Stochasticity and the limits to confidence when estimating R_0 of Ebola and other emerging infectious diseases

Abstract

Dynamic models - often deterministic in nature - were used to estimate the basic reproductive number, R_0, of the 2014-5 Ebola virus disease (EVD) epidemic outbreak in West Africa. Estimates of R_0 were then used to project the likelihood for large outbreak sizes, e.g., exceeding hundreds of thousands of cases. Yet fitting deterministic models can lead to over-confidence in the confidence intervals of the fitted R_0, and, in turn, the type and scope of necessary interventions. In this manuscript we propose a hybrid stochastic-deterministic method to estimate R_0 and associated confidence intervals (CIs). The core idea is that stochastic realizations of an underlying deterministic model can be used to evaluate the compatibility of candidate values of R_0 with observed epidemic curves. The compatibility is based on comparing the distribution of expected epidemic growth rates with the observed epidemic growth rate given "process noise", i.e., arising due to stochastic transmission, recovery and death events. By applying our method to reported EVD case counts from Guinea, Liberia and Sierra Leone, we show that prior estimates of R_0 based on deterministic fits appear to be more confident than analysis of stochastic trajectories suggests should be possible. Moving forward, we recommend including a hybrid stochastic-deterministic fitting procedure when quantifying the full R_0 CI at the onset of an epidemic due to multiple sources of noise.