Fig 1.
Model structure for 2014 Ebola outbreak in West Africa.
Solid arrows indicate transition from one compartment to another, dashed arrows indicate virus transmission due to contact with infectives. The virus can be transmitted to susceptible hosts (S) from infectious patients in the community (I), hospitalized patients (H) or patients who died of the disease and are not yet buried (D). Upon infection, susceptible hosts enter a latent phase (E), in which they are not yet infective. After symptoms onset, they become infective and might be hospitalized, recover from the disease or die and remain infectious until buried (B). Hospitalized patients might abandon the healthcare facilities and return to community, otherwise they either recover or die of the disease. Hosts who recovered from the infection are removed (R) from the chain of transmission.
Table 1.
Parameter estimates for the 2014 Ebola outbreak.
Parameter descriptions, fitted values and ranges used for parameter sensitivity analysis. Comparable values can be found in references indicated in the last column.
Table 2.
Estimates for intervention parameters.
Parameter descriptions, fitted values and ranges used for parameter sensitivity analysis. Comparable values can be found in references indicated in the last column.
Fig 2.
Data fit for Ebola cases in West Africa from week 1 to week 40.
The blue dots show the cumulative number of cases reported by [23] from week 1 (ending 3 Jan 2014) to week 40 (ending 3 Oct 2014). The cumulative number of cases reported is the sum of confirmed, suspected and probable cases. The red curve shows the fit with parameter values in Table 1. The orange region shows the total number of cases predicted by the model (95% CI).
Fig 3.
Partial rank correlation coefficients (PRCCs) of the ten parameters that influence disease spread.
Parameter values from the ranges in Tables 1 and 2 are considered. Parameters with PRCC larger than zero are positively correlated with 𝓡eff(t), that is, the effective reproduction number at time t increases as these parameter values are increased. Parameters with negative PRCC will decrease 𝓡eff(t) as they are increased. Variations in the burial rate and in the transmission rate at funerals have the greatest effect on the reproduction number, in particular at the beginning (t = 0) of the epidemic (a). Fig (b) and (c) show how the relative importance of the parameters on the effective reproduction number changes in time.
Fig 4.
Data fit for Ebola cases in West Africa from week 1 to week 60 and prediction until week 120.
The blue dots show the cumulative number of cases reported by [7, 23, 24]. The cumulative number of cases reported in Fig 2 is the sum of confirmed, suspected and probable cases. The red curve shows the fit obtained with parameter values in Table 1. At week 40 (ending 3 Oct 2014) intervention strategies are introduced. The green curve shows the model fit from week 40 to week 59 (ending 13 Feb 2015), with parameter values in Table 2. The light green curve shows model prediction until week 120 (ending 15 April 2016). The orange region shows the model-predicted total number of cases (95% CI) from the introduction of intervention strategies. The green charts on the right shows which proportion of the estimated cases at week 120 are due to contacts in the community (23%, 6191 out of 26809 cases), contacts in the hospitals (8%, 2173 out of 26809 cases) and contacts at funerals (69%, 18445 out of 26809 cases). If intervention strategies are not introduced at week 40 (black dashed curve), the numerical solution curve deviates from the real data considerably.
Fig 5.
Partial rank correlation coefficients (PRCCs) of the five intervention parameters that influence the cumulative number of cases.
Parameter values from the ranges in Table 2 are considered. Parameters with PRCC larger than zero are positively correlated with the total number of hosts who have been infected over the course of the epidemic. Parameters with negative PRCC will decrease the number of hosts who have been infected over the course of the epidemic, as they are increased. The greatest effect will be observed with variations in the burial rate, in the transmission rate at funerals and in the transmission rate in hospitals.
Fig 6.
The effects of intervention on the cumulative number of cases.
Sensitivity analysis of the total number of cases during the course of the epidemic. The key intervention parameters, namely, the transmission rate at funerals (φ), the transmission rate in hospitals (θ) and the time from death to burial (1/b) help to control the attack rate of the epidemic. Blue area corresponds to lower cumulative number of cases, the orange area corresponds to higher cumulative number of cases.
Fig 7.
The importance of timely intervention in 2014 Ebola outbreak.
Predicted number of cumulative cases: numerical simulations of the mathematical model (solid lines) and values estimated by the final size formula (2) (dashed lines). The later intervention occurs, the higher the number of Ebola cases. Simulations were done for hypothetical and immediately effective intervention at week 25 (blue), week 30 (light blue), week 35 (yellow), week 40 (orange), week 45 (red). If no intervention strategies are introduced (black curve), the number of Ebola cases grows exponentially.
Fig 8.
A new Ebola outbreak is possible if control is relaxed.
Model fit for the number of new weekly reported cases, corresponding to the cumulative cases in Fig 4. The blue dots show new weekly cases reported by [7, 23, 24]. The red curve shows the fit obtained with parameter values in Table 1 up to week 40 (ending 3 Oct 2014). The dark green curve shows the model fit from the introduction of control measures at week 40 to week 59 (ending 13 Feb 2015), with parameter values in Table 2. The light green curve shows model prediction until week 200 (ending 27 October 2017). The gray curve shows the model prediction assuming that, at week 120 (ending 15 April 2016), intervention strategies are relaxed to the following values: ,
,
,
and
.