Estimating the Probability of a Major Outbreak from the Timing of Early Cases: An Indeterminate Problem?

Conservation biologists, as well as veterinary and public health officials, would benefit greatly from being able to forecast whether outbreaks of infectious disease will be major. For values of the basic reproductive number (R0) between one and two, infectious disease outbreaks have a reasonable chance of either fading out at an early stage or, in the absence of intervention, spreading widely within the population. If it were possible to predict when fadeout was likely to occur, the need for costly precautionary control strategies could be minimized. However, the predictability of even simple epidemic processes remains largely unexplored. Here we conduct an examination of simulated data from the early stages of a fatal disease outbreak and explore how observable information might be useful for predicting major outbreaks. Specifically, would knowing the time of deaths for the first few cases allow us to predict whether an outbreak will be major? Using two approaches, trajectory matching and discriminant function analysis, we find that even in our best-case scenario (with accurate knowledge of epidemiological parameters, and precise times of death), it was not possible to reliably predict the outcome of a stochastic Susceptible-Exposed-Infectious-Recovered (SEIR) process.