The evolution of a communicable disease in a human population is not entirely predictable. However, the spreading process can be assumed to vary smoothly in time. The time-dependent infection process can be linked to observations of the epidemic’s evolution by convolving it with a stochastic delay model. In retrospective analyses of epidemics, when the observations are the dates of exhibition of patients’ symptoms, the delay is the incubation period. In case of biosurveillance data, the delay is caused by incubation and a (hospital) visit delay, modeled as independent random variables. A model for observational error is also required. The time-dependent infection/spread rate may be inferred from observations by a deconvolution process. The smooth temporal variation of the infection rate allows its representation using a low dimensional parametric model, and the inference may be performed with relatively little data. For large outbreaks, the data may be available early in the epidemic, allowing timely modeling of the outbreak. Short-term forecasts using the model could thereafter be used for medical planning.
Objective
We present a statistical method to characterize an epidemic of a communicable disease from a time series of patients exhibiting symptoms. Characterization is defined as estimating an unobserved, time-dependent infection rate and associated parameters that completely define the evolution of an epidemic. The problem is posed as one of Bayesian inference, where parameters are inferred with quantified uncertainty. The method is demonstrated on synthetic and historical epidemic data.