review article a systematic review of early modelling ... · review article a systematic review of...

REVIEW ARTICLEA systematic review of early modelling studies of Ebola virusdisease in West Africa

Z. S. Y. WONG1,2*, C. M. BUI2, A. A. CHUGHTAI2 AND C. R. MACINTYRE3

1Centre for Clinical Epidemiology St. Luke’s International University, Chuo-ku, Tokyo, Japan2School of Public Health and Community Medicine, The University of New South Wales, Sydney, NSW,Australia3College of Public Service and Community Solutions, Arizona State University, Tempe, AZ, 85287, United States

Received 21 September 2016; Final revision 29 November 2016; Accepted 5 January 2017;first published online 7 February 2017

SUMMARY

Phenomenological and mechanistic models are widely used to assist resource planning forpandemics and emerging infections. We conducted a systematic review, to compare methods andoutputs of published phenomenological and mechanistic modelling studies pertaining to the2013–2016 Ebola virus disease (EVD) epidemics in four West African countries – Sierra Leone,Liberia, Guinea and Nigeria. We searched Pubmed, Embase and Scopus databases for relevantEnglish language publications up to December 2015. Of the 874 articles identified, 41 met ourinclusion criteria. We evaluated these selected studies based on: the sources of the case data used,and modelling approaches, compartments used, population mixing assumptions, model fittingand calibration approaches, sensitivity analysis used and data bias considerations. We synthesisedresults of the estimated epidemiological parameters: basic reproductive number (R0), serialinterval, latent period, infectious period and case fatality rate, and examined their relationships.The median of the estimated mean R0 values were between 1·30 and 1·84 in Sierra Leone,Liberia and Guinea. Much higher R0 value of 9·01 was described for Nigeria. We investigatedseveral issues with uncertainty around EVD modes of transmission, and unknown observationbiases from early reported case data. We found that epidemic models offered R0 mean estimateswhich are country-specific, but these estimates are not associating with the use of several keydisease parameters within the plausible ranges. We find simple models generally yielded similarestimates of R0 compared with more complex models. Models that accounted for datauncertainty issues have offered a higher case forecast compared with actual case observation.Simple model which offers transparency to public health policy makers could play a critical rolefor advising rapid policy decisions under an epidemic emergency.

Key words: Ebola virus, infectious disease, modelling.

INTRODUCTION

The largest Ebola virus disease (EVD) epidemic in his-tory began in Guinea in December 2013. As of 30March 2016, the EVD epidemic resulted in over28 600 cases and 11 300 fatalities mainly in Guinea,Liberia and Sierra Leone [1]. The most recent reported

* Author for correspondence: Z. S. Y. Wong, Centre for ClinicalEpidemiology St. Luke’s International University, OMURASusumu & Mieko Memorial St. Luke’s Center for ClinicalAcademia, 5/F, 3-6-2 Tsukiji, Chuo-ku, Tokyo, 104-0045, Japan.(Email: [email protected])

Epidemiol. Infect. (2017), 145, 1069–1094. © Cambridge University Press 2017doi:10.1017/S0950268817000164

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case was reported in Liberia in March 2016 and WHOhas warned that we may find new flare-ups in theaffected countries [2]. With over 17 000 survivors inWest Africa and chronic persistence of virus in somesurvivors [3], such flare ups have already occurredand may continue to be a risk. During an epidemicemergency, it is important to provide scientific justifi-cation for rapid policy decisions. Early epidemicmodels can frame policy decisions by providing epi-demiological characteristics to aid effective diseasecontrol – they allow policy makers and scientists tocharacterise disease epidemiology parameters (suchas basic reproduction number (R0), serial interval,infectious period) based on limited/early disease sur-veillance data, which can assist in understandinghow a disease spreads during the early phase of anoutbreak.

For previous EVD outbreaks in the DemocraticRepublic ofCongo (1995) andUganda (2000),modellingapproaches consisted of both traditional Susceptible–(Exposed)–Infected–Removedmodels andmore context-specific compartment models (which account for thehospital transmissions and post-death transmissions).Modelling these hospital and post-death transmissionscan provide justification for intervention effects indifferent transmission contexts [4]. Choice of thesemodelling approaches may impact modelling outputs,for example, a study [5] revealed that estimates of R0

tend to be underestimated if post-death transmissiondynamics are neglected. For the current EVD epidemic,both traditional and context-specific approaches havealso been employed; however, the impact of compart-ment model designs on epidemic parameters estimationand trajectory projectionhave not yet been systematicallyevaluated – this is one motivation for our review.

Another motivating factor of this research is tocompare outputs of models that do or do not accountfor underreporting – which is an issue that is presentduring most outbreaks, but was thought to be a con-siderably significant issue during the EVD epidemic,due to a number of reasons [6]. Firstly, EVD casescan be asymptomatic [7, 8]. Secondly, West Africa isone of the poorest regions of the world, their healthsystems, let alone their surveillance capabilities areseverely limited – in a study from the Centers ofDisease Control and Prevention (CDC), timelinessof reporting was found to be particularly lacking dur-ing the early phases of the EVD outbreak [9]. Lastly, aprevailing distrust of Western medicine, particularly inmore rural regions, has been thought to deter casesfrom presenting to health facilities [10]. This review

systematically compares models, which have or havenot accounted for underreporting.

There aremany difficulties which are inherent in earlyepidemic models, such as uncertainty regarding diseaseepidemiology, modes of transmission and unknownrates of underreporting. In this study, we build on thework of a recently published EVD modelling review[11] – we systematically evaluate different modellingmethods used to study the current EVD outbreak inWest Africa and their outputs on key disease para-meters, focusing on investigating the impact of usingmodels with different compartmental structures andwhich account for underreporting. Our objective is toprovide directions for futuremodelling efforts in settingswhere early disease outbreak data may be limited.

METHODS

A systematic review was conducted in compliancewith the preferred reporting items for systematicreview and meta-analyses (PRISMA) checklist(http://www.prisma-statement.org/) [12].

Search strategy

Three online databases (Pubmed, Embase andScopus) were searched for relevant literature pub-lished between January 2014 and December 2015.We only focused on Ebola modelling studies pub-lished in about 2 years of the start of the outbreakas early publications provided insight and directionto global and national emerging diseases responseand control decisions. These databases cover indexinternational journals in the multi-disciplinary fieldof: public health, biomedical and pharmaceuticalresearch, clinical and experimental research, healthpolicy and management, and scientific, technical andsocial science research. For each database, we con-ducted a search with the following search keys:‘ebola’ AND ‘model*’. All searches included articletitle, abstract and keywords. The search was limitedto studies in the English language. The detailed searchstrategy was slightly adjusted according to the specificdatabase settings and was reported in SupplementaryDocument 1. In order to minimise the chance of miss-ing references, we carried out hand search of keyEbola modelling papers from internet and all theincluded studies were cross-checked with the papersidentified from our initial scoping review. The key lit-erature search was carried out on 1 June 2016 and thefinal search was carried out on 18 November 2016.

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Inclusion and exclusion criteria

Studies were included if they aimed: (1) to project thetrajectory of disease outbreak or (2) to provide earlyepidemiological parameters estimation of Ebola(including R0, serial interval, latent period, infectiousperiod and case fatality rate) using modelling meth-ods. Only those studies using the current EVD out-break data were included. Studies were excluded ifthe models presented focused only on evaluating inter-vention strategies without offering parameter esti-mates or trajectory projection – evaluating suchmodels was determined to be outside the scope ofthis review. Studies pertaining to EVD outbreaksprior to 2014 were also excluded. Narrative studies,response policy studies, process model studies, phylo-genetic and biological or genetic modelling studieswere also excluded. We included all relevant model-ling studies based on the above criteria and systemat-ically registered key features and attributes associatedwith modelling techniques, design and major assump-tions taken for epidemic estimation and projection.

Selection of studies

We conducted a two-step screening process. In the firstscreening, titles and abstracts were independentlyscreened by two reviewers – any discrepancies wereresolved by discussion and/or referring to the full-text.In the second screening, remaining studies were includedor excluded based on contents within the full-text.

Once all studies were identified, we collected quan-titative and qualitative information pertaining to themodel presented in each study. We focused on synthe-sising study outcomes that: (1) account for data uncer-tainty and (2) used hospitalisation and/or funeralcompartments. We also summarised and tabulatedqualitative descriptions of what questions the modelaims to answer, the country of interest, type ofmodel presented, source and date of the case dataand model fitting. We quantitatively analysed esti-mates of key epidemiological parameters, includingthe R0, serial interval, latency period, infectious periodand case fatality rate. We then synthesised the esti-mated R0 by country, use of compartment, consider-ation of underreporting; and then investigated therelationship between the R0 estimation with otherparameters. Summary statistics, boxplots, scatterplots,non-parametric significance tests (including Mood’smedian test, Kruskal–Wallis test and Spearman test)were used, where appropriate. All of the analysis

was performed using an R version 3.3·1 64 bit plat-form with the packages ‘plotrix’ and ‘zoo’.

RESULTS

Definition of modelling terms used in this study islisted in Table 1. Phenomenological models are recog-nised methods (such as summary statistics, regressionmodels and predictive models), which offer computa-tional solutions to determine values of key disease epi-demiological characteristics. Mechanistic modelsdescribe the transmission of infectious diseases bycategorising host populations into various stages ofinfection. The R0 is an important parameter whichallows epidemiologists and modellers to quantifyhow easily a disease can spread, and how effectiveinterventions need to be in order to achieve diseasecontrol. R0 is defined as the expected number of sec-ondary cases generated by one infected individualover the course of their infection in a fully susceptiblepopulation [13] (i.e. before interventions are put inplace or immunity develops).

Of the 874 studies identified through the onlinedatabase search, 496 duplicates were removed. Afterpreliminary title and abstract screening, 351 studieswere excluded. Seventeen were excluded through asecond screening of the full-text of articles, based onthe exclusion criteria. Four additional studies wereidentified through hand-searching. Finally, 41 studiesmet the inclusion criteria and were included in thereview (see Figure 1).

From the 41 studies we selected for our review, 16studies were published in 2014 and 25 were publishedin 2015. Thirty-five studies aimed for EVD parameterestimation, 27 offered trajectory projection and 21 stud-ies provided both parameter estimation and trajectoryprojection. There are 11 phenomenological modellingstudies, 29 mechanistic modelling studies and one studyemployed both modelling methods. Among these 41studies, 14 accounted for data uncertainty or data biasissues. There are five homogeneous models and 25 ofthe reviewed studies incorporated heterogeneous mixingassumption.Among those heterogeneousmixing studies,17 considered a hospitalised compartment, 16 considereda funeral compartment and 12 incorporated both hospi-talised and funeral compartments.

Overview of EVD modelling studies

Tables 2–4 summarised our descriptive results byresearch aim. Thirty-one out of the 41 included studies

Modelling studies of Ebola virus disease 1071



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have specified referencing case data from WorldHealth Organization (WHO) [1]. The WHO sourceprovided cumulative numbers of reported confirmed,probable and suspected cases and deaths. Other com-monly used data include: National Ministry of Healthdata from the affected countries (such as [17]), CDCMorbidity and Mortality Weekly Reports [18] and/or synthesised data from public data repositories(such as Caitlin Rivers of Virginia PolytechnicInstitute [19] and Virology Down Under blog [20]).Demographic and population data were taken fromsources such as the Central Intelligence Agency(CIA) factbook [21], United Nation (UN) reports[22] and national census. In many studies, model para-meters were derived from models of past Ebolaoutbreaks [23, 24] and/or early published models ofthe current Ebola epidemic [9, 25]. For instance,

Althaus’ study in 2014 [26] adopted estimates of incu-bation and infectious periods from the 1995 EVD out-break in Congo, and the team published a study forNigeria in 2015 [27] that incorporated the estimatedincubation period from a 1976 EVD outbreak inZaire.

When developing an epidemic model with morein-depth detailed compartment structures, manystate parameters (i.e. parameters defining the transi-tion between infection stages) will be required andcalibrated. For example, Barbarossa et al. [28] createda model with seven compartments (including hospita-lised and buried) and estimated state parameters basedon the outcomes of a range of earlier EVD modellingstudies [24, 29–31]. It is noted that model parametersshould be estimated with caution as they are prone tobiases, and the intended prediction outcomes can be

Table 1. Modelling terms definitions

Term Definition

Phenomenologicalmodels

Mathematical/statistical expressions that relate different epidemic observations to each other, wherethe relationship seeks to best describe the data. Descriptive statistics or regression-based models aresome of the examples

Mechanistic models The nature of disease spread relationship is compartmentalised by observed biological processes thatare thought to have given rise to the data. The biological possesses could be parameterised and thatcould be inferred independently from observational outbreak data. These models can beimplemented by system-level perspective, such as ordinary differential equations (ODEs), orstochastic models or agent-based models

Homogenous mixing Homogeneous model assumes that all hosts have identical rate of disease-causing contacts. Thesimple susceptible-(exposed)-infected-removed model without consideration of additionalpopulation heterogeneity are considered as homogeneous mixing in this study

Heterogeneous mixing Heterogeneous model sub-divides population into different groups, depending upon characteristicsthat may influence the risk of receiving and transmitting an infection [14]. Models considering anyhost heterogeneities or included additional compartments (such as hospital and/or funeral) areconsidered as heterogeneous mixing here

Basic reproductionnumber

Basic reproduction number is the expected number of secondary cases generated by one infectedindividual over the course of their infection in a fully susceptible population [13] (i.e. beforeinterventions are put in place or immunity develops)

Serial interval Serial interval is defined as the time between illness onset in the primary case to illness onset in thesecondary case [15]. Understanding serial interval and their moment generating function wouldhelp shaping the relationship between epidemic growth rates and reproductive numbers [16]

Latency period Latency period is the time between infected individual to become infectious. This metric can beconverted to the rate at which an exposed becomes infective as a modelling parameter for thosemodels considering exposed stage

Infectious period Infectious period is defined as the period that an infected person transmits disease to a susceptibleperson. The reciprocal of infectious period determines the removal/recovery rate for epidemicmodelling

Case fatality rate Case fatality rate is the proportion of deaths of cases over the course of the diseaseUnderreporting Underreporting is interpreted as surveillance systems that fail to reflect all infection cases in a given

population. Most of the modern surveillance systems are affected by a degree of underestimation ofthe true incidence of disease [6] due to asymptomatic cases, inability of disease recognition anddetection

Compartment model Compartment model is a type of modelling methods used for mimicking the way how a disease istransmitted among stages of a population system




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highly sensitive to small changes in some parameters.Twenty-eight of the review studies have carried outsensitivity analysis (so-called stress tests) to examinethe robustness of modelling outcomes.

Synthesised results: estimates of epidemiologicalparameters

Thirty-five studies offer epidemiological parameter esti-mation and 29 of them estimated the R0. We evaluatedthe estimated mean of R0 by country, compartment con-siderationandaccounting forunderreporting, as shown inFigure 2 and reported the details values in SupplementaryDocument 2 Tables S1–S3. The median of the R0 meanestimate for the ongoing epidemic (overall) is 1·78 (inter-quartile range: 1·44, 1·80), 1·30 (interquartile range: 1·24,1·51) for Guinea, 1·84 (interquartile range: 1·69, 2·10) forLiberia, 1·70 (interquartile range: 1·34, 2·05) for SierraLeone and 9·01 for Nigeria. Kruskal–Wallis non-parametric test result showed that the estimated R0 donot have identical data distributions across the includedcountries (P value40·05) when we considered Nigerianestimates – which had much higher R0 estimate compar-ing with other countries. We performed additionalKruskal–Wallis test (without considering Nigeria esti-mate) and showed that there is an identical data distribu-tions across other included countries (We cannot rejectnull hypothesis).Whenwe performed additional pairwiseMood’s median tests between each pair of countries

(without Nigeria), we found the median values of esti-mated R0 are generally not significantly different (apartfrom the pair between Guinea and Liberia). The resultsof additional Kruskal–Wallis test and pairwise testsbetween each pair of countries were reported inSupplementary Document 1 Figure S3. A trend line indi-cates the potential temporal patterns of the reported R0

estimation from the bottom-right panel of Figure 2 andthere is a slight increasing trend of R0 when more recentdata were used in each study.

The median of R0 values of 1·90 (interquartilerange: 1·90, 2·10) is found for those models account-ing for underreporting and 1·71 (interquartile range:1·40, 1·96) for those not accounting for underreport-ing. The median of the estimated mean R0 values isreported as 1·49, 1·80, 1·78 and 1·73 for those models,which considered compartments with hospital,funeral, hospital and funeral, and without hospitaland funeral stages, respectively. The Kruskal–Wallisand Mood’s median test results revealed that we can-not reject the null hypotheses – i.e. the estimated meanof R0 remains insignificantly different, regardless ofthe model’s consideration of compartments (with hos-pital and/or funeral) or accounting for underreporting.The above results yield the same when we do not con-sider the Nigerian study data. The results werereported in Supplementary Document 1 Figure S3.

We also synthesised the values of other key model-ling parameters, including serial interval, latency

Fig. 1. PRISMA flow diagram of the selection process for including studies in review.




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Table 2. An overview of modelling studies of Ebola and study designs (Research aim: Parameter estimation)

References Dataset/factors

Description ofmodellingapproaches

Compartments, ifapplicable

Assumption ofpopulationmixing, ifapplicable

Model fitting andcalibration approach, ifapplicable

Sensitivity analysis,if applicable

Description ofaccount for databias, if applicable

Agusto et al.[32]

Case data form WHOreports [1].Population datafrom Guinea census

Compartmentalmathematicalmodel whichstratifiespopulation intothose in thecommunity andthose in healthcarefacilities andincorporatesdiseasetransmissionfeatures in suchunits

Susceptible–exposed–symptomatic–recovered–deceased–cremated(SEIRDC)

Model dividedpopulation intoindividuals fromthe communityand individualswho work inhealthcaresettings andsubdividedindividuals fromthe communityinto those whovisit healthcaresettings and therest of the public

Some model parameterswere fitted using datafrom other study.Threshold quantity R0 isestimated using theEbola data for Guineaand the demographicparameter

R0 was the responsefunction ofsensitivity analysisof other modelparameters.partial-rankcorrelationcoefficients(PRCCs) was used

NA

Ajelliet al. [33]

Data consisted ofroutine health dataand medical recordsof the outbreak in thePukehun District.Also analysedregisters of twoEbola holdingcentres, contacttracing forms andinterviewedhealthcare workers

Reported summarystatistics of keyepidemiologicalparameters,generate time seriesplots anddevelopedtransmission chainfor the outbreakusing outbreakdata

NA NA Fitted distributionnumber of secondarycases using negativebinomial model

NA NA

Althaus [26] Case data from WHOreports [1].Parameters fromprevious Ebolaoutbreaks

Transmission modelwith a set of ODEsand usedmaximum-likelihoodestimates todetermine R0

Susceptible–exposed–infectious–recovered(SEIR)

Assumedhomogeneousmixing

Fitted the model to thereported data of infectedcases and deaths inGuinea, Sierra Leoneand Liberia andprovided themaximum-likelihoodestimates of R0

NA NA

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Browneet al. [34]

Case data from WHOreports [1]

Deterministic modelthat traces back totransmissions, andincorporate diseasetraits and controltogether

Susceptible–exposed–infectious(hospitalised/reported)– infectious(not hospitalisedand unreported)–cumulativehospitalised/reported

Modelled keyfeatures ofcontact tracingandhospitalisation

NA Studied the effectsof modelparameters on theeffectivereproductionnumber using LHSand PRCC

NA

Gomes et al.[29]

Case data from WHOreports [1].Population datafrom ‘GriddedPopulation of theWorld’. Air traveldata from theInternational AirTransportAssociation andOfficial AirlineGuide. Mobility datafrom administrativeregions

Used the GlobalEpidemic andMobility Model togenerate stochastic,individual basedsimulations ofEVD spreadworldwide

Susceptible–exposed–infectious–hospitalised–deathbut not yet buried–removed (SEIHFR)

Model includedhospitalised andfuneralcompartmentand accountedfor differentpopulation sizesaround theworld, includingdifferent trafficflows

Multi-model inferenceapproach was used tocalibrate on data fromofficial WHO data. Alsoperformed Latinhypercube sampling(LHS) of the parameterspace

Performedsensitivity analysisassuming 80%airline trafficreduction fromand to WestAfrican countriesaffected by EVDand 50%underreporting

Tested on 50%underreportingassumption

Hsieh [35] Case data fromWHO [1]

Developedmathematicalmodel, theRichards model, topredict thecumulative numberof reported cases ofinfections usingvariables, such asfinal case number,per capita growthrate, the exponentof deviation of thecumulative casecurve and turningpoint of theepidemic

NA NA Fitted the model to theEbola data duringvarious time intervals

NA NA

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Khan et al.[36]

WHO situationreports [1], correctedcase data from CDC,parameters takenfrom other studies

Used a deterministicODE transmissionmodel whichdifferentiateshigh-risk (e.g.health-workers)and low-riskpopulations.Estimated theeffective contactrate using anordinaryleast-squaresestimation

Susceptible–exposed–infected–hospitalised–recovered (SEIHR)

Modeldifferentiatedhigh-risk andlow-riskpopulations

Ordinary least-squares(OLS) estimation wasused to obtain optimalvalue of transmissionrate and then estimate R0

NA Both raw reporteddata and correcteddata (usingcorrected CDCdata) were checked

Kiskowski[37]

Case data fromWikipedia, WHOreports [1].Incubation andinfectious periodsbased on previousmodelling studies

Used a stochasticnetwork modelwith three levels ofcommunitystructure(households andcommunities ofhouseholds withina countrypopulation) tomodel SEIRtransmissiondynamics for theEVD spread

Susceptible–exposed–infectious–recovered(SEIR)

Used three levelsof communitystructure in thestochastic model,including(households andcommunities ofhouseholdswithin a countrypopulation)

A comparison of generalR-square coefficients wasused to identifyparameter valuesproviding a good fit tothe empirical data. R wasverified by changing eachparameter one-at-a-time

Local sensitivityanalysis wascarried out toconclude that Rvalues were locallyoptimised for thegiven choice ofother parametervalues

NA

Kucharskiet al. [38]

Case data from WHO[1] and Sierra LeoneMinistry of Health[17]

Developed ODEmodel with theconsideration ofhospitalisation invarious healthcareunits and thosewho are notascertained toinfection

Susceptible–exposed–infectious(ascertained)–infectious (notascertained)–healthcare in EbolaHolding Centers(EHC)/CommunityCare Center (CCC)–Ebola TreatmentUnit (ETU)–removed(SEIIHHR)

Assumedindividuals whoare ascertainedinitially seekhealthcare inEHCs/CCCs. Ifno beds areavailable,individuals willbe sent to ETUs

Fitted the model to casedata reported in eachdistrict of Sierra Leoneusing Bayesian approach

Sensitivity analysiswere performed toexamine the effectof varyingpercentage of caseascertainment oninfection cases

Incorporated acompartment thatconsider aproportion ofinfection cases arenot ascertained

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Li et al. [39] Case data from WHOreports [1].Population datafrom WHO website.Birth data from CIAfactbook [21] andWikipedia. Deathrate from Wikipedia

Developeddifferentialequations model,using least-squaresmethod forparametersestimation. Usedpartial rankcorrelationcoefficients foruncertainty andsensitivity analysisof R0

Susceptible–exposed–infectious–treated/recovered (SEIR)


Fitted the observedvariables with onset anddeath data of EVD byleast-squares method

Sensitivity analysisof R0 wereperformed byexamining sevenparameters withPRCCs

NA

Merler et al.[40]

Demographic HealthSurvey data, Casedata from LiberianMinistry of Health &Social WelfareSituation Reportsand WHO situationreports [1],Household size datafrom DemographicHealth Survey data.Population densityPopulation of theWorld. Locations ofhospitals and clinicsfromOpenStreetMap.Parameters fromother studies

A spatialagent-based modelthat matchedpopulation densityestimates iddeveloped.Markovchain Monte Carlois used to calibratethe model

Susceptible–exposed–infectious–funeral–recovered (SEIFR)

Model accountsfor differences intransmission inhouseholds,generalcommunity,hospitals andfunerals

Matching an early reportfrom WHO, Markovchain Monte Carloapproach is used toexplore the likelihood ofthe recorded number ofdeaths in healthcareworkers and in thegeneral population basedon official reports.Random-walkMetropolis-Hastingssampling was used toexplore the parameterspace

Sensitivity analyseswere carried outwith respect tomainepidemiologicalparameters, on thetransmission in thegeneralcommunity and ontransmission inhospitals

Considered aunder-reportingscenario in whichthe study stillassumed 100%reporting inhealthcare workersbut a 50%reporting in thegeneral population

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Valdez et al.[41]

Case data fromWHO [1]

Developedstochastic modelwith 10compartmentalstates to considervarioushospitalisation anddead groups usingGillespie algorithm

Susceptible–exposed–infected but notinfectious–infected–hospitalised–recovered-dead(SEIHRF)

Consideredinfected andhospitalisedindividualsaccording totheir fate. Forinstance, thosewho are infected,will behospitalised, andwill die as oneclass and thosewho are infected,won’t behospitalised, andwill die as classanother

Calibrated the model withthe data by themaximum-likelihoodmethod. Computed theleast-square values of themodel outcomes basedon a set of parametersgenerated using LHSfrom plausible parameterspace

Sensitivity analyseswere performed toexamine therobustness of theestimated values ofthe transmissioncoefficients whenparameters change

NA

Weitz andDushoff [5]

Case data from theCaitlin Rivers githubwebsite [19]

Transmission modelusing ensembleadjustmentKalman filter(EAKF) to modela population ofdeceased infectiousindividuals

Susceptible–exposed–infected–contaminateddeceased–isolatedinfectious–removed(SEICIIR)

Modellingcontainment andisolationcompartments

Parameters estimatedusing a least-squarescurve fitting algorithm toobtain a choice ofparameters withrelatively accurate fit

NA NA

Yamin et al.[42]

Model parametersfrom other studies,Liberia Institute ofStatistics andGeo-InformationServices. Incidenceand case fatalityreports, contacttracing data obtainedfrom Ministry ofHealth and SocialWelfare, Republic ofLiberia

Transmission modelthat considers threesequential phasesincludingincubation, earlysymptomatic, andlate symptomaticand accounts forviral loaddifferences insurvivors andnon-survivors

Incubation-earlysymptomatic-latesymptomatic

Accounted forviral loaddifferences insurvivors andnon-survivors

Sampling possible rangesof epidemiologicalparameters to generatecontact distribution forcontact data. Thenumber of secondarycases arose wascalculated

NA NA

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Table 3. An overview of modelling studies of Ebola and study designs (Research aim: Trajectory prediction)

References Dataset/Factors

Description ofModellingApproaches


Assumption ofpopulation mixing, ifapplicable

Model fitting andcalibrationapproach, ifapplicable

Sensitivity analysis, ifapplicable


Area et al. [43] Case data fromWHO [1]

Developed classicaldifferentialequations andfractional SEIRmodel to predict theoutbreak trajectory

Susceptible–exposed–infectious–removed(SEIR)


Fitted models withthe real data andobtainedparameters valuesusing l^2 norm

NA NA

Bellan et al. [44] Unspecified Compared theprojections of twosimple models (withand withoutasymptomaticinfection) based onthe Ebola epidemicin Liberia

NA NA NA NA Modelledscenarios thatdoes not accountfor asymptomaticinfections andaccount for thepresence ofasymoptomicinfection

Dong et al. [45] Case data fromWHO [1]

Ebola case predictionwas obtained by aSEIIRF model withthe consideration ofpost-death andhospitalisationcompartments

Susceptible–exposed–infected–recovered–hospitalised–buried(SEIIRHF)

Considered those whohave died and are inthe process of beingburied and numberof people in hospitalwho develop to firststage or second stageof infection

Fitted caseprediction curvewith real databoth in total casesand death cases

NA NA

Drake et al. [46] Case data fromWHO [1], LiberiaMinistry ofHealth or UnitedNations Officefor theCoordination ofHumanitarianAffairs(UN-OCHA)

Developed amulti-type branchingprocess model thatincorporates keyheterogeneities andtime-varyingparameters to mimicchanging humanbehaviour andcontrols in Liberia.Focused on thenumbers of newinfections caused byeach caseconsidering offspringdistributions

Two generations ofinfection in amulti-type branchingprocess model

Accounted forsubpopulationdifferences,including hospitaltreatment vs.community care,transmission atfunerals, andscenario-dependenttransmission riskdifferences duringcare-giving

Fitted ensemblemodel fromplausibleparameters withthe case data inLiberia and alsofitted outcome toinfectiongenerations inHCWs and in thecommunity

Investigated thesensitivity of themodel to parametersusing LHS over amuch wider range ofthe least-squares fitfor each parameter

Assumedunder-reportingby a factor of 2·5

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Table 3 (cont.)

References Dataset/Factors

Description ofModellingApproaches



Model fitting andcalibrationapproach, ifapplicable



Fast et al. [47] Case data from theLiberian Ministryof Health andSocial welfare adlocal countyhealth offices.ETU admissionsdata fromGithub. Socialmobilisation datafrom WHO andUNICEF reports.Parameters fromUNICEF reports,WHO reports [1].Population datafrom LiberianInstitute ofStatistics andGeo-informationServices

Transmission modelbased on contactnetwork. Accountsfor change inattitudes thatunderlie behaviourchange by simulatingthe progress of theEVD epidemic withand withoutpopulationbehaviour change,then comparingscenarios withobserved data

Susceptible-exposed-infected-hospitalised-buried-unburied fatality-recovered(SEIHFCFBR)

Contact networkmodel consideredindividuals as nodesand disease-spreading contacts asedges.Hospitalisation andfatality componentswere included

Model was fitted toweekly cases inLofa County byconsidering thefitting metric ofmean absoluteerror

NA The modelconsidered onlycases that soughttreatment or weresafely buried, butmodelled all cases

White et al. [48] Case data fromWHO [1] anddaily counts fromthe public pressreleases from theSierra LeoneanMinistry ofHealth [17]

Developedcompartmentalmodel with sixcompartments todescribe theoutbreaks in SierraLeone

Susceptible–exposed–infectious (not yetreported)–treated(reported)–dead(unreported)–recovered(reported)–dead(reported)(SEOTRDTRTD)

Considered infectedand hospitalisedindividualsaccording to theirreported status

Implemented anensembletrajectory modeland generated amatrix ofplausibleparameter valuesto fit the modelfor the first 56days

NA Used 2·5correction factorestimated by theCDC to correctforunderreporting

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Table 4. An overview of modelling studies of Ebola and study designs (Research aims: Parameter estimation and Trajectory prediction)

Reference Dataset/FactorsDescription ofModelling Approaches





Description ofaccount for data bias,if applicable

Althaus et al. [27] Case data frompublished reports.Parameters fromprevious EVDoutbreaks

Transmission model witha set of ODEs and usedMaximum likelihoodestimates to determinemodel parameters(baseline transmissionrate, rate at whichcontrol measuresreduce transmission,case fatality rate)

SEIR Assumed homogeneousmixing

Fitted a dynamictransmission model todata about reportedcases and deaths ofEVD during a smallurban outbreak inNigeria usingMaximum likelihoodmethods

NA NA

Barbarossa et al.[28]

Case data from WHOreports [1]. Parametersestimated from variousstudies

Compartmentalpopulation modelbased on Legrand’sstudy [24] thatdistinguishes betweencommunity andhospitalised patients,and recognisesimportance of deceasedindividuals who canstill transmit the virusat burials

Susceptible–latent–infectious–hospitalised–dead–buried–removed(SEIHBDR)

Model divided infectiouspopulation into thosewho exist in thecommunity and thosewho exist in hospitals,and consideredpost-death transmission

Fitted model outcomesto the WHO reports forweekly case incidence.The data were fit withpiecewise exponentialcurves

Studied the effects ofmodel parameters onthe basic reproductionnumber and on the finalepidemic size. LHS isused to generate arepresentative sampleset of test parametersfrom the ranges.Focused mostly on thesensitivity of the time ofintervention. PRCCsanalysis was reported

NA

Camacho et al.[49]

Case data from SierraLeone Ministry ofHealth and Sanitationand WHO reports [1].Data on ETCs, EHCs,CCCs from TheHumanitarian DataExchange. Proportionof symptomatic casesfrom the UN for EbolaEmergency Responseand the NationalEmergency ResponseCentre

Transmission model withtime-dependenttransmission rate,accounting forhospitalisation anddelay in case reporting

Susceptible–exposed1–exposed2–infectious–infectious(hospitalisation)–removed

Modelling individualsprogressed throughstages, includinghospitalisationcompartment

Fitted model to the timeseries of weeklyreported cases usingBayesian approach

Sensitivity analysis wasperformed by takingaveraged posteriordistribution of R over aperiod of Jan 2015

Assumed proportionof symptomaticcases reported at60%, accounted forthe potentialvariability inaccuracy ofreporting over timeand accounted forover-disperseddelay between onsetof symptoms andnotification ofreported cases

Chowell et al. [50] Case data from WHOreports [1]

Logistic growth modelsfitted with the minimalamount of case data

NA NA Fitted logistic growthmodels to thecumulative number ofcases usingleast-squares

NA NA

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Table 4 (cont.)







Evans andMammadov [51]

Case data fromWHO [1] Estimated thereproduction numbersfor the total period ofepidemic and fordifferent consequenttime intervals usingsimple linear model andconsidered the averageinfectious period as atime-dependentparameter

NA NA Fitted model outcomewith the cumulativenumbers of infectedcases and deaths usingglobal optimisationalgorithm DSO

NA NA

Fasina et al. [52] Case data from WHOreports [1] and publicsource

Simplified version ofLegrand’s model [24]accounting forcontribution ofcommunity andhealthcare settings byadjusting baselinetransmission rates,diagnostic rates, andenhancement ofinfection controlmeasures

Susceptible–exposed–infectious–hospitalised–removedfrom isolation afterrecovery or death(SEIHP)

Model divided infectiousindividuals into groupsin the community andisolation in a hospital

Assessed the timing ofcontrol interventionson the size of the EVDoutbreak in Nigeria byextensive simulationruns

NA NA

Fisman and Tuite[53]

Case data from WHOreports [1], CaitlinRivers github website[19]

Incidence Decay withExponentialAdjustment (IDEA)model using maximum-likelihood methods toidentify best-fit modelparameters

NA NA Used maximum-likelihood methods toidentify the optimal,best and worst casemodel parameters forthe IDEA model

Sensitivity analysis wereperformed by varyingvaccine efficacy

NA

Fisman et al. [54] Case data from CaitlinRivers github website[19], Virologically-confirmed case countsby date from theVirology Down Underblog [20]

IDEA model, a twoparametermathematical modeldescribes exponentialgrowth simultaneousdecay, was used toproject epidemic curveaccounting forincidence decay

NA NA Model was fitted to timeseries data iteratively,using a progressivelyincreasing number ofoutbreak generations.Best fit parametervalues are estimated byfitting; – objectivefunction: minimise theroot mean-squareddistance between modelestimates and empiricaldata

Checked separate modelsto epidemic curvesderived from reporteddeaths, curves basedonly on virologicallyconfirmed cases, as wellas curves based onvarying assumptionsabout case-underreporting

Fitted separatemodels usingassumptions aboutcase underreporting(50% and 100%).

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Table 4 (cont.)







Lewnard et al.[55]

Montserrado case data,Number of Beds inEbola TreatmentCentres from Ministryof Health and SocialWelfare, Liberia Ebolasituation reports. Totalpopulation ofMontserrado fromRepublic of Liberia2008 Population andHousing Census. Timeto burial, relativetransmission rate fromprevious study.International SOSHospital response andisolation/treatmentcentres also used todetermine Number ofBeds in ETCs

Developed a differentialequation model whichincludes a latentpopulation (L), twotypes of recoverypopulations (R),differentiation ofascertained (A) cases(which do notcontribute tocommunitytransmission)


Modelled cumulativecases and mortality as aPoisson-distributedrandom variable.Model calibrated bysampling via MarkovChain Monte Carlousing a Metropolis–Hastings acceptancerule

NA Addressedunderreporting ordelays in reportingby fitting model toestimate the delaybetween thebeginning of theinfectious periodand time ofascertainment

Liu et al. [56] Case data fromWHO [1] Logistic, Gompertz,Rosenzweg andRichards models weredeveloped andcompared

NA NA Fitted the model usingprecise estimates byBayes factors andobtained modelparameters

NA NA

Meltzer et al. [9] Infectious period fromThe World Bankwebsite, CDC website.Likelihood of a patientgoing to an ETU andthe number of days thata patient in each patientcategory would spendin the hospital. Actualnumber of beds in use –from expert opinion

EbolaResponse, aMarkov chain model,categorises patientsetting (i) hospitalisedfacility, (ii) home/community where thereis reduced diseasetransmission, (iii) homewith no effectiveisolation. Model alsoaccounts for under-reporting of cases, andallows for importedcases or cases with noknown contacts

Susceptible–infected–incubation–infectious–infectious (burial)–recovered

Considered those whodie but whose burialprovides risk foronward transmission.Patients werecategorised intohospitalised in an Ebolatreatment unit (ETU)or medical care facility,home or in acommunity setting andhome with no effectiveisolation

Model parameters werealtered to produce amatched outcome withthe reported cases todate using goodness-of-fit test

NA A underreportingcorrection factor of2·5 was used toestimate future totalcases

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Table 4 (cont.)







Nishiura andChowell [57]

Case data form WHOreports [1]

Mathematical modellingconsidering time- andcountry-specificincidence data toestimate reproductivenumbers, usinglikelihood-basedmethod for real-timeparameter estimation.Estimated dailyincidence curves byfitting smoothing splineto county-specificcumulative curves ofcases

NA NA Fitted a smoothingspline to cumulativereported cases bycountry and adjustedthe spline functionbased on the dailyincidence time series

Sensitivity analyses ofreproduction numberwere carried out byvarying the meangeneration time

NA

Pandey et al. [30] Demographic data fromthe 2008 National,Housing Census ofLiberia. Case data fromLiberian Ministry ofHealth and SocialWelfare

Transmission modeltakes into accounttransmission within andbetween thecommunity, hospitalsand funerals

Susceptible–latent–infected–deceased–recovered–buried(SEIFRD)

Stratifiedepidemiological classinto compartments thatcorrespond to thegeneral community,hospitals and funerals

Used weighted least-squares to fit the modelto case data. Convertedevent-based stochasticmodel to a discrete-timedifference equationmodel. Then evaluatedthe difference equationmodel, fitted the outputto the data, andcalculated the best-fitestimates of certainparameters byminimising theweighted least-squaresdifference between themodel output and thedata with the Quasi-Newton algorithm

Done extensivesensitivity analysis andelasticity analysis oninterventioneffectiveness tovariation inepidemiologicalparameters. PRCCswas used

Refitted model toaccount for a rangeof plausibleunderreporting.Varied the levels ofunder-reporting ofEbola cases in bothcommunity andhospitals, as well asonly communities

Rivers et al. [58] Case data from WHOreports [1] andMinistry of Health ofLiberia and SierraLeone (available onlinefrom the Caitlin Riversgithub website) [19]

Compartmental modeladapted fromLegrand’s study [24];stochastic model wasimplemented usingGillespie’s algorithm

Susceptible–exposed–infectious–hospitalised–funeral–removed (SEIHFR)

Model accounted forthose who arehospitalised anddeceased individualswho can still transmitvirus

A deterministic versionof the model was fit andvalidated to the currentoutbreak data usingleast-squaresoptimisation. The last15 days of reportedcases were given one-quarter of the weight inthe model topreferentially fit themost recent data

NA NA

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Shaman et al. [59] Case data from WHOreports [1]

An ensembleSusceptible–exposed–infectious–recovered-X(SEIRX)–EAKFframework usingobservations, dynamicmodelling and Bayesianinference to generatesimulations

SEIRX Additional Xcompartments wereintroduced to describeassimilation ofmortality and casefatality rate

Fitted the modelvariables andparameters with weeklyobservations andallowed for timevarying of variablesand Rt parameters

Sensitivity analysis wereperformed by changingmodel structure, andvarying population sizeand initial parameterranges

NA

Shen et al. [60] Case data fromWHO [1] Developed mathematicalODE model to studyEbola infection withisolation, mediaimpact, post-deathtransmission andvaccination

Susceptible–vaccinated–latent (undetectable)–latent (detectable)–infectious withsymptoms–isolatedindividuals–dead buthave not been buried–recovered

Considered those whohave died and are in theprocess of being buried

Fitted the model toepidemiological data ofreported cumulativenumbers of infectedcases and deaths

Examined the mostsensitive parameters tothe R0 and the finalepidemic size.LHS and PRCCmethods were used

NA

Siettos et al. [61] Time series count data,including cumulativeincidence, from WHOreports. Cumulativedeaths data fromWikipedia and WHOcase reports [1].Demographic datafrom United Nations[22]

Agent-based modelusing a small-worldnetwork constructedusing the Watts &Strogatz algorithm

Susceptible–exposed–infected–dead (but notyet buried)–dead (safelyburied)–removed

Agent-based modelconsidered individualsinteract through asmall-world network

Fitted two networkcharacteristics and fourepidemic rates withreported outbreak data

NA NA

Towers et al. [62] Case data fromHealthMap, WHOreports [1]

Fitted piecewiseexponential curvesalong the data timeseries to estimate theevolving rate ofexponential rise (ordecline) in cases. SEIRmodel developed toestimate the temporalpatterns of the effectivereproduction numberfor the outbreak in eachcountry


Fitted piecewiseexponential function toestimate rates ofexponential rise fromthe average daily EVDincidence data

Sensitivity analyses wereperformed usingLHS and PRCCmethods to test therobustness of resultwith respect to the exactnumber of contiguouspoints used for the fits

NA

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Table 4 (cont.)







Webb et al. [63] Case data from WHOreports [1]. Parametersfrom various studies

Differential equationswith compartments ofthe epidemicpopulation thatsimulated forwardprojection of epidemicusing Continuous TimeMarkov Chain. Modelincorporates contacttracing of infectiouscases. Bothdeterministic andstochastic models wererun

SEICIIR Modelling containmentand isolationcompartments

Parameters estimatedusing a least-squarescurve fitting algorithmto obtain a choice ofparameters withrelatively accurate fit

Sensitivity analyses wereperformed in twocontact tracingparameters. Thecontact tracingparameters were testedin sensitivity analysis

A ratio of unreportedcase of 1·78 is usedfor estimation

WHO [25] Case data frominvestigation formsfrom confirmed,probable and suspectedEVD cases identified inGuinea, Liberia,Nigeria, and SierraLeone; also frominformal case reports;data from diagnosticlaboratories; data fromburials

Projected case numbersusing two methods: (i)regression method and(ii) stochastic branchingprocess model

NA NA Epidemiologicalparameters were fittedwith gammaprobabilitydistributions

Sensitivity analyses wereperformed by assumingdifferent mean serialintervals of 11 and 13and including suspectedas well as confirmedand probable cases inthe analysis

NA

WHO [64] Case data from viralhaemorrhagic feverdata collection forms,treatment facilities,contact tracing forms

Reported summarystatistics and predictionoutcomes throughsimple model fitted todata. Used weightedaverage to estimate theduration reported of theobserved means of thedistributions ofdurations fromhospitalisation todischarge andhospitalisation to death

NA NA Gamma distributionswere fitted to confirmedand probable cases

NA NA

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period, infectious period and case fatality rate, asshown in Figure 3 (and Supplementary Document 1Figure S4). The median of the mean serial interval is14·35 days (interquartile range: 12·28, 16·35), latencyperiod is 9·70 days (interquartile range: 8·80, 10·38),the infectious period is 7 days (interquartile range:4·00, 10·00) and case fatality rate is 0·68 (interquartilerange: 0·48, 0·71) (the distributions by country areshown in Figure 3).

We also studied the relationship between estimatedR0 and the used or estimated epidemiology para-meters. Different studies may estimate/fine tune theseparameters or use previously published values whenproducing R0 estimates. Figure 4 demonstrates therelationship between the estimated R0 with differentserial interval, latency period, infectious period andfatality rates (We also reported the same figure with-out considering the Nigerian data in SupplementaryDocument 1 Figure S4). Based on the results, we donot observe any obvious trend of R0 estimates fromstudies using/estimating various mean values of serialinterval, incubation period and infectious period. Wecarried out correlation tests between these values(for pairwise complete observations) and theSpearman test results were insignificant (on overalland per-country basis). The synthesised values ofreported epidemiological parameters in terms of R0,serial interval, latency period, infectious period andcase fatality can be found in the SupplementaryDocument 2 Table S2.

Synthesised results and figures stratified by model-ling types, approaches, mixing assumptions and sensi-tivity analyses are provided in SupplementaryDocuments 1 Figures S5–S12 and SupplementaryDocuments 2. We do not observe significant differencein the distributions of R0 mean estimate from thoseincluded studies did or did not carry out sensitivity ana-lysis – as most sensitivity analyses are typically con-ducted in orthogonal manner to estimate relatedparameters. Furthermore, R0 is also sometime beingused as a response function of sensitivity analysis ofother model parameters. Additionally, 27 studiesoffered epidemic trajectory projection and providedestimated number of cases (without additional inter-vention). Figure 5 shows the relationship betweenmodel prediction to WHO case observation ratio(matched with forecast target date) and account forunderreporting and consideration of compartment.The median values of ratio between prediction andobservation are significantly different (P value 4 0·1)in the pair between do and do not account for

underreporting [median ratio of those do account forunderreporting is 4·35 (interquartile range: 1·52,15·03) and do not account for underreporting is 1·19(interquartile range: 0·98, 1·53)]. However, we do notobserve a significant relationship in the pairs of differ-ent compartments used. We also paired up models thatoffered model prediction with and without consideringunderreporting and carried out the same set of analysis.The matched models analysis results are provided inSupplementary Document 1 Figure S12. The synthe-sised results of epidemic projection with indication ofaccounting for data uncertainty and used of hospital-isation and/or funeral compartments are also providedin the Supplementary Document 2 Table S3.

DISCUSSION

We systematically reviewed 2014–2015 Ebola model-ling studies, which provided epidemiological insightsto the current Ebola and future outbreaks. We evalu-ated the selected studies based on the sources of thecase data used, and modelling approaches by model-ling aim and we further synthesised the reported R0

results and the distributions of key epidemiologicalparameters based on compartment designs, and con-sideration of underreporting. We found that epidemicmodels offered R0 mean estimates for this EVD arecountry-specific, but these are not associating withseveral key disease parameters, compartment designsand accounting for underreporting.

In this EVD outbreak, we noticed a significantly dif-ferent relationship between the contexts (i.e. the coun-try of interest) with estimations in R0 (particularlywith regards to Nigeria, which had a much higher R0

estimate). We only observed differences in the valuesof estimated/used serial interval, latency period, infec-tious period and case fatality rates by country but themedian differences are not statistically significant.

We generally did not observe any apparent system-atic pattern in the distribution of estimated R0 whenspecifying different compartments. This may be dueto one fundamental issue that models are generallyfitted based on observed epidemiology data from thesame original sources and other associated model para-meters within the model could be calibrated altogetherto achieve model fitting. This also coincides with ourfinding –models that utilised different mean serialintervals, incubation periods and infectious periodswithin plausible ranges yielded similar estimates of R0.

R0 can be expressed as the product of transmissionprobability per contact, number of contacts per time




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unit and duration of infectious period; however, thesequantities are usually difficult to parameterise directlyfrom observing a outbreak [14]. In a simplified epi-demic model assumption, the lengths (and distribu-tions) of serial interval [16] and infectious period[65] are influential to R0 estimation. Furthermore,inclusion of a latency period into a model would resultin a slower epidemic growth rate after pathogen inva-sion due to individuals needing to pass through theexposed class before they can contribute to the trans-mission process [14].

Although serial interval, latency period and infec-tious period are computationally related to the esti-mate of R0 (differences account for compartmentalcontact heterogeneity and epidemic model

assumptions), we observed that the use of differentmean serial intervals, incubation periods and infec-tious periods yield similar estimates of R0. However,we only compared the relationship by median dura-tions of these epidemiological parameters – using dif-ferent mean distributions may produce a differenteffect with the same values.

Due to changes in reporting systems and/or publicawareness of disease over time, there may have beenunknown observation biases and errors over time(i.e. there may be higher rates of disease reportingdue to greater public awareness of the disease). Theincluded studies that considered underreporting issuesgenerally offered similar R0 estimates to those withoutincorporated underreporting and offered a larger case

Fig. 2. Summary of estimated basic reproduction numbers (topleft) by West African countries (G, Guinea; L, Liberia; N,Nigeria; O, Overall; and SL, Sierra Leone), (topright) by account for underreporting, (bottomleft) consideration ofcompartment (F, funeral; H, hospitalisation; H+F, both hospitalisation and funeral; N, not considered), (bottomright) lastupdated data used (with trend line of R0 estimation). Kruskal–Wallis non-parametric test result showed that thedifferences between the medians of the estimated R0 mean by country (excluding Nigeria) are statistically insignificant(P value > 0·05). Furthermore, we cannot find any significant relationship to reject the null hypotheses for thoseaccounting for underreporting and different compartments used (by both Kruskal–Wallis and Mood’s median tests).




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forecast compared with actual case observation at theforecast target date. Without high-quality and reliabledata, it is challenging to accurately estimate theimpact of time-dependent changing factors andincorporate them into a model. We recommend healthauthorities endeavour to share detailed epidemiologicattributes related to reported cases, including geo-graphical locations of cases, information on contactnetworks and date of symptom onset. The availabilityof ongoing case data can help to recognise hiddenchanges of disease patterns over time. Health author-ities could consider providing time-dependent asso-ciated correction factors according to the practicalunderreporting situations and force of interventionstrategies. Furthermore, incorporating surveillance

outcomes from phylogenetic [66] and serological [67]studies would potentially useful for advising theunderlying emerging disease transmission characteris-tics and identify undetected cases. These would beuseful to modellers for accurately calibrating epi-demiological models based on actual outbreak situa-tions, which can then feedback meaningfully intodecision support during the outbreak.

Furthermore, we observed that many included mod-els in this review have inferred data about diseasebehaviour using disease parameters calculated fromprevious EVD outbreaks. It is noted that this Ebolaoutbreak has similar parameters estimates with the pre-viously EVD outbreak parameters given by Drakeet al. [4]. Furthermore, it will be useful to develop a

Fig. 3. Summary of estimated epidemiology parameters by country (G, Guinea; L, Liberia; N, Nigeria; O, Overall; SL,Sierra Leone) for (topleft) serial interval, (topright) incubation period, (bottomleft) infectious period, (bottomright) fatalityrate. Kruskal–Wallis non-parametric test results showed that we cannot reject the null hypotheses – i.e. the mean values ofthese epidemiology parameters have identical data distributions from the included countries.




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centralised reference data platform, which allows forsharing of epidemiological parameters. This wouldenable modellers to use/calibrate disease parametersbased on comparable metrics. Together with otherEVD modelling review outcomes [4, 11], this study out-come laid groundwork for such reference.

During the later stage of the EVD epidemic, newevidence emerged that EVD can survive in variousbody fluids during convalescence [68, 69] and mayresult in transmission of infection [70–75]. WHO hasrecently highlighted the potential of the occurrenceof EVD flare-ups and disease re-introduction [2]. Atthe post-EVD outbreak stage, accounting for risk oftransmission from ‘recovered’ EVD patients [76, 77]should be a priority for future EVD modelling.

Accuracy, transparency and flexibility are the majorconsiderations when formulating models for infectiousdiseases [14]. The EbolaRepsonse tool created by theCDC [9], which allows users to project the numberof Ebola cases in Liberia and Sierra Leone using asimple model implemented on a Microsoft ExcelWorksheet. The WHO Response Team [31] studywas one of the first studies providing a detailed epi-demiological description of the EVD epidemic usingprimary data collected from hospitals and patients –the study also provided short-term projections of theepidemic for Guinea, Liberia and Sierra Leone.These early modelling studies are some of those suc-cessful examples that demonstrate how timely andeffectively use of phenomenological and mechanistic

Fig. 4. Relationship between estimated R0 and epidemiology parameters. (topleft) serial interval, (topright) incubationperiod, (bottomleft) infectious period, (bottomright) fatality rate. (G, Guinea; L, Liberia; N, Nigeria; O, Overall; SL,Sierra Leone) (Spearman tests among these pairs (for pairwise complete observations) are all insignificant). Only completepairs between R0 and epidemiology parameters are shown in this figure.




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modelling methods support emerging disease under-standing and public health responses.

Modelling outcomes can be different depending onthe epidemiological characteristics of the emergingdiseases and the interplay among pathogen, host andenvironment. For this EVD outbreak, simpler modelsgenerally yielded similar estimates of R0 regardless ofthe consideration of additional hospitalisation and/orfuneral compartments and underreporting. However,context-specific models, which mimic the way a dis-ease is transmitted among stages realistically andmeaningfully, allow for justification for intervention

effects under different transmission contexts. Underan epidemic emergency, a “simple enough but notsimpler” model, which allows for understanding ofkey epidemic dynamics (i.e. offer transparency to pub-lic health policy makers), may play a critical role foradvising rapid policy decisions and predicting out-break progression at the early phase of an outbreak.

CONCLUSION

Newly emerging infectious diseases are the most challen-ging to manage due to the uncertainties in clinical

Fig. 5. Summary of ratio between predicted cases and WHO reported cases (matched with forecast target date). (topleft)forecast target date, (topright) by West African countries (G, Guinea; L, Liberia; N, Nigeria; O, Overall; and SL, SierraLeone), (bottomleft) by account for underreporting, (bottomright) consideration of compartment (F, funeral; H,hospitalisation; H + F, both hospitalisation and funeral; N, not considered). The Mood’s two sample median test from thepair between do and do not account for underreporting shows that the median values of ratio between prediction andobservation are significantly different (P value 4 0·1). We cannot reject the null hypotheses of the pairs of differentcompartments used (by both Kruskal–Wallis and Mood’s tests).




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impact and transmissibility. Epidemiological parametersare usually difficult to observe directly from an emerginginfectious disease outbreak and would require modellingmethods to accurately estimate at the early phase of adisease outbreak. Epidemic modelling is a quantitativeapproach to understanding disease transmission withina specific population and provides indications of futuretrends. Such models are well-recognised tools to aid pol-icy formulation in the early phase of epidemics.

Despite varied complexity and methods, the esti-mates of R0 yielded from numerous studies were rea-sonably consistent in this EVD outbreak regardless ofconcurrent use of other associated epidemiology para-meters. Different model design decision did not appearto meaningfully impact the resulting R0 estimates butmodels that accounted for data uncertainty offered alarger case forecast compared with actual case observa-tion at the forecast target date. Simple early modelsremain informative to reference, and provide a founda-tion for more complex transmission modelling tounderstand the progression of a disease outbreak.

SUPPLEMENTARY MATERIAL

The supplementary material for this article can befound at https://doi.org/10.1017/S0950268817000164.

ACKNOWLEDGEMENTS

This study was supported by National Health &Medical Research Council (NHMRC) – ProjectGrant (Australia) – APP1082524.

AUTHORS ’ CONTRIBUTIONSTATEMENT

The study was conceived by Z.W. and R.M. Z.W., C.B., A.C. and R.M. contributing to the study design.Research data/information was retrieved and inter-preted by Z.W. and C.B. Z.W. and C.B. led the writ-ing of the paper and all authors revised and refined thearguments. All authors approved the article.

DECLARATION OF INTEREST

None.

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