2.1. Model definition

As in (Merler et al., 2015; Ajelli et al., 2016), the population was grouped in households and hospitals, and health care workers were explicitly represented. Infection transmission was stochastic and specific interventions were simulated. The model accounted for three routes of transmission: transmission in households and to the extended family, transmission in hospitals, and transmission during funerals (to household and extended family members). The population of Liberia was subdivided into 15 administrative counties; for each county we placed the corresponding capital in the exact location given by GPS coordinates and with the exact number of inhabitants as obtained from census data. Simulated individuals were grouped into households and assigned to villages and capital city by preserving the population density at the level of county, and in order to match demographic information derived from the 2007 Demographic Health Surveys (Program, 2007) on household size and demographics for Liberia (see the Supplementary information for details). Hospitals were located on the territory according to their actual location as reported in the Humanitarian Data Exchange database (United Nations Office for the Coordination of Humanitarian Affairs, 2015). Each hospital was characterized by number of beds and number of health care workers (HCW), which were determined in order to match statistics available from the WHO Regional Office for Africa (WHO Regional Office for Africa, 2014). The counties considered, the population density, and the location of hospitals is shown in Fig. 1A.

A Map of Liberia with county capitals, major hospitals and population. B Ebola transmission dynamic scheme. The values and the distribution of the transition times are reported in the Supplementary Information.

Each individual in the population was explicitly simulated as an agent of the individual based model, with an associated epidemiological status. The natural history of the disease followed the one used in (Merler et al., 2015), as outlined in Figure 1 B. Specifically, susceptible individuals could acquire infection after contact with an infectious individual and become latent (asymptomatic). At the end of the latent period, assumed to be equal to the incubation period for Ebola as there is no evidence of Ebola transmission before symptom onset, latent individuals became infectious (symptomatic). Infectious individuals could transmit the infection, to both household members and members of the extended family. Ebola infections would either lead to hospitalization, death or recovery. Hospitalized individuals could transmit the infection to HCW and inpatients; afterwards, they would either die or recover. However, after recovery, a hospitalized individual remained in the hospital (though no longer infectious) for an additional period of time before being discharged. Deceased individuals could transmit infection to household and extended family members during funerals, and were then removed from the model. As in the West African Ebola outbreak, we accounted for contact tracing, an important aspect of disease control. In the Ebola forecasting challenge model, individuals belonging to the contact tracing pool were constantly checked and admitted to a hospital/ETU at the onset of symptoms.

The progression of infection is characterized by seven key time periods defining the natural history of the disease: the incubation period (which is the time between infection and the onset of symptoms); the interval from symptom onset to hospital admission; the interval from hospital admission to death; the interval from hospital admission to the end of infectivity; the interval from hospital admission to discharge; the interval from symptom onset to death; the interval from symptom onset to the end of the infectivity. Each key time period in the infection process was randomly sampled for every individual. In particular, time from death to burial was assumed to follow a truncated exponential distribution with mean 2 days and maximum 3 days, while all other key time periods (such as the incubation period, the time from symptom onset to admission, etc.) were assumed to be gamma distributed, in agreement with (WHO Ebola Response Team, 2014). Values for these parameters were chosen in such a way as to obtain plausible scenarios for an Ebola epidemic similar to the one experienced in West Africa (see Supplementary Information for a full list of parameters). In the early transmission phase the reproduction number was calibrated to be around 1.5–1.6, in agreement with early estimates in West Africa (WHO Ebola Response Team, 2014; Chowell and Nishiura, 2014; Nishiura and Chowell, 2014; Fisman et al., 2014; Merler et al., 2015; Gomes et al., 2014).

As in (Ajelli et al., 2016), the Ebola Forecasting Challenge model included two important features observed in the 2014–15 Ebola epidemic: heterogeneity in transmission rates among individuals, and differences in susceptibility to infection between children and adults. This choice was supported by modeling studies of the2014–15 Ebola epidemic in West Africa, which highlighted that a small fraction of infected individuals were responsible for a large majority of secondary cases (presence of superspreaders) (Ajelli et al., 2015; Althaus, 2015; Faye et al., 2015; WHO Ebola Response Team, 2016a), recently confirmed in (WHO Ebola Response Team, 2016b; Lau et al., 2017). In the model we assumed that each infectious individual had a different infection transmission potential, which was sampled from a gamma distribution of mean 1 and a given shape. This is equivalent to using a negative binomial distribution for the distribution of secondary cases, with dispersion equal to the shape of the gamma distribution. Further, in line with previous studies of the 2014–15 West African outbreak (Ajelli et al., 2015; WHO Ebola Response Team, 2015), we assumed an age-dependent risk of infection, with children being less susceptible to infection with the Ebola virus than adults. Accordingly, we introduced a parameter accounting for the relative susceptibility of 0–14 years old, equal to one-fourth of that of adults (Ajelli et al., 2015). Lastly, the Challenge model differed from that in (Merler et al., 2015) in terms of the distributions of key time periods and implemented interventions. More details on the computational implementation of the transmission mechanisms are provided in the Supplementary Information.