Using information theory to optimise epidemic models for real-time prediction and estimation

Abstract

The effective reproduction number, R t , is a key time-varying prognostic for the growth rate of any infectious disease epidemic. Significant changes in R t can forewarn about new transmissions within a population or predict the efficacy of interventions. Inferring R t reliably and in real-time from observed time-series of infected (demographic) data is an important problem in population dynamics. The renewal or branching process model is a popular solution that has been applied to Ebola and Zika virus disease outbreaks, among others, and is currently being used to investigate the ongoing COVID-19 pandemic. This model estimates R t using a heuristically chosen piecewise function. While this facilitates real-time detection of statistically significant R t changes, inference is highly sensitive to the function choice. Improperly chosen piecewise models might ignore meaningful changes or over-interpret noise-induced ones, yet produce visually reasonable estimates. No principled piecewise selection scheme exists. We develop a practical yet rigorous scheme using the accumulated prediction error (APE) metric from information theory, which deems the model capable of describing the observed data using the fewest bits as most justified. We derive exact posterior prediction distributions for infected population size and integrate these within an APE framework to obtain an exact and reliable method for identifying the piecewise function best supported by available epidemic data. We find that this choice optimises short-term prediction accuracy and can rapidly detect salient fluctuations in R t , and hence the infected population growth rate, in real-time over the course of an unfolding epidemic. Moreover, we emphasise the need for formal selection by exposing how common heuristic choices, which seem sensible, can be misleading. Our APE-based method is easily computed and broadly applicable to statistically similar models found in phylogenetics and macroevolution, for example. Our results explore the relationships among estimate precision, forecast reliability and model complexity.

An exact method for quantifying the reliability of end-of-epidemic declarations in real time

“…We solve Eq. (7) by making use of known renewal model results derived in [10,21,23] and outlined in Methods. The renewal transmission model allows us to estimate the effective reproduction number R s and hence compute z s in real time (see Fig.…”

“…1. Usually we are interested in estimating the R s numbers in real time from the progressing I s 1 [10,20,21]. This effective reproduction number is important for forecasting the kinetics of the epidemic.…”

“…Eq. (2) completely describes the uncertainty surrounding one-step-ahead incidence predictions and is causal because all of its terms (including Λ s+1 ) only depend on the past observed incidence curve I s 1 [21]. If a random variable y ∼ NB(α, p) then P(…”

Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves

“…A2: Validation against APEestim. We compare estimates from EpiFilter (right panels) with optimised ones from EpiEstim (called APEestim, left panels [14]) over various epidemic scenarios, simulated using Eq. (1).…”

O potencial de propagação da COVID-19 e a tomada de decisão governamental: uma análise retrospectiva em Florianópolis, Brasil

“…The method proposed by Cori et al 26 was used in this calculation because it is suitable for real-time estimates 2,26 . The method proposed by Parag and Donelly 27 was used to estimate the best smoothing window in the 30-day periods. A gamma distribution with a mean of 4.8 and a standard deviation of 2.3 was used to express the serial range distribution, which is used in the estimate of R t…”