Reconstructing influenza incidence by deconvolution of daily mortality time series
Open accessAbstract
We propose a mathematically straightforward method to infer the incidence curve of an epidemic from a recorded daily death curve and time-to-death distribution; the method is based on the Richardson–Lucy deconvolution scheme from optics. We apply the method to reconstruct the incidence curves for the 1918 influenza epidemic in Philadelphia and New York State. The incidence curves are then used to estimate epidemiological quantities, such as daily reproductive numbers and infectivity ratios. We found that during a brief period before the official control measures were implemented in Philadelphia, the drop in the daily number of new infections due to an average infector was much larger than expected from the depletion of susceptibles during that period; this finding was subjected to extensive sensitivity analysis. Combining this with recorded evidence about public behavior, we conclude that public awareness and change in behavior is likely to have had a major role in the slowdown of the epidemic even in a city whose response to the 1918 influenza epidemic is considered to have been among the worst in the U.S.
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Estimates of I maximizing Eq. 1 obtained with an expectation maximization algorithm are typically unstable.
“Estimates of I maximizing Eq. 1 can be obtained with an expectation maximization algorithm (6, 33–35), but the outcome is typically unstable (36).”
From Socioeconomic status determines COVID-19 incidence and related mortality in Santiago, Chile (2021) · cites this paper as [35]
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Self-citation
- Authors
- Goldstein, E., Dushoff, J., Ma, J., Plotkin, J. B., Earn, D. J. D., & Lipsitch, M.
- Affiliations
- Harvard University (US)
- Michael G. DeGroote Institute for Infectious Disease Research (CA)
- McMaster University (CA)
- University of Pennsylvania (US)
- Corresponding author
- Goldstein, Edward
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2009-12-22
- Volume
- 106
- Issue
- 51
- Pages
- 21825-21829
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC2796142
- OpenAlex
- W2163930085
- Cited by
- 94
- References
- 29
- Citations by year
- 2026: 1 · 2025: 6 · 2024: 12 · 2023: 7 · 2022: 17 · 2021: 17 · 2020: 14 · 2019: 2 · 2018: 1 · 2016: 2 · 2014: 3 · 2013: 5 · 2012: 2
- FWCI
- 1.57
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Digital Access to Scholarship at Harvard (DASH) (Harvard University) (submittedVersion, cc-by)
- Funders
- National Institutes of Health (5u01gm076497-03)
- Canadian Institutes of Health Research
- National Institute of General Medical Sciences (U01GM076497, 1U54GM088588, 5U01GM076497)
- National Institute of Allergy and Infectious Diseases (U54AI057168)
- Topics
- Health Sciences › Medicine › Epidemiology › Influenza Virus Research Studies
- Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
- Physical Sciences › Mathematics › Modeling and Simulation › COVID-19 epidemiological studies
- Keywords
- Richardson-Lucy deconvolution, 1918 influenza pandemic, Philadelphia, New York State, reproduction number, public behavior, epidemic control measures, sensitivity analysis
- MeSH terms
- Disease Outbreaks, Humans, Influenza, Human, New York, Philadelphia, Incidence, History, 20th Century
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