.C. Gomes

2

, Ana Pastore y Piontti

2

, Luca Rossi

3

,

Dennis L. Chao

4

_{, Ira M. Longini Jr.}

5

_{, M. Elizabeth Halloran}

4,6

_,

Alessandro Vespignani

2,7∗

1_{Bruno Kessler Foundation, Trento, Italy}

2_{Laboratory for the Modeling of Biological and Socio-technical Systems,}

Northeastern University, Boston, MA 02115, USA

3_{Institute for Scientific Interchange (ISI), Torino, Italy} 4_{Vaccine and Infectious Disease Division,}

Fred Hutchinson Cancer Research Center, Seattle, WA 98109, USA

5_{Department of Biostatistics, College of Public Health}

and Health Professions, and Emerging Pathogens Institute, University of Florida, Gainesville, FL 32611, USA

6_{Department of Biostatistics, University of Washington, Seattle, WA 98195, USA} 7_{Institute for Quantitative Social Sciences}

at Harvard University, Cambridge, MA 02138, USA

∗_{corresponding author; E-mail: [email protected].}

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1 Methods

1.1 Epidemiological and demographic data

The number of cases and deaths occurring both in the general population and among HCW were obtained from the WHO situation reports1_{and from the Liberian Ministry of Health and Social Welfare situation}

reports.2

The population density of Liberia is taken from The Gridded Population of the World produced by the Center for International Earth Science Information Network (CIESIN) of the Earth Institute at Columbia University.3_{Data on the distribution of household size, hospitals capacity and number of HCW are also}

available.4,5

According to the latest census data (2009), Liberia has a population of 4,092,260 residing in an area of 111,369 km2, corresponding to a grid of 3,157 cells in the model. By using a standard procedure,6,7the modelled individuals are grouped into randomly assigned households whose size is based on DHS data and are geographically placed to match the gridded population density estimates.

According to OpenStreetMap (http://wiki.openstreetmap.org/wiki/

2014_West_Africa_Ebola_Response, accessed September 25, 2014), Liberia has 24 hospitals and clinics

for which the exact locations are known. Although OpenStreetMap data might not be comprehensive, this is the only information on geographical location of hospitals in Liberia available to us.The number of HCW and beds for each hospital are determined to match available national statistics on the total number of available beds and total number of HCW, which are 7 and 3.2 per 10,000 inhabitants, respectively5_–

modelled hospitals have on average 54 HCW (95%CI: 42–67) and 119 beds (95%CI: 101–138). HCW are sampled from the population living within 15 km of the hospital.

Hospitals in the model admit individuals suffering from Ebola until August 16, 2014; in fact, in early August the Liberian Ministry of Health and Social Welfare, with support from various NGO, initiated a large-scale nationwide intervention with the opening of dedicated facilities separate from general hospitals, called Ebola treatment units (ETUs).10 This situation is included in the model, by assuming that since August 16, 2014 new Ebola patients are admitted only to ETUs, while those who were already in treatment in general hospitals are progressively discharged (or they die). As of November 19, 2014 nine ETUs were open in six different counties of Liberia,8,10 _{whose location, beds capacity and}

number of HCW is known;8–10_{all this information (see Tab. S1) were used to build ETUs in the model.}

Since the bodies of who died from EVD are extremely infectious, in order to prevent contagion associated with funeral practices burial teams were progressively trained and equipped throughout the country. This led to 2373 safe and dignified burials as of November 12, 2014.1_{We model this intervention}

by assuming that the adoption of this practice increases linearly after August 16, 2014 in such a way that

Table S1: List of active Ebola Treatment Units (ETUs) in Liberia as of November 19, 2014. Data from Humanitarian Data Exchange8_{, WHO}9_{, CDC}10_.

County Name Latitude Longitude Beds Staff

Bomi Senjeh 6.86734006 -10.83093972 100 NA Bong Gbarnga 7.00472 -9.554999 55 84 Lofa Foya 8.3789113 -10.2057566 140 210 Margibi Firestone 6.35305998 -10.4697199 31 NA Montserrado Island Clinic 6.38438065 -10.78712 150 315 Montserrado ELWA 2 6.23965 -10.696 100 84 Montserrado ELWA 3 6.24443999 -10.70028 250 630 Montserrado MoD 6.27027999 -10.73417 100 210 Nimba Ganta 7.23797355 -8.98100091 36 120

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90% of funerals is conducted in a safe manner within two months.

1.2 Transmission model and Ebola natural history

Each individual of the population, explicitly simulated as an agent of the individual-based model, has an associated epidemiological status. The different stages of Ebola transmission are modelled by adopting an epidemic model originally introduced by Legrand et al.11_{: susceptible individuals (S) can acquire}

infection after contact with an infectious individual and become exposed (asymptomatic), E; at the end of the incubation period lasting 11.4 days on average,12 _{and assumed equal to the latent period}

(as pre-symptomatic transmission is very unlikely to occur and it has not been proved for EVD yet), infectious (symptomatic) individuals, I, can transmit infection at home (to both household members and members of the additional households). Infectious individuals at home then may either be hospitalized (H) with 80% probability13,14 5 days on average after symptom onset12, die (F) 7.5 days on average after symptom onset,12or recover (R) after 7.9 days on average (as resulting from the difference between the time from symptom onset to death and from symptom onset to end of infectiousness as reported in Gomes et al.13). Hospitalized individuals may either die 4.2 days on average after hospitalization,12 or recover 4.6 days on average after hospitalization (as resulting from the difference between the time from hospitalization to death and from hospitalization to end of infectiousness as reported in Gomes et al.13_{). However, after recovery a hospitalized individual remains in the hospital (though no longer}

infectious) for an additional period: the total average time from hospitalization to discharge is 11.8 days on average.12 _{Deceased individuals may transmit infection during their funeral (to household members}

and to the general community) for 2 days on average and are then removed (R).11 _{The overall case}

fatality ratio is assumed to be 54% as reported in the WHO report released on September 16, 2014 and referring to cases until September 9 – this value is consistent with 92 deaths in 183 cases among HCW as of September 26.2 _{An extensive sensitivity analysis of the above parameters is provided below.}

The model accounts for three routes of transmission: transmission in households and in the gen-eral community (to additional households) when the infected individuals are at home; transmission in hospitals; and transmission during funerals (to household and additional household members).

Simulations were initialized with 10 infected individuals geographically distributed in Liberia based on the locations of the first cases reported to the WHO, namely in Montserrado and Lofa districts. The national-level simulations were run until there were 24 deaths, at which point the simulated date is set to June 16, 2014. This procedure, previously used in Merler et al.7_{, synchronizes all simulations to start}

with the observed conditions at the beginning of the outbreak in Liberia.

Transmission within households The transmission is assumed to be homogeneous between members

of the same household. At timet, a non-hospitalized infectious individualj transmits EVD to all other members of her or his household with the following force of infection:

λj(t) =

βf

Nfj(t)

whereβf is the transmission rate in households (assumed to be the same for all households), andNfj(t)

is the household size at timet(thus excluding deceased and hospitalized members).

This is equivalent to saying that a susceptible individualiis exposed to the following force of infection in the household:

λ?i(t) =

βfIfi(t)

Nfi(t)

where βf is the transmission rate within households, Nfi(t) is the household size at timet, and Ifi(t)

is the number of non-hospitalized infectious individuals in householdfi. In the rest of the Section we

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Transmission in the general community Each household is linked to two additional households, which are sampled from households within 10 km proportionally to the population density to account for contacts occurring in the general community that, in the case of EVD, mainly correspond to contacts between relatives (for instance for taking care of sick individuals). Let aj be the set of additional

households for an infectious (non hospitalized) individualj. Note thatajdoes not include the household

of individualj and thus does not includej. Individual j transmits the infection to the members of aj

with force of infection:

λj(t) =

σβf

Naj(t)

whereNaj(t) is number of individuals in aj at timet andσ is the ratio of the transmission rate in the

additional households compared to that in the household of individualj (0≤σ≤1).

A sensitivity analysis performed by assuming different number of additional households and different distance at which they are chosen is reported below.

Transmission during burial ceremonies During unsafe burials, a deceased individual j transmits

EVD to her/his household members and members of the additional householdsajsimilarly to transmission

in households, namely:

λj(t) =

βf

Nfj(t)

to household members and

λj(t) =

σβf

Naj(t)

to members of the additional households. Note that the same set of households involved in the general community transmission is assumed also for burial ceremonies.

Transmission during traditional burial practices in West Africa has been shown to be responsible for about 9% of overall infections,12 _{so we assume that a certain fraction of individuals attending a burial}

ceremony may contract Ebola from the deceased. In particular, we assume that at risk individuals during a burial ceremony are those belonging to the household and community settings (i.e., household members and members of the additional households –two in the baseline scenario– of the deceased). This follows the idea that the specific network of contacts who are at highest risk of contracting the disease from a symptomatic Ebola case is almost the same as those who would be involved in washing and preparing the body for burial ceremony (see Hewlett et al.15_{for a description of burial procedures). As the timeline of}

Ebola infections due to transmission during funerals would be hardly traceable, we decided not to add in the model an additional parameter regulating transmission during funerals, while we assume the same transmission rate of household contacts. Despite this unsophisticated choice, the estimated proportion of cases linked to burial events predicted by the model is consistent with estimates derived from the analysis of case report data.12 Moreover, we show that the fraction of transmissions during funerals remains constant under a variety of modelling assumptions (for instance, varying assumptions about the network of contacts attending burial ceremonies, reporting rate, and hospitalization probability), thus supporting our modelling choice. A sensitivity analysis on the transmission rate during funerals is presented in Section 4. A limitation of our model is that when a married adult female dies, burial is generally done in the woman’s village. This has the potential to increase spatial transmission, though when the female partner’s home is distant, burial may have to take place in the husband’s village. We did not consider this because of the lack of reliable data to parameterize the model.

Transmission in hospitals During the first phase of the epidemic in Liberia, until early August,

the lack of dedicated facilities caused Ebola patients to be admitted to general hospitals, where specific protocols for EVD management could hardly be applied.

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Modelling EVD transmission in hospitals clearly represents a difficult task as the kind of contact responsible for transmission in this setting is still unclear. As reported by all agencies1,2, a large number of health care workers has contracted the disease while caring for Ebola patients without appropriate protective equipment, and many have died. In addition, the poor conditions under which many healthcare settings operate and the lack of general precautions (e.g., the use of non-disposable and non-sterilized medical equipment and instruments such as needles) allow the spread of infection not only to HCW but also to other patients. Thus, it is reasonable to assume as in our model that also non-Ebola patients are exposed to the risk of contracting the disease. Given the undeniable uncertainty regarding EVD transmission in hospital settings, two alternative scenarios were considered.

The first one corresponds to assuming that an EVD case is able to transmit the infection to HCW and outpatients (1,148,064 visits in 2008 in Liberia16_{), for instance through contacts in waiting areas; the}

second one considers EVD transmission to HCW and inpatients. The two scenarios can be considered to be at the opposite side of the spectrum of possibilities of Ebola transmission within the hospital setting. In fact, the first scenario assumes that hospitalized EVD cases can transmit the infection to a larger pool of susceptible individuals (each day outpatients, either infected or not, are replaced by a pool of new outpatients), with substantial turnover and increased mixing with respect to the second, more conservative, scenario (inpatients, either infected or not, remain hospitalized for seven days on average, according to16).

The two scenarios are detailed as follows. Individuals infected with Ebola have a probability of 80% of being hospitalized. At every time step of the simulation, symptomatic Ebola cases seeking care at hospitals are assigned to the nearest hospital with beds available. In detail, the following procedure was employed to hospitalize symptomatic Ebola cases: let{h1, . . . , hn} be the hospitals in Liberia sorted in

order of increasing distance from the house of an Ebola case and letbibe the number of available beds in

hospitalhi. The Ebola case is hospitalized in the first hospital withbi>0. If there are no hospitals with

available beds, the Ebola case is not hospitalized. Afterwards, the same procedure is used to hospitalize non-Ebola cases. Non-Ebola cases are randomly sampled from the population with probability such that full capacity of all hospitals in Liberia is reached. Non-Ebola cases remain hospitalized either for one day (first scenario, the one presented in the main text, with individuals representing outpatients) or for seven days on average (second scenario, with individuals representing inpatients). If there are no hospitals with available beds, cases are not hospitalized until new beds become available. As for the number of available bedsbi, in the first scenario it corresponds to the number of beds of hospitalhiminus the number of Ebola

cases currently hospitalized in hospital hi; in the second scenario, the number of non-Ebola inpatients

currently hospitalized in hospitalhi is additionally subtracted.

In principle, one might argue that looking for the nearest hospital with available beds may take more than one day (while we assume this is done the very day of transition from house to hospital). However, this simple procedure has the advantage to preserve the estimated time from onset of symptoms to hospitalization, namely 5 days on average. Indeed, the estimate itself may also depend on the time required to seek for an hospital with available beds.

A hospitalized infectious individual j transmits the infection to both susceptible hospitalized indi-viduals (corresponding to outpatients or to inpatients, depending on the considered scenario) and HCW with force of infection

λj(t) =

βh

Nhj(t)

whereβhis the transmission rate in hospital, andNhj(t) is the overall number of hospitalized individuals

and HCW in hospitalhj.

The choice of explicitly modelling hospitals requires an additional free parameter regulating the trans-mission within this setting. However, the availability of recorded deaths among HCW and the inclusion of such data in the likelihood function allows the estimation of this additional parameter though, obviously with some uncertainty.

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Transmission in ETUs Since early August 2014, ETUs started being more widespread in Liberia with increasing bed capacity, thus in the model Ebola patients are no longer admitted to general hospitals after August 16. Since only patients fulfilling the clinical Ebola case definition are admitted to ETUs, we postulate that, differently from general hospitals, patient-to-patient transmission is not possible (trans-mission between confirmed cases and suspect, non-Ebola cases before laboratory confirmation can be considered as negligible). On the other hand, HCW can still get infected with Ebola within ETUs, but one order of magnitude less than in general hospitals (reflecting the adoption of specific protocols for EVD patients management).17

The assignment of Ebola patients to ETUs can be summarised as follows: individuals infected with Ebola have a 80% probability of being hospitalized (to ETUs). At every time step of the simulation, symptomatic Ebola cases seeking care are assigned to the nearest ETU with beds available, following a procedure similar to the one implemented for the assignment to hospital (prior to August 16).

An infectious individual j, hospitalized in ETU, transmits the infection only to HCW, with force of infection equal to the force of infection in general hospitals with the transmission rate in hospital,βh,

rescaled by a 0.05 factor, to account for the lower infection probability of HCW in this setting with respect to general hospitals.17

Overall force of infection and probability of getting infected At any time t of the

simula-tion (we consider a time step ∆t = 1 day), any susceptible individual i has a probability pi(t) =

1−exp−∆tP

jλj(t)

of being infected from each infectious individualj in the population.

The transmission rates in the different settingsβf,βh and the scaling factorσdepend on the specific

population model used and on socio-demographic factors, and thus need to be estimated.

Basic reproduction number The basic reproduction numberR0is defined as the average number of

secondary infections caused by a typical primary infection in a fully susceptible population.18_{A relation}

exists betweenR0and the generation time (i.e., the time elapsing between infection of a primary case and

infection of a secondary case caused by the primary case) and exponential growth rate of the epidemic.19

In the case of an exponentially distributed generation time, this relation is simply given by R0 =

1 +rTg, whereris the exponential growth rate of the simulated epidemic during the initial phase (when

the depletion of susceptible individuals is negligible) andTg is the estimated generation time.

For generic distributions of Tg, as widely accepted in the literature,6,12,20–23 we need to use the

following procedure. First of all, we calculate the generation time empirically by keeping track of it in model simulations, and we fit an appropriate distribution to the resulting generation time frequencies (a Gamma distribution in our case). The basic reproduction number can thus be computed as:

R0=

1

R∞

0 γˆ(τ)e−rτdτ

where ˆγ(τ) is the fitted Gamma distribution for the generation time. By assuming no underreporting we estimate a generation time of 18·1 days (SD: 12·3 days), which is fitted by a Gamma distribution of parameters shape 2·39 (SE: 0·014) and rate 0·13 (SE: 0·0008). By assuming 50% reporting we estimate a generation time of 17·2 days (SD: 12·4 days), which is fitted by a Gamma distribution of shape 2·13 (SE: 0·026) and rate 0·12 (SE: 0·002). In this way, the resultingR0 accounts for both the stochasticity of

the simulations and the transmission rates obtained from the Markov chain Monte Carlo procedure (see next section).

1.3 Markov chain Monte Carlo calibration

The model has three unknown parameters, all related to virus transmissibility (βh,βf,σ); the parameter

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0 4000 8000 0 4000 8000 0 4000 8000 Iteration number βf Iteration number βh Iteration number σ βf Frequency 0.0 0.1 0.2 0.3 0.4 βh Frequency 0.2 0.6 1.0 σ Frequency 0.2 0.6 1.0 βf βh 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 1.0 0.6 0.2 1.0 0.6 0.2 1.0 0.6 0.2 1.0 0.6 0.2 0.4 0.2 0.0 1.0 0.6 0.2 1500 500 0 3000 1000 0 2500 1000 0 βf σ 0.2 0.4 0.6 0.8 1.0 βh σ

A

B

C

Figure S1: AValues of the model parameters as estimated during the MCMC calibration procedure. B

Distribution of model parameters. CPairwise plot of model pararameters.

distribution in the interval [0,1000] for the prior of both parameters to reflect the lack of information. The prior distribution of σ is uniform [0,1]. The posterior distribution of Θ was explored by Markov chain Monte Carlo (MCMC) sampling applied to the likelihood of the recorded number of deaths among HCW and in the general population in the entire country of Liberia (thus not accounting for spatial information). Specifically, by assuming the number of deaths among HCW and in the general population to be Poisson distributed around the mean and independent for each time interval, we can write the total likelihood as the product of two distinct likelihood functions,Lhcw and Lgp. In detailLhcw is defined

as Lhcw =Q n

i=1P(hcwwi(Θ);ki), n is the number of data points, P is the probability of observing ki

events from a Poisson distribution with mean hcwwi(Θ), where ki is the observed number of deaths

among HCW in time intervali,wi(Θ) is the predicted number of deaths among HCW in time interval

i(assuming the candidate parameter vector Θ), and hcw is the reporting rate of deaths among HCW.

We defineLgp analogously. In order to give the same weight to the two likelihood functions we use four

data points (n= 4) for each one as obtained by grouping temporal data on a (almost) weekly basis over the period July 20 - August 15, 2014. In the baseline scenario, we set the reporting rates of deaths both

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Observed cumulative cases Predicted cu m ulati ve cases 10 10 2 103 104 10 102 ₁₀3 ₁₀4

Predicted week of first case

Observed week of first case

25 27 29 31 33 35 37 Maryland RiverCess River Gee Sinoe Bomi Bong Gbarpolu Grand Cape Mount Grand Bassa Grand Gedeh Grand Kru A B July 7 August 3 August 31 September 28 October 21 40 37 34 31 28 25

Figure S2: A: Predicted versus observed cumulative number of cases by county. The seven counties analyzed here, namely Lofa, Montserrado & Margibi, Bong, Grand Bassa, Nimba and Bomi, account for about 97% of overall cases as of November 2014. Dot size is proportional to the number of individuals living in the county. Results refer to simulations assuming the baseline scenario (reporting rate 100% and hospitalization rate 80%). BPredicted versus observed week of the first case in different counties of Liberia. Only the counties with no reported cases before June 16, 2004 (week 25, corresponding to time 0 in model simulations) are shown. Solid line represents the linear model fit, dashed lines represent 95% confidence interval of the linear model.

among HCW and in the general population to be equal to one. In addition, to provide an upper bound to our prediction, we investigate a second scenario (underreporting scenario) where we still assumehcw= 1,

butgp= 0·5 – accounting for the possibly high underreporting of Ebola deaths in the population. Such

a value is similar to that reported by the CDC and derived from the recorded and estimated bed in use in hospitals.17

Random-walk Metropolis-Hastings sampling is used to estimate Θ. At each iteration, the likelihood of a new candidate vector of parameters is evaluated and the candidate is either accepted or rejected following the usual Metropolis-Hastings algorithm.24As simulations are stochastic, whenever new candidate vectors are not accepted 10 times in row, the likelihood of the current parameter set is re-evaluated and the new likelihood accepted with probability 1.25 _{This ensures that the chain does not remain trapped in a local}

maximum. The values of the logarithm of the transmission rates (i.e., the first two components of Θ) of a new candidate parameter vector are randomly sampled from normal distributions having mean equal to the logarithm of the current transmission rate and varianceδ2_.26 _{This guarantees that candidate values}

of the transmission rates are positive. A similar procedure is used to guarantee that candidate values of

σlie in [0,1].

The three values ofδare chosen in such a way to guarantee a good acceptance rate (around 20%). We perform 10,000 iterations. We check convergence by considering several different starting points and by visual inspection (see Figure S1A). Estimated parameters distributions are depicted in Figure S1B, where we can observe that transmission rates distributions are unimodal; on the other hand, the method is not able to discriminate a mode forσ, except that its value cannot be too low (that is, there is transmission to additional households). In addition, transmission rates are correlated (Figure S1C); however, given the current knowledge on transmission mechanisms, the most plausible configuration of the two cannot be ascertained.

We discard the first 2,000 iterations as burn-in period and, in order to get a set of independent samples (thus avoiding auto-correlation between adjacent samples), we consider one sample every 8 of

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Time (days)

Daily

number of n

ew deaths

Aug 15 Oct 15 Dec 15

ETU and safe burials ETU, safe burials and: protection kit cov. 50% protection kit cov. 70% protection kit cov. 90%

25 20 15 10 5 0

Figure S3: Median daily number of deaths as predicted by the model under different coverages of household protective kits. Intervention efficacy is assumed to be 50%, hospitalization rate is 80%.

the remaining iterations. The reported mean values and confidence intervals are then computed from these 1,000 stochastic realizations of the model, and thus account for both the stochasticity of model realizations and the uncertainty in model parameters estimates.

2 Spatial spread

The geographical spread of EVD cases across Liberia can be analysed more in depth by considering the partitioning of cases into the 15 counties of the nation. We use county-specific data covering a period of about 4 months; specifically, related to the dates of July 7, August 3, August 31, September 28, and October 21 2014. By considering all datapoints together, we find a Pearson correlation of 0·85 (p-value

<0·0001), see Fig. S2A. The model is able to predict quite well the cumulative number of cases occurring in all counties. We also check the correspondence between observed and predicted week of the first case arriving in each county: all counties except Grand Gedeh fall into the 95% confidence interval of the linear model fit between the two quantities Fig. S2B. Observed and predicted weeks of first case are correlated (0·52, p-value = 0·047). Correlation increases to 0·65 (p-value = 0·011) by excluding Grand Gedeh from the analysis.

3 Effectiveness of intervention strategies

We model the effectiveness of deploying household protection kits as described in the main text, but assuming a lower intervention efficacy, namely 50%. Under this assumption we find that intervention is less effective, in that a coverage of at least 70% is required to observe a consistent impact in terms of daily number of new deaths (see Fig. S3).

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Table S2: Parameter estimates when 60% of cases are hospitalized.

100% reporting 50% reporting

mean (95%CI) mean (95%CI)

βf (days−1) 0·12 (0·07–0·20) 0·81 (0·34–1·42)

βh (days−1) 0·44 (0·27–0·68) 0·20 (0·10–0·33)

σ 0·79 (0·36–0·99) 0·16 (0·04–0·48) household and community transmission* (%) 52·5 (35·9–66·6) 81·2 (74·4–86·2) hospital transmission* (%) 39·4 (23·5–58·1) 8·9 (4·5–16·0) funeral transmission* (%) 8·1 (5·5–10·7) 9·9 (8·4–11·4) * as of August 16, 2014.

4 Sensitivity analysis with respect to main epidemiological

pa-rameters

Model estimates and predictions depend on two critical parameters, namely underreporting and propor-tion of hospitalized cases, whose values are uncertain. As for the former, in the main text we discuss variability of estimates and model predictions by assuming the reporting rate in the general population varies from 50% to 100% and we show results assuming a 80% hospitalization rate, as resulting from the analysis of previous EVD outbreaks.14However, no estimates are available yet for the ongoing outbreak; therefore alternative scenarios on the hospitalization rate, and consequently on the fraction of recorded EVD deaths occurring during hospital stay, are investigated as well.

By assuming the proportion of hospitalized Ebola cases equal to 60%, model fit and predictions at August 16, 2014 do not differ substantially from those reported in the main text (see Fig. S4). The estimated proportions of cases in the different settings (households/community, hospitals, funerals) are quite stable with respect to the 100%reporting, 80% hospitalization scenario. Model predictions are similar: for instance, the predicted number of EVD deaths at August 16, 2014 is 399 (95%CI: 332–480) by assuming 60% hospitalization rate and 401 (95%CI: 332–478) by assuming 80% hospitalization rate.

In the underreporting scenario, assuming that 60% of Ebola cases are hospitalized leads to a slight increase in the proportion of cases generated in households and community, and to a consequent pro-portional decrease of transmission in hospitals (see Fig. S5, and Table S2), while cases generated during funerals do not change substantially. This difference stems from the fact that the non-hospitalized cases can be accounted for only by enhancing transmission in the household and general community, because the finite capacity in the hospitals limits the number of transmissions occurring in that specific setting.

In the underreporting scenario, assuming that 80% of Ebola cases are hospitalized, but only 50% of deaths are notified would mean that only about 62% of EVD deaths occurring during hospital stay are recorded – such a value, which may in principle look very low, would tentatively account for the difficulty of hospital personnel in timely reporting of EVD cases and related deaths. On the other hand, large uncertainty is also associated with the fraction of hospitalized Ebola cases. As reported in the main text, the estimated household SAR by assuming hospitalization of 80% and reporting 100% is 18·5% (95%CI 7·2–30·4). The estimated household SAR becomes 36·1% (95%CI 21·8–55·9) by assuming hospitalization 80% and reporting 50%. As the household SAR was estimated to be about 16% for the 1995 outbreak in Democratic Republic of the Congo,27 _{these results indicate that the scenario assuming 50% reporting}

likely represents an upper limit to the transmissibility of Ebola in Liberia. Field estimates of household SAR for the ongoing outbreak would greatly contribute to narrowing uncertainty of model estimates.

We also analyse potential differences in the pattern of geographical spread by assuming 100% or 50% reporting (and hospitalization equal to 80% as in the main text). Side by side comparison of Fig. S6 and Fig. S7 shows that the main pattern of spread – most cases concentrated in the districts of Lofa

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Total deaths HCW deaths 10 10 2 103 104 10 10 2 103 10 10 1 2 103 104 Total cases Total deaths HCW deaths 10 10 2 103 104 10 10 2 103 10 10 1 2 103 104 Total cases Time (days)Ju l16 Aug16 6 1 n u J Time (days)Ju l16 Aug16 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J B A

Figure S4: ATop panel: cumulative number (on the log scale) of EVD deaths over time in the general population of Liberia by assuming 100% reporting and 60% hospitalization. Dots refer to the data recorded in the WHO reports (dark dots only were used in model initialization and calibration). Lines and shaded areas refer to estimated average and 95%CI model predictions. Middle panel: cumulative number (in log scale) of EVD cases (confirmed, probable and suspected) over time in the general population. Colours as in top panel. Bottom panel: cumulative number (in log scale) of EVD deaths over time among health care workers. Colours as in top panel. BAsAbut assuming 50% reporting.

House/Comm. Hospital Funeral

Transmission settings Tr ansmission (%) Tr ansmission (%) HCW HM 70 60 50 40 30 20 10 0 100 80 60 40 20 0 B A Rep=100% Hosp=80% Rep=100% Hosp=60% Rep=50% Hosp=80% Rep=50% Hosp=60% Rep=100% Hosp=80% Rep=100% Hosp=60% Rep=50% Hosp=80% Rep=50% Hosp=60%

Figure S5: AProportions of transmission in households and community, in hospitals and during funerals as of August 16, 2014 by assuming different reporting rates in the general population, namely 50% and 100%, and different hospitalization rates, namely 60% and 80%. B Proportion of cases among HCW and proportion of cases due to contacts between household members as of August 16, 2014 by assuming different reporting and hospitalization rates (as inA).

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Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama June 16 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama July 14 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama August 11 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama September 8 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama October 6 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama November 3 0 0−1 1−10 10−100 >100 9 8 7 6 5 4

Figure S6: Geographical spread: predicted cumulative number of EVD cases per cell over time in Liberia by assuming reporting rate 100% and hospitalization rate 80%. Each cell corresponds to an area of about 25 km2_.

(Northern part of the country, close to the borders with Sierra Leone and Guinea), Montserrado (the county of Monrovia), Margibi, Bong and Nimba – is well described by both models, even though the model with 50% reporting estimates a much higher number of cases.

Results reported in the main text are based on the assumption that the case fatality ratio is 54%, as reported in the WHO report released on September 16, 2014 and referring to cases until September 9 – this value is consistent with 92 deaths in 183 cases among HCW as of September 26.2 _{Results shown in}

Fig. S8 show that by assuming a case fatality ratio of 70·8%, as resulting from recent estimates,12_model

fit and predictions at August 16, 2014 do not differ substantially from those reported in the main text. Moreover, estimates of transmission by setting do not differ substantially from that obtained by assuming a case fatality ratio of 54%. As expected, we obtained a slight increase of transmission at funerals, and a decrease of transmission in hospitals (see Tab. S3).

We perform a sensitivity analysis also on funeral transmission. By assuming the transmission rate at funerals to be two or three times that in household/general community, model predictions at August

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Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama June 16 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama July 14 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama August 11 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama September 8 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama October 6 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama November 3 0 0−1 1−10 10−100 >100 9 8 7 6 5 4

Figure S7: Geographical spread: predicted cumulative number of EVD cases per cell over time in Liberia by assuming reporting rate 50% and hospitalization rate 80%. Each cell corresponds to an area of about 25 km2.

Table S3: Parameter estimates by assuming 80% of cases are hospitalized and 100% reporting.

CFR 54% CFR 70·8%

βf (days−1) 0·15 (0·04–0·28) 0·19 (0·11–0·48)

βh (days−1) 0·33 (0·15–0·67) 0·28 (0·15–0·46)

16, 2014 are essentially the same of the baseline scenario. However, the fraction of transmission in the household/general community setting decreases proportionally to the increase of the funeral transmission

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Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Total deaths HCW deaths 10 10 2 103 104 10 10 2 103 10 10 1 2 103 104 Total cases

Figure S8: Cumulative number (in log scale) of EVD cases (confirmed, probable and suspected) over time in the general population of Liberia, when a 100% reporting rate in the general population is assumed. Dots refer to the data recorded in the WHO reports. Line and shaded area refer to estimated average and 95%CI model predictions, respectively. The assumed hospitalization rate is 80% and case fatality rate is 70·8%.

Table S4: Parameter values used in the baseline simulations in the main text and alternative parameter-ization.13

parameter Baseline Legrand et al.11,13

average duration of incubation period 11·4 days 7 days average time from symptom onset to death 7·5 days 9·6 days average time from symptom onset to recovery for survivors 7·9 days 10 days average time from symptom onset to hospitalization 5 days 5 days proportion of cases hospitalized 80% 80% average time from hospitalization to death 4·2 days 4·6 days average time from hospitalization to recovery for survivors 4·6 days 5 days average time from hospitalization to dismissal for survivors 11·8 days – average time from death to burial 2 days 2 days overall case fatality ratio 54% 55%

rate, and the fraction of transmission in the funeral setting increases correspondingly; when we assume a two-fold funeral transmission rate, we obtain 19·3% (95%CI 14·8–21·8) transmission at funerals, while when we assume a three-fold funeral transmission rate we obtain 26·1% (95%CI 21·3–28·9) transmission

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Baseline Legrand et al.11

βf (days−1) 0·15 (0·04–0·28) 0·14 (0·07–0·25)

βh (days−1) 0·33 (0·15–0·67) 0·26 (0·12–0·44)

at funerals. As the currently available estimate of the fraction of Ebola cases with possible exposure at funerals is about 9%,12 _{we consider as baseline scenario the one where the transmission rate at funerals}

is the same as in the household/general community setting, where we estimate a fraction of transmission at funerals of 8·6% (95%CI 3·2–11·8).

The model is parameterized according to more recent estimates of key time periods.12However, large uncertainty still exists about some of these estimates. A full sensitivity analysis of model estimates accounting for parameter variability is not feasible with our model. However, here we show that model estimates do not vary substantially by assuming parameter values estimated from previous outbreaks.11 Parameter values are reported in Tab. S4, results are reported in Tab. S5.

5 Sensitivity analysis on the transmission in the general

com-munity

Baseline simulations reported in the main text are based on the assumption that an infectious non hospitalized individual transmits the infection to household members and members of two additional households (accounting for both relatives and transmission in the community). The two additional households are chosen at a distance no larger than 10 km. Here we show that reported results are robust with respect to these modelling assumptions; in particular we vary the number of additional households (5 or 10), and their maximum distance from the index household (2·5 km or 20 km).

In detail, Fig. S9 shows that fit and model predictions at August 16, 2014 do not differ substantially by varying these two quantities. Fig. S10 shows that the proportion of transmission in the different settings remains stable. Fig. S11 shows that the pattern of spatial spread is not much affected by the maximum distance at which additional households are located. In particular, these results support the hypothesis that the observed pattern of spread is mainly ascribable to hospitals where Ebola and non-Ebola patients look for care, thus favouring the mixing of individuals that are in different geographical locations but access the same hospital. On average there are no differences in the geographic spread in the long run, except for a slight decrease in the number of cases when considering the model with additional households at a distance no larger than 2.5 km. In fact, in this case local outbreaks may saturate in low density areas thus resulting in a lower number of cases with respect to baseline simulations reported in the main text.

6 Sensitivity analysis on transmission in hospitals

In the main text we show results assuming that every day hospitalized Ebola cases can transmit the infection in hospitals to HCW and to a number of susceptible individuals equal to the number of available

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Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Total deaths HCW deaths D C B A 10 10 2 103 104 10 10 2 103 10 10 1 2 103 104 Total cases Total deaths HCW deaths 10 10 2 103 104 10 10 2 103 10 10 1 2 103 104 Total cases Total deaths HCW deaths 10 10 2 103 104 10 10 2 103 10 10 1 2 103 104 Total cases Total deaths HCW deaths 10 10 2 103 104 10 10 2 103 10 10 1 2 103 104 Total cases

Figure S9: A The three subpanels show cumulative number (on the log scale) of EVD deaths, total cases and EVD deaths among health care workers over time in Liberia by assuming 100% reporting and 80% hospitalization and by assuming five additional households (baseline simulations shown in the main text assume two additional households) at a distance no larger than 10 km from the index household (as in the baseline simulations). Dots refer to the data recorded in the WHO reports (dark dots only were used in model initialization and calibration). Lines and shaded areas refer to estimated average and 95%CI model predictions. B As Abut assuming 10 additional households (baseline simulations shown in the main text assume two additional households) at a distance no further than 10 km from the index household (as in the baseline simulations). C AsA but assuming two additional households (as in the baseline simulations) at a distance no further than 2.5 km from the index household (baseline simulations shown in the main text assume a distance no further than 10 km). DasAbut assuming two additional households (as in the baseline simulations) at a distance no further than 20 km from the index household (baseline simulations shown in the main text assume a distance no further than 10 km).

beds not occupied by Ebola cases. This follows the idea that not only HCW and non-Ebola inpatients are exposed to the risk of infection, but also other categories of individuals, namely outpatients and relatives of non-Ebola inpatients. In this section we discuss results based on the more conservative hypothesis that only HCW and non-Ebola inpatients are exposed to the risk of infection. We recall that these patients

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Transmission settings

Tr

ansmission (%)

House Hospital Funeral AH=10 D=10 km AH=2 D=2.5 km AH=5 D=10 km AH=2 D=20 km Tr ansmission (%) HCW HM AH=10 D=10 km AH=2 D=2.5 km AH=5 D=10 km AH=2 D=20 km 70 60 50 40 30 20 10 0 100 80 60 40 20 0 B A

Figure S10: A Proportions of transmission in households and community, in hospitals and during funerals as of August 16, 2014 by varying the number of additional households and their distance from the index household by assuming 100% reporting and 80% hospitalization. BProportion of cases among HCW and proportion of cases due to contacts between household members as of August 16, 2014 by varying the number of additional households and their distance from the index household.

remain hospitalized for 7 days on average, thus substantially reducing the transmission to patients in hospitals (HCW are exposed to the same risk of infection).

By comparing results reported in Fig.1 of the main text and Fig. S12, it emerges that model fit and predictions at August 16, 2014 do not differ substantially by varying these modelling assumptions. However, as expected, the proportion of cases generated in households, community and hospitals differs in the two models (see Fig. S13 and Tab. S6). In particular, by assuming that only HCW and non-Ebola inpatients are exposed to the risk of infection, the proportion of cases generated through contacts in hospitals decreases from 38·4% (95%CI: 17·4–76·4) of the baseline simulations to 30·3% (95%CI: 14·6– 47·8). This decrease is lower than that resulting from the assumption that outpatients are also exposed to the risk of infection, 80% of Ebola cases is hospitalized, but reporting in the general community is 50% (see Fig. S13). The larger variability of model estimates under the baseline scenario (outpatients are also exposed to the risk of infection, 80% of Ebola cases are hospitalized, and 100% reporting) justifies our choice of showing these simulations in the main text. In fact, we are not in the position to disentangle which model of transmission in hospitals is closest to the real situation.

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Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama June 16 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama July 14 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama August 11 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama June 16 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama July 14 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama August 11 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama September 8 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama October 6 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama November 3 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama September 8 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama October 6 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 Longitude Latitude −12 −10 −8 Monrovia Saniquellie Harper Greenville Buchanan Voinjama November 3 0 0−1 1−10 10−100 >100 9 8 7 6 5 4 16/6 14/7 11/8 8/9 6/10 3 /11 16/6 14/7 11/8 8/9 6/10 3 /11 Time 4 2 0 -2 -4 Time D C B A 6 4 2 0 -2 -4 Difference Difference

Figure S11: APredicted cumulative number of EVD cases per cell over time in Liberia by assuming reporting rate 100% and hospitalization rate 80% and by assuming that non-hospitalized infectious in-dividuals transmit the infection to two additional households at a distance no further than 2.5 km from the index households. Each cell corresponds to an area of about 25 km2. B Distribution (2·5%, 50%, 75%, 97·5% quantiles) of the difference between the number of predicted cases in each cell by assuming distance no further than 2·5 km and by assuming a distance no further than 10 km (baseline simulations shown in the main text). C Predicted cumulative number of EVD cases per cell over time in Liberia by assuming reporting rate 100% and hospitalization rate 80% and by assuming that non-hospitalized infectious individuals transmit the infection to two additional households at a distance no further than 20 km from the index households. Each cell corresponds to an area of about 25 km2_. _D _Distribution

(2·5%, 50%, 75%, 97·5% quantiles) of the difference between the number of predicted cases in each cell by assuming a distance no further than 20 km and by assuming a distance no further than 10 km (baseline simulations shown in the main text).

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Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Time (days) 6 1 g u A 6 1 l u J 6 1 n u J Total deaths HCW deaths 10 10 2 103 104 10 10 2 103 10 10 1 2 103 104 Total cases

Figure S12: Top panel: cumulative number (on the log scale) of EVD deaths over time in the general population of Liberia by assuming 100% reporting, 80% hospitalization, under the hypothesis that only HCW and non-Ebola inpatients (hospitalization lasts 7 days on average) are at risk of getting infected in hospitals. Dots refer to the data recorded in the WHO reports (dark dots only were used in model initialization and calibration). Lines and shaded areas refer to estimated average and 95%CI model predictions. Middle panel: cumulative number (on the log scale) of EVD cases (confirmed, probable and suspected) over time in the general population. Colours as in top panel. Bottom panel: cumulative number (on the log scale) of EVD deaths over time among health care workers. Colours as in top panel.

outpatients inpatients

βf (days−1) 0·15 (0·04–0·28) 0·21 (0·11–0·62)

βh (days−1) 0·33 (0·15–0·67) 0·28 (0·14–0·5)

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Rep=100% Hosp=80% Rep=100% Hosp*=80% Rep=100% Hosp=60% Rep=50% Hosp=80%

House/Comm. Hospital Funeral Rep=100% Hosp=80% Rep=100% Hosp*=80% Rep=100% Hosp=60% Rep=50% Hosp=80% Transmission settings Tr ansmission (%) Tr ansmission (%) HCW HM 70 60 50 40 30 20 10 0 100 80 60 40 20 0 B A

Figure S13: A Proportions of transmission in households and community, in hospitals and during funerals as of August 16, 2014 under different hypotheses about reporting rate, hospitalization rate and by considering two different transmission models in hospitals: one where only HCW and inpatients are at risk of infection (scenario Hosp*), and a second one where also outpatients are at risk (scenario Hosp). B Proportion of cases among HCW and proportion of cases due to contacts between household members as of August 16, 2014 under different hypotheses about reporting rate, hospitalization rate and by considering two different transmission models in hospitals: one where only HCW and inpatients are at risk of infection (scenario Hosp*), and another where also outpatients are at risk (scenario Hosp).

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Supplementary webappendix