Essential information: Uncertainty and optimal control of Ebola outbreaks

Abstract

Early resolution of uncertainty during an epidemic outbreak can lead to rapid and efficient decision making, provided that the uncertainty affects prioritization of actions. The wide range in caseload projections for the 2014 Ebola outbreak caused great concern and debate about the utility of models. By coding and running 37 published Ebola models with five candidate interventions, we found that, despite this large variation in caseload projection, the ranking of management options was relatively consistent. Reducing funeral transmission and reducing community transmission were generally ranked as the two best options. Value of information (VoI) analyses show that caseloads could be reduced by 11% by resolving all model-specific uncertainties, with information about model structure accounting for 82% of this reduction and uncertainty about caseload only accounting for 12%. Our study shows that the uncertainty that is of most interest epidemiologically may not be the same as the uncertainty that is most relevant for management. If the goal is to improve management outcomes, then the focus of study should be to identify and resolve those uncertainties that most hinder the choice of an optimal intervention. Our study further shows that simplifying multiple alternative models into a smaller number of relevant groups (here, with shared structure) could streamline the decision-making process and may allow for a better integration of epidemiological modeling and decision making for policy.

Keywords: VoI; decision making; epidemiological outbreak management; value of information.

Fig. 1.

Unconstrained caseload projections (Upper) and ranks of five management actions (Lower) under 37 published compartmental Ebola models with SEIHFR (representing susceptible, exposed, infectious, hospitalized, funeral, and removed compartments), SEIHR, SEIFR, or SEIR structures. For each model, five management actions were ranked from the worst (with highest caseload projection) as shown in light red to the best (with lowest caseload projection) as shown in dark red. Simulated population size is 10,000 people, and the effectiveness is 30% for each management action.

Fig. 2.

The number of models for which a particular intervention is recommended as optimal for the interventions of (A) reducing funeral transmission, (B) reducing community transmission, (C) reducing case fatality ratio, (D) reducing hospital transmission, and (E) increasing hospitalization. Evaluation was based on comparisons of caseload projections under each specific management action over a gradient of changes ranging from 10 to 100% against all of the other management actions with a baseline intensity of 30%.

Fig. S1.

The management effect required for each of five management actions to become the optimal action under 37 published compartmental Ebola models. All 37 models are presented within the row for each action reordered by rank for that action. Evaluation was based on comparisons of caseload projections under each specific management action over a gradient of changes ranging from 10 to 100% against all of the other management actions with a baseline intensity of 30% change. The number of models for which a particular intervention is recommended as optimal generally increased with the intervention efficacy. Considering the intervention of reducing funeral transmission as an example, if the efficacy of an intervention to reduce funeral transmission is below 10%, no models recommend that intervention as optimal. When the efficacy increases to 20%, 4/37 models recommend it as optima; when the efficacy increases to 30%, 22/37 models recommend it as optimal. The number of models recommending an intervention to reduce funeral transmission as optimal is positively correlated with the efficacy of the intervention.

Fig. S2.

Flow diagram of the global model to represent each of 37 cited models as a submodel. Compartments in the global model are described as below. A full description of model parameters is in Dataset S1. Links to code to run all of the models are available in SI Text: Parameters.R, Functions.R, and Running models.R. E_c, exposed (infected but not yet infectious) individuals in the community; E_cd, exposed (infected and detectable but not yet infectious) individuals in the community; E_hw, exposed healthcare workers in hospital; E_rh, exposed healthcare workers in the community; E_v, hospital-visiting exposed individuals; F_c, infectious (dead) individuals in the funeral compartment from the community; F_h, patients who died in the hospital entering the funeral compartment; I_c1, infectious individuals in the early infectious compartment in the community; I_c2, infectious individuals in the late infectious compartment in the community; I_ccc1, infectious individuals at the early infectious stage in Ebola community care centers; I_ccc2, infectious individuals at the late infectious stage in Ebola community care centers; I⁻_ccc2, Ebola virus-negative patients with Ebola-like symptoms in Ebola community care centers; I_h1, infectious individuals at the early infectious stage in the hospital; I_h2, infectious individuals at the late infectious stage in the hospital; I⁻_h2, Ebola virus-negative patients with Ebola-like symptoms in the hospital; I_hw1, infectious healthcare workers in hospital; I_rh1, infectious healthcare workers in the community; I_v1, hospital-visiting infectious individuals at the early infectious stage; R, individuals removed from the chain of transmission through either recovery or burial; R_ccc, recovered individuals in Ebola community care centers; R_h, recovered individuals in the hospital; S_c, susceptible individuals in the community; S_hw, susceptible healthcare workers in the hospital; S_rh, susceptible healthcare workers in the community; S_v, hospital-visiting susceptible individuals.