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

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  • Kris V Parag
  • Christl A Donnelly

Abstract

The effective reproduction number, Rt, is a key time-varying prognostic for the growth rate of any infectious disease epidemic. Significant changes in Rt can forewarn about new transmissions within a population or predict the efficacy of interventions. Inferring Rt 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 Rt using a heuristically chosen piecewise function. While this facilitates real-time detection of statistically significant Rt 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 Rt, 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.Author summary: Understanding how the population of infected individuals (which may be humans, animals or plants) fluctuates in size over the course of an epidemic is an important problem in epidemiology and ecology. The effective reproduction number, R, provides an intuitive and useful way of describing these fluctuations by characterising the growth rate of the infected population. An R > 1 signifies a burgeoning epidemic whereas R

Suggested Citation

  • Kris V Parag & Christl A Donnelly, 2020. "Using information theory to optimise epidemic models for real-time prediction and estimation," PLOS Computational Biology, Public Library of Science, vol. 16(7), pages 1-20, July.
    • Handle: RePEc:plo:pcbi00:1007990
    DOI: 10.1371/journal.pcbi.1007990
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    References listed on IDEAS

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    1. Peter D. Grünwald, 2007. "The Minimum Description Length Principle," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262072815, December.
    2. Sebastian Funk & Anton Camacho & Adam J Kucharski & Rachel Lowe & Rosalind M Eggo & W John Edmunds, 2019. "Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area region of Sierra Leone, 2014-15," PLOS Computational Biology, Public Library of Science, vol. 15(2), pages 1-17, February.
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    Cited by:

    1. Sophia Beckett Velez, 2021. "Idiosyncratic Viral Loss Theory: Systemic Operational Losses in Banks," JRFM, MDPI, vol. 14(2), pages 1-13, February.

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