Further reading

The following is a highly subjective list of papers we would recommend to read for those interested in engaging further with the topics discussed here. You can also access this via Zotero in an open living library, which you are welcome to contribute to.

Delay estimation

  • Park et al. (2024) provide a comprehensive overview of challenges in estimating delay distribution and how to overcome them.
  • Charniga et al. (2024) summarises challenges in estimating delay distributions into a set of best practices.

\(R_t\) estimation

  • Gostic et al. (2020) provides an overview of some of the challenges in estimating reproduction numbers.
  • Brockhaus et al. (2023) compares reproduction number estimates from different models and investigates their differences.

Nowcasting

  • Wolffram et al. (2023) compares the performance of a range of methods that were used in a nowcasting hub and investigates what might explain performance differences.
  • Lison et al. (2024) develops a generative model for nowcasting and \(R_t\) estimation and compares its performance to an approach where the steps for estimating incidence and reproduction number are separated.
  • Stoner, Economou, and Halliday (2020) contains a nice review of different methods for nowcasting evaluates a range of methods, in addition to introducing a new approach.

Forecasting

  • Funk et al. (2019) evaluates the performance of a forecasting method that combines a mechanistic SEIR model with a random walk prior for the reproduction number.
  • Held, Meyer, and Bracher (2017) makes a compelling argument for the use of probabilistic forecasts and evaluates spatial forecasts based on routine surveillance data.
  • Lopez et al. (2024) describes the difficulty encountered in making accurate forecasts in COVID-19 cases in the US COVID-19 Forecast Hub.
  • Asher (2018) describes model that implements an extension to the random walk with a drift term.
  • “CDCgov/Wastewater-Informed-Covid-Forecasting” (2025), code repo for Wastewater-informed COVID-19 forecasting.
  • Hyndman and Athanasopoulos (2021) is a free online text book on forecasting with a range of time series models and a great resource for finding out more about them.

Ensembles

  • Sherratt et al. (2023) investigates the performance of different ensembles in the European COVID-19 Forecast Hub.
  • Amaral et al. (2025) discusses the challenges in improving on the predictive performance of simpler approaches using weighted ensembles.

References

Amaral, André Victor Ribeiro, Daniel Wolffram, Paula Moraga, and Johannes Bracher. 2025. “Post-Processing and Weighted Combination of Infectious Disease Nowcasts.” PLoS Computational Biology 21 (3): e1012836. https://doi.org/10.1371/journal.pcbi.1012836.
Asher, Jason. 2018. “Forecasting Ebola with a Regression Transmission Model.” Epidemics 22 (March): 50–55. https://doi.org/10.1016/j.epidem.2017.02.009.
Brockhaus, Elisabeth K., Daniel Wolffram, Tanja Stadler, Michael Osthege, Tanmay Mitra, Jonas M. Littek, Ekaterina Krymova, et al. 2023. “Why Are Different Estimates of the Effective Reproductive Number so Different? A Case Study on COVID-19 in Germany.” PLOS Computational Biology 19 (11): e1011653. https://doi.org/10.1371/journal.pcbi.1011653.
“CDCgov/Wastewater-Informed-Covid-Forecasting.” 2025. Centers for Disease Control and Prevention.
Charniga, Kelly, Sang Woo Park, Andrei R. Akhmetzhanov, Anne Cori, Jonathan Dushoff, Sebastian Funk, Katelyn M. Gostic, et al. 2024. “Best Practices for Estimating and Reporting Epidemiological Delay Distributions of Infectious Diseases.” PLOS Computational Biology 20 (10): e1012520. https://doi.org/10.1371/journal.pcbi.1012520.
Funk, Sebastian, Anton Camacho, Adam J. Kucharski, Rachel Lowe, Rosalind M. Eggo, and 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 15 (2): e1006785. https://doi.org/10.1371/journal.pcbi.1006785.
Gostic, Katelyn M., Lauren McGough, Edward B. Baskerville, Sam Abbott, Keya Joshi, Christine Tedijanto, Rebecca Kahn, et al. 2020. “Practical Considerations for Measuring the Effective Reproductive Number, Rt.” PLOS Computational Biology 16 (12): e1008409. https://doi.org/10.1371/journal.pcbi.1008409.
Held, Leonhard, Sebastian Meyer, and Johannes Bracher. 2017. “Probabilistic Forecasting in Infectious Disease Epidemiology: The 13th Armitage Lecture.” Statistics in Medicine 36 (22): 3443–60. https://doi.org/10.1002/sim.7363.
Hyndman, Rob J, and George Athanasopoulos. 2021. Forecasting: Principles and Practice. 3rd ed. Melbourne, Australia: OTexts.
Lison, Adrian, Sam Abbott, Jana Huisman, and Tanja Stadler. 2024. “Generative Bayesian Modeling to Nowcast the Effective Reproduction Number from Line List Data with Missing Symptom Onset Dates.” PLOS Computational Biology 20 (4): e1012021. https://doi.org/10.1371/journal.pcbi.1012021.
Lopez, Velma K., Estee Y. Cramer, Robert Pagano, John M. Drake, Eamon B. O’Dea, Madeline Adee, Turgay Ayer, et al. 2024. “Challenges of COVID-19 Case Forecasting in the US, 2020–2021.” PLOS Computational Biology 20 (5): e1011200. https://doi.org/10.1371/journal.pcbi.1011200.
Park, Sang Woo, Andrei R. Akhmetzhanov, Kelly Charniga, Anne Cori, Nicholas G. Davies, Jonathan Dushoff, Sebastian Funk, et al. 2024. “Estimating Epidemiological Delay Distributions for Infectious Diseases.” medRxiv. https://doi.org/10.1101/2024.01.12.24301247.
Sherratt, Katharine, Hugo Gruson, Rok Grah, Helen Johnson, Rene Niehus, Bastian Prasse, Frank Sandmann, et al. 2023. “Predictive Performance of Multi-Model Ensemble Forecasts of COVID-19 Across European Nations.” Edited by Amy Wesolowski, Neil M Ferguson, Jeffrey L Shaman, and Sen Pei. eLife 12 (April): e81916. https://doi.org/10.7554/eLife.81916.
Stoner, Oliver, Theo Economou, and Alba Halliday. 2020. “A Powerful Modelling Framework for Nowcasting and Forecasting COVID-19 and Other Diseases.” arXiv. https://doi.org/10.48550/arXiv.1912.05965.
Wolffram, Daniel, Sam Abbott, Matthias an der Heiden, Sebastian Funk, Felix Günther, Davide Hailer, Stefan Heyder, et al. 2023. “Collaborative Nowcasting of COVID-19 Hospitalization Incidences in Germany.” PLOS Computational Biology 19 (8): e1011394. https://doi.org/10.1371/journal.pcbi.1011394.