Table 4.

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

Reference	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
Althaus et al. [27]	Case data from published reports. Parameters from previous EVD outbreaks	Transmission model with a set of ODEs and used Maximum likelihood estimates to determine model parameters (baseline transmission rate, rate at which control measures reduce transmission, case fatality rate)	SEIR	Assumed homogeneous mixing	Fitted a dynamic transmission model to data about reported cases and deaths of EVD during a small urban outbreak in Nigeria using Maximum likelihood methods	NA	NA
Barbarossa et al. [28]	Case data from WHO reports [1]. Parameters estimated from various studies	Compartmental population model based on Legrand's study [24] that distinguishes between community and hospitalised patients, and recognises importance of deceased individuals who can still transmit the virus at burials	Susceptible–latent–infectious–hospitalised–dead–buried–removed (SEIHBDR)	Model divided infectious population into those who exist in the community and those who exist in hospitals, and considered post-death transmission	Fitted model outcomes to the WHO reports for weekly case incidence. The data were fit with piecewise exponential curves	Studied the effects of model parameters on the basic reproduction number and on the final epidemic size. LHS is used to generate a representative sample set of test parameters from the ranges. Focused mostly on the sensitivity of the time of intervention. PRCCs analysis was reported	NA
Camacho et al. [49]	Case data from Sierra Leone Ministry of Health and Sanitation and WHO reports [1]. Data on ETCs, EHCs, CCCs from The Humanitarian Data Exchange. Proportion of symptomatic cases from the UN for Ebola Emergency Response and the National Emergency Response Centre	Transmission model with time-dependent transmission rate, accounting for hospitalisation and delay in case reporting	Susceptible–exposed1–exposed2–infectious–infectious (hospitalisation)–removed	Modelling individuals progressed through stages, including hospitalisation compartment	Fitted model to the time series of weekly reported cases using Bayesian approach	Sensitivity analysis was performed by taking averaged posterior distribution of R over a period of Jan 2015	Assumed proportion of symptomatic cases reported at 60%, accounted for the potential variability in accuracy of reporting over time and accounted for over-dispersed delay between onset of symptoms and notification of reported cases
Chowell et al. [50]	Case data from WHO reports [1]	Logistic growth models fitted with the minimal amount of case data	NA	NA	Fitted logistic growth models to the cumulative number of cases using least-squares	NA	NA
Evans and Mammadov [51]	Case data from WHO [1]	Estimated the reproduction numbers for the total period of epidemic and for different consequent time intervals using simple linear model and considered the average infectious period as a time-dependent parameter	NA	NA	Fitted model outcome with the cumulative numbers of infected cases and deaths using global optimisation algorithm DSO	NA	NA
Fasina et al. [52]	Case data from WHO reports [1] and public source	Simplified version of Legrand's model [24] accounting for contribution of community and healthcare settings by adjusting baseline transmission rates, diagnostic rates, and enhancement of infection control measures	Susceptible–exposed–infectious–hospitalised–removed from isolation after recovery or death (SEIHP)	Model divided infectious individuals into groups in the community and isolation in a hospital	Assessed the timing of control interventions on the size of the EVD outbreak in Nigeria by extensive simulation runs	NA	NA
Fisman and Tuite [53]	Case data from WHO reports [1], Caitlin Rivers github website [19]	Incidence Decay with Exponential Adjustment (IDEA) model using maximum-likelihood methods to identify best-fit model parameters	NA	NA	Used maximum-likelihood methods to identify the optimal, best and worst case model parameters for the IDEA model	Sensitivity analysis were performed by varying vaccine efficacy	NA
Fisman et al. [54]	Case data from Caitlin Rivers github website [19], Virologically-confirmed case counts by date from the Virology Down Under blog [20]	IDEA model, a two parameter mathematical model describes exponential growth simultaneous decay, was used to project epidemic curve accounting for incidence decay	NA	NA	Model was fitted to time series data iteratively, using a progressively increasing number of outbreak generations. Best fit parameter values are estimated by fitting; – objective function: minimise the root mean-squared distance between model estimates and empirical data	Checked separate models to epidemic curves derived from reported deaths, curves based only on virologically confirmed cases, as well as curves based on varying assumptions about case-underreporting	Fitted separate models using assumptions about case underreporting (50% and 100%).
Lewnard et al. [55]	Montserrado case data, Number of Beds in Ebola Treatment Centres from Ministry of Health and Social Welfare, Liberia Ebola situation reports. Total population of Montserrado from Republic of Liberia 2008 Population and Housing Census. Time to burial, relative transmission rate from previous study. International SOS Hospital response and isolation/treatment centres also used to determine Number of Beds in ETCs	Developed a differential equation model which includes a latent population (L), two types of recovery populations (R), differentiation of ascertained (A) cases (which do not contribute to community transmission)	SEIR	Assumed homogeneous mixing	Modelled cumulative cases and mortality as a Poisson-distributed random variable. Model calibrated by sampling via Markov Chain Monte Carlo using a Metropolis–Hastings acceptance rule	NA	Addressed underreporting or delays in reporting by fitting model to estimate the delay between the beginning of the infectious period and time of ascertainment
Liu et al. [56]	Case data from WHO [1]	Logistic, Gompertz, Rosenzweg and Richards models were developed and compared	NA	NA	Fitted the model using precise estimates by Bayes factors and obtained model parameters	NA	NA
Meltzer et al. [9]	Infectious period from The World Bank website, CDC website. Likelihood of a patient going to an ETU and the number of days that a patient in each patient category would spend in the hospital. Actual number of beds in use – from expert opinion	EbolaResponse, a Markov chain model, categorises patient setting (i) hospitalised facility, (ii) home/community where there is reduced disease transmission, (iii) home with no effective isolation. Model also accounts for under-reporting of cases, and allows for imported cases or cases with no known contacts	Susceptible–infected–incubation–infectious–infectious (burial)–recovered	Considered those who die but whose burial provides risk for onward transmission. Patients were categorised into hospitalised in an Ebola treatment unit (ETU) or medical care facility, home or in a community setting and home with no effective isolation	Model parameters were altered to produce a matched outcome with the reported cases to date using goodness-of-fit test	NA	A underreporting correction factor of 2·5 was used to estimate future total cases
Nishiura and Chowell [57]	Case data form WHO reports [1]	Mathematical modelling considering time- and country-specific incidence data to estimate reproductive numbers, using likelihood-based method for real-time parameter estimation. Estimated daily incidence curves by fitting smoothing spline to county-specific cumulative curves of cases	NA	NA	Fitted a smoothing spline to cumulative reported cases by country and adjusted the spline function based on the daily incidence time series	Sensitivity analyses of reproduction number were carried out by varying the mean generation time	NA
Pandey et al. [30]	Demographic data from the 2008 National, Housing Census of Liberia. Case data from Liberian Ministry of Health and Social Welfare	Transmission model takes into account transmission within and between the community, hospitals and funerals	Susceptible–latent–infected–deceased–recovered–buried (SEIFRD)	Stratified epidemiological class into compartments that correspond to the general community, hospitals and funerals	Used weighted least-squares to fit the model to case data. Converted event-based stochastic model to a discrete-time difference equation model. Then evaluated the difference equation model, fitted the output to the data, and calculated the best-fit estimates of certain parameters by minimising the weighted least-squares difference between the model output and the data with the Quasi-Newton algorithm	Done extensive sensitivity analysis and elasticity analysis on intervention effectiveness to variation in epidemiological parameters. PRCCs was used	Refitted model to account for a range of plausible underreporting. Varied the levels of under-reporting of Ebola cases in both community and hospitals, as well as only communities
Rivers et al. [58]	Case data from WHO reports  [1] and Ministry of Health of Liberia and Sierra Leone (available online from the Caitlin Rivers github website) [19]	Compartmental model adapted from Legrand's study [24]; stochastic model was implemented using Gillespie's algorithm	Susceptible–exposed–infectious–hospitalised–funeral–removed (SEIHFR)	Model accounted for those who are hospitalised and deceased individuals who can still transmit virus	A deterministic version of the model was fit and validated to the current outbreak data using least-squares optimisation. The last 15 days of reported cases were given one -quarter of the weight in the model to preferentially fit the most recent data	NA	NA
Shaman et al. [59]	Case data from WHO reports [1]	An ensemble Susceptible–exposed–infectious–recovered-X (SEIRX)–EAKF framework using observations, dynamic modelling and Bayesian inference to generate simulations	SEIRX	Additional X compartments were introduced to describe assimilation of mortality and case fatality rate	Fitted the model variables and parameters with weekly observations and allowed for time varying of variables and Rt parameters	Sensitivity analysis were performed by changing model structure, and varying population size and initial parameter ranges	NA
Shen et al. [60]	Case data from WHO [1]	Developed mathematical ODE model to study Ebola infection with isolation, media impact, post-death transmission and vaccination	Susceptible–vaccinated–latent (undetectable)–latent (detectable)–infectious with symptoms–isolated individuals–dead but have not been buried–recovered	Considered those who have died and are in the process of being buried	Fitted the model to epidemiological data of reported cumulative numbers of infected cases and deaths	Examined the most sensitive parameters to the R0 and the final epidemic size. LHS and PRCC methods were used	NA
Siettos et al. [61]	Time series count data, including cumulative incidence, from WHO reports. Cumulative deaths data from Wikipedia and WHO case reports [1]. Demographic data from United Nations [22]	Agent-based model using a small-world network constructed using the Watts & Strogatz algorithm	Susceptible–exposed–infected–dead (but not yet buried)–dead (safely buried)–removed	Agent-based model considered individuals interact through a small-world network	Fitted two network characteristics and four epidemic rates with reported outbreak data	NA	NA
Towers et al. [62]	Case data from HealthMap, WHO reports [1]	Fitted piecewise exponential curves along the data time series to estimate the evolving rate of exponential rise (or decline) in cases. SEIR model developed to estimate the temporal patterns of the effective reproduction number for the outbreak in each country	SEIR	Assumed homogeneous mixing	Fitted piecewise exponential function to estimate rates of exponential rise from the average daily EVD incidence data	Sensitivity analyses were performed using LHS and PRCC methods to test the robustness of result with respect to the exact number of contiguous points used for the fits	NA
Webb et al. [63]	Case data from WHO reports [1]. Parameters from various studies	Differential equations with compartments of the epidemic population that simulated forward projection of epidemic using Continuous Time Markov Chain. Model incorporates contact tracing of infectious cases. Both deterministic and stochastic models were run	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	Sensitivity analyses were performed in two contact tracing parameters. The contact tracing parameters were tested in sensitivity analysis	A ratio of unreported case of 1·78 is used for estimation
WHO [25]	Case data from investigation forms from confirmed, probable and suspected EVD cases identified in Guinea, Liberia, Nigeria, and Sierra Leone; also from informal case reports; data from diagnostic laboratories; data from burials	Projected case numbers using two methods: (i) regression method and (ii) stochastic branching process model	NA	NA	Epidemiological parameters were fitted with gamma probability distributions	Sensitivity analyses were performed by assuming different mean serial intervals of 11 and 13 and including suspected as well as confirmed and probable cases in the analysis	NA
WHO [64]	Case data from viral haemorrhagic fever data collection forms, treatment facilities, contact tracing forms	Reported summary statistics and prediction outcomes through simple model fitted to data. Used weighted average to estimate the duration reported of the observed means of the distributions of durations from hospitalisation to discharge and hospitalisation to death	NA	NA	Gamma distributions were fitted to confirmed and probable cases	NA	NA