Table 2.

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

References	Dataset/factors	Description of modelling approaches	Compartments, if applicable	Assumption of population mixing, if applicable	Model fitting and calibration approach, if applicable	Sensitivity analysis, if applicable	Description of account for data bias, if applicable
Agusto et al. [32]	Case data form WHO reports [1]. Population data from Guinea census	Compartmental mathematical model which stratifies population into those in the community and those in healthcare facilities and incorporates disease transmission features in such units	Susceptible–exposed–symptomatic–recovered–deceased–cremated (SEIRDC)	Model divided population into individuals from the community and individuals who work in healthcare settings and subdivided individuals from the community into those who visit healthcare settings and the rest of the public	Some model parameters were fitted using data from other study. Threshold quantity R0 is estimated using the Ebola data for Guinea and the demographic parameter	R0 was the response function of sensitivity analysis of other model parameters. partial-rank correlation coefficients (PRCCs) was used	NA
Ajelli et al. [33]	Data consisted of routine health data and medical records of the outbreak in the Pukehun District. Also analysed registers of two Ebola holding centres, contact tracing forms and interviewed healthcare workers	Reported summary statistics of key epidemiological parameters, generate time series plots and developed transmission chain for the outbreak using outbreak data	NA	NA	Fitted distribution number of secondary cases using negative binomial model	NA	NA
Althaus [26]	Case data from WHO reports [1]. Parameters from previous Ebola outbreaks	Transmission model with a set of ODEs and used maximum-likelihood estimates to determine R0	Susceptible–exposed–infectious–recovered (SEIR)	Assumed homogeneous mixing	Fitted the model to the reported data of infected cases and deaths in Guinea, Sierra Leone and Liberia and provided the maximum-likelihood estimates of R0	NA	NA
Browne et al. [34]	Case data from WHO reports [1]	Deterministic model that traces back to transmissions, and incorporate disease traits and control together	Susceptible–exposed–infectious (hospitalised/reported)– infectious (not hospitalised and unreported)–cumulative hospitalised/reported	Modelled key features of contact tracing and hospitalisation	NA	Studied the effects of model parameters on the effective reproduction number using LHS and PRCC	NA
Gomes et al. [29]	Case data from WHO reports [1]. Population data from ‘Gridded Population of the World’. Air travel data from the International Air Transport Association and Official Airline Guide. Mobility data from administrative regions	Used the Global Epidemic and Mobility Model to generate stochastic, individual based simulations of EVD spread worldwide	Susceptible–exposed–infectious–hospitalised–death but not yet buried–removed (SEIHFR)	Model included hospitalised and funeral compartment and accounted for different population sizes around the world, including different traffic flows	Multi-model inference approach was used to calibrate on data from official WHO data. Also performed Latin hypercube sampling (LHS) of the parameter space	Performed sensitivity analysis assuming 80% airline traffic reduction from and to West African countries affected by EVD and 50% underreporting	Tested on 50% underreporting assumption
Hsieh [35]	Case data from WHO [1]	Developed mathematical model, the Richards model, to predict the cumulative number of reported cases of infections using variables, such as final case number, per capita growth rate, the exponent of deviation of the cumulative case curve and turning point of the epidemic	NA	NA	Fitted the model to the Ebola data during various time intervals	NA	NA
Khan et al. [36]	WHO situation reports [1], corrected case data from CDC, parameters taken from other studies	Used a deterministic ODE transmission model which differentiates high-risk (e.g. health-workers) and low-risk populations. Estimated the effective contact rate using an ordinary least-squares estimation	Susceptible–exposed–infected–hospitalised–recovered (SEIHR)	Model differentiated high-risk and low-risk populations	Ordinary least-squares (OLS) estimation was used to obtain optimal value of transmission rate and then estimate R0	NA	Both raw reported data and corrected data (using corrected CDC data) were checked
Kiskowski [37]	Case data from Wikipedia, WHO reports [1]. Incubation and infectious periods based on previous modelling studies	Used a stochastic network model with three levels of community structure (households and communities of households within a country population) to model SEIR transmission dynamics for the EVD spread	Susceptible–exposed–infectious–recovered (SEIR)	Used three levels of community structure in the stochastic model, including (households and communities of households within a country population)	A comparison of general R-square coefficients was used to identify parameter values providing a good fit to the empirical data. R was verified by changing each parameter one-at-a-time	Local sensitivity analysis was carried out to conclude that R values were locally optimised for the given choice of other parameter values	NA
Kucharski et al. [38]	Case data from WHO [1] and Sierra Leone Ministry of Health [17]	Developed ODE model with the consideration of hospitalisation in various healthcare units and those who are not ascertained to infection	Susceptible–exposed–infectious (ascertained)–infectious (not ascertained)–healthcare in Ebola Holding Centers (EHC)/Community Care Center (CCC)–Ebola Treatment Unit (ETU)–removed (SEIIHHR)	Assumed individuals who are ascertained initially seek healthcare in EHCs/CCCs. If no beds are available, individuals will be sent to ETUs	Fitted the model to case data reported in each district of Sierra Leone using Bayesian approach	Sensitivity analysis were performed to examine the effect of varying percentage of case ascertainment on infection cases	Incorporated a compartment that consider a proportion of infection cases are not ascertained
Li et al. [39]	Case data from WHO reports [1]. Population data from WHO website. Birth data from CIA factbook [21] and Wikipedia. Death rate from Wikipedia	Developed differential equations model, using least-squares method for parameters estimation. Used partial rank correlation coefficients for uncertainty and sensitivity analysis of R0	Susceptible–exposed–infectious–treated/recovered (SEIR)	Assumed homogeneous mixing	Fitted the observed variables with onset and death data of EVD by least-squares method	Sensitivity analysis of R0 were performed by examining seven parameters with PRCCs	NA
Merler et al. [40]	Demographic Health Survey data, Case data from Liberian Ministry of Health & Social Welfare Situation Reports and WHO situation reports [1], Household size data from Demographic Health Survey data. Population density Population of the World. Locations of hospitals and clinics from OpenStreetMap. Parameters from other studies	A spatial agent-based model that matched population density estimates id developed. Markov chain Monte Carlo is used to calibrate the model	Susceptible–exposed–infectious–funeral–recovered (SEIFR)	Model accounts for differences in transmission in households, general community, hospitals and funerals	Matching an early report from WHO, Markov chain Monte Carlo approach is used to explore the likelihood of the recorded number of deaths in healthcare workers and in the general population based on official reports. Random-walk Metropolis-Hastings sampling was used to explore the parameter space	Sensitivity analyses were carried out with respect to main epidemiological parameters, on the transmission in the general community and on transmission in hospitals	Considered a under-reporting scenario in which the study still assumed 100% reporting in healthcare workers but a 50% reporting in the general population
Valdez et al. [41]	Case data from WHO [1]	Developed stochastic model with 10 compartmental states to consider various hospitalisation and dead groups using Gillespie algorithm	Susceptible–exposed–infected but not infectious–infected–hospitalised–recovered-dead (SEIHRF)	Considered infected and hospitalised individuals according to their fate. For instance, those who are infected, will be hospitalised, and will die as one class and those who are infected, won't be hospitalised, and will die as class another	Calibrated the model with the data by the maximum-likelihood method. Computed the least-square values of the model outcomes based on a set of parameters generated using LHS from plausible parameter space	Sensitivity analyses were performed to examine the robustness of the estimated values of the transmission coefficients when parameters change	NA
Weitz and Dushoff [5]	Case data from the Caitlin Rivers github website [19]	Transmission model using ensemble adjustment Kalman filter (EAKF) to model a population of deceased infectious individuals	Susceptible–exposed–infected–contaminated deceased–isolated infectious–removed (SEICIIR)	Modelling containment and isolation compartments	Parameters estimated using a least-squares curve fitting algorithm to obtain a choice of parameters with relatively accurate fit	NA	NA
Yamin et al. [42]	Model parameters from other studies, Liberia Institute of Statistics and Geo-Information Services. Incidence and case fatality reports, contact tracing data obtained from Ministry of Health and Social Welfare, Republic of Liberia	Transmission model that considers three sequential phases including incubation, early symptomatic, and late symptomatic and accounts for viral load differences in survivors and non-survivors	Incubation-early symptomatic-late symptomatic	Accounted for viral load differences in survivors and non-survivors	Sampling possible ranges of epidemiological parameters to generate contact distribution for contact data. The number of secondary cases arose was calculated	NA	NA