add covid_vs_flu analysis
This commit is contained in:
Marc Bevand
Executable
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#!/usr/bin/python3
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#
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# Author: Marc Bevand — @zorinaq
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import sys
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import matplotlib.pyplot as plt
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import matplotlib.ticker as ticker
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import numpy as np
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import scipy.stats
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from scipy.optimize import curve_fit
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maxage = 100
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# Age-stratified IFR estimates for COVID-19
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ifrs_covid = [
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# Calculated from Spanish ENE-COVID study
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# (see calc_ifr.py)
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('ENE-COVID', {
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(0,9): 0.003,
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(10,19): 0.004,
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(20,29): 0.015,
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(30,39): 0.030,
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(40,49): 0.064,
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(50,59): 0.213,
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(60,69): 0.718,
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(70,79): 2.384,
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(80,89): 8.466,
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(90,maxage): 12.497,
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}),
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# US CDC estimate as of 10 Sep 2020
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# https://www.cdc.gov/coronavirus/2019-ncov/hcp/planning-scenarios.html
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# (table 1)
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('US CDC', {
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(0,19): 0.003,
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(20,49): 0.02,
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(50,69): 0.5,
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(70,maxage): 5.4,
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}),
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# Verity et al.
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# https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30243-7/fulltext
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# (table 1)
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('Verity', {
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(0,9): 0.00161,
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(10,19): 0.00695,
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(20,29): 0.0309,
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(30,39): 0.0844,
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(40,49): 0.161,
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(50,59): 0.595,
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(60,69): 1.93,
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(70,79): 4.28,
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(80,maxage): 7.80,
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}),
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# Levin et al.
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# https://www.medrxiv.org/content/10.1101/2020.07.23.20160895v5
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# (table 3)
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('Levin', {
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(0,34): 0.004,
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(35,44): 0.06,
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(45,54): 0.2,
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(55,64): 0.7,
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(65,74): 2.3,
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(75,84): 7.6,
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(85,maxage): 22.3,
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}),
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# Perez-Saez et al.
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# https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30584-3/fulltext
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('Perez-Saez', {
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(5,9): 0.0016,
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(10,19): 0.00032,
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(20,49): 0.0092,
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(50,64): 0.14,
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(65,maxage): 5.6,
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}),
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# Poletti et al.
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# https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.31.2001383
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# (table 1, column "Any time")
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('Poletti', {
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(0,19): 0,
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(20,49): 0,
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(50,59): 0.46,
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(60,69): 1.42,
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(70,79): 6.87,
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(80,maxage): 18.35,
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}),
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# Picon et al.
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# https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7493765/
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# (table 2)
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('Picon', {
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(20,39): 0.08,
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(40,59): 0.24,
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(60,maxage): 4.63,
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}),
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# Gudbjartsson et al.: Humoral Immune Response to SARS-CoV-2 in Iceland
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# https://www.nejm.org/doi/full/10.1056/NEJMoa2026116
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# Supplementary Appendix 1
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# https://www.nejm.org/doi/suppl/10.1056/NEJMoa2026116/suppl_file/nejmoa2026116_appendix_1.pdf
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# (table S7)
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('Gudbjartsson', {
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(0,70): 0.1,
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(71,80): 2.4,
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(81,maxage): 11.2,
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}),
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# Public Health Agency of Sweden
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# https://www.folkhalsomyndigheten.se/contentassets/53c0dc391be54f5d959ead9131edb771/infection-fatality-rate-covid-19-stockholm-technical-report.pdf
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# (table B.1)
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('PHAS', {
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(0,49): 0.01,
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(50,59): 0.27,
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(60,69): 0.45,
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(70,79): 1.92,
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(80,89): 7.20,
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(90,maxage): 16.21,
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}),
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# O’Driscoll et al.: Age-specific mortality and immunity patterns of SARS-CoV-2 infection in 45 countries
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# https://www.medrxiv.org/content/10.1101/2020.08.24.20180851v1
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# (table S4)
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('O’Driscoll', {
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(0,4): 0.002,
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(5,9): 0,
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(10,14): 0,
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(15,19): 0.002,
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(20,24): 0.004,
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(25,29): 0.009,
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(30,34): 0.017,
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(35,39): 0.029,
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(40,44): 0.053,
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(45,49): 0.086,
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(50,54): 0.154,
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(55,59): 0.241,
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(60,64): 0.359,
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(65,69): 0.642,
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(70,74): 1.076,
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(75,79): 2.276,
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(80,maxage): 7.274,
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}),
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# Ward et al.: Antibody prevalence for SARS-CoV-2 in England following first peak of the pandemic: REACT2 study in 100,000 adults
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# https://www.medrxiv.org/content/10.1101/2020.08.12.20173690v2
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# Supplementary Appendix
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# https://www.medrxiv.org/highwire/filestream/93745/field_highwire_adjunct_files/0/2020.08.12.20173690-1.docx
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# (table S2a, column "Based on confirmed COVID-19 deaths")
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('REACT2', {
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(15,44): 0.03,
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(45,64): 0.52,
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(65,74): 3.87,
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(75,maxage): 18.71,
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}),
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# Yang et al.: Estimating the infection fatality risk of COVID-19 in New York City during the spring 2020 pandemic wave
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# https://www.medrxiv.org/content/10.1101/2020.06.27.20141689v2
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# (table 1)
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('Yang', {
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(0,24): 0.0097,
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(25,44): 0.12,
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(45,64): 0.94,
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(65,74): 4.87,
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(75,maxage): 14.17,
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}),
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# Molenberghs et al.: Belgian Covid-19 Mortality, Excess Deaths, Number of Deaths per Million, and Infection Fatality Rates
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# https://www.medrxiv.org/content/10.1101/2020.06.20.20136234v1
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# (table 6)
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('Molenberghs', {
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(0,24): 0.0005,
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(25,44): 0.017,
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(45,64): 0.21,
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(65,74): 2.24,
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(75,84): 4.29,
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(85,maxage): 11.77,
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}),
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]
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# In the CDC influenza burden pages (eg. table 1 in
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# https://www.cdc.gov/flu/about/burden/2018-2019.html), only symptomatic
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# illnesses are estimated. We must account for asymptomatic ones as well.
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#
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# In https://www.cdc.gov/flu/about/keyfacts.htm the CDC implies 55-60% of
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# illnesses are symptomatic:
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#
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# «on average, about 8% of the U.S. population gets sick from flu each season,
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# with a range of between 3% and 11%, depending on the season.
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# [...]
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# The commonly cited 5% to 20% estimate was based on a study that examined both
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# symptomatic and asymptomatic influenza illness, which means it also looked at
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# people who may have had the flu but never knew it because they didn’t have
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# any symptoms. The 3% to 11% range is an estimate of the proportion of people
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# who have symptomatic flu illness.»
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#
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# The CDC thus acknowledges that 55-60% of illnesses are symptomatic:
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# 3/5 = 60%
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# 11/20 = 55%
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#
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# We use the mid-point, 57.5%, as an estimate to account for both symptomatic
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# and asymptomatic illnesses.
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cdc_sympt = .575
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# Age-stratified IFR estimates for seasonal influenza
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ifrs_flu = [
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# US CDC 2018-2019 influenza burden
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# https://www.cdc.gov/flu/about/burden/2018-2019.html
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('US CDC 2018-2019', {
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(0,4): 266/3_633_104 * 100 * cdc_sympt,
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(5,17): 211/7_663_310 * 100 * cdc_sympt,
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(18,49): 2_450/11_913_203 * 100 * cdc_sympt,
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(50,64): 5_676/9_238_038 * 100 * cdc_sympt,
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(65,maxage): 25_555/3_073_227 * 100 * cdc_sympt,
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}),
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# US CDC 2017-2018 influenza burden
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# https://www.cdc.gov/flu/about/burden/2017-2018.htm
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('US CDC 2017-2018', {
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(0,4): 115/3_678_342 * 100 * cdc_sympt,
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(5,17): 528/7_512_601 * 100 * cdc_sympt,
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(18,49): 2_803/14_428_065 * 100 * cdc_sympt,
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(50,64): 6_751/13_237_932 * 100 * cdc_sympt,
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(65,maxage): 50_903/5_945_690 * 100 * cdc_sympt,
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}),
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# US CDC 2016-2017 influenza burden
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# https://www.cdc.gov/flu/about/burden/2016-2017.html
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('US CDC 2016-2017', {
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(0,4): 126/2_381_218 * 100 * cdc_sympt,
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(5,17): 125/6_452_110 * 100 * cdc_sympt,
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(18,49): 1_365/9_292_804 * 100 * cdc_sympt,
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(50,64): 3_780/7_448_184 * 100 * cdc_sympt,
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(65,maxage): 32_833/3_646_206 * 100 * cdc_sympt,
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}),
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# US CDC 2015-2016 influenza burden
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# https://www.cdc.gov/flu/about/burden/2015-2016.html
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('US CDC 2015-2016', {
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(0,4): 180/2_195_276 * 100 * cdc_sympt,
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(5,17): 88/4_140_269 * 100 * cdc_sympt,
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(18,49): 1_703/9_121_242 * 100 * cdc_sympt,
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(50,64): 3_277/6_640_358 * 100 * cdc_sympt,
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(65,maxage): 17_458/1_407_174 * 100 * cdc_sympt,
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}),
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# US CDC 2014-2015 influenza burden
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# https://www.cdc.gov/flu/about/burden/2014-2015.html
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('US CDC 2014-2015', {
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(0,4): 396/3_207_314 * 100 * cdc_sympt,
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(5,17): 407/6_388_401 * 100 * cdc_sympt,
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(18,49): 985/8_606_083 * 100 * cdc_sympt,
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(50,64): 4_780/7_283_766 * 100 * cdc_sympt,
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(65,maxage): 44_808/4_679_888 * 100 * cdc_sympt,
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}),
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]
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def col(is_covid, i):
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if is_covid:
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return plt.cm.OrRd(255 - i * 8)
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else:
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return plt.cm.Blues(255 - i * 30)
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def plot(ax, ifrs, is_covid):
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lstyles = ('solid', 'dashed', 'dashdot', 'dotted')
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markers = ('o', 's', 'v', '^', '<', '>', 'P', '*', 'X', 'D', 'p')
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i = 0
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for ifr in ifrs:
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name, ifr_by_age = ifr
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x, y = [], []
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for age_group, ifr_val in sorted(ifr_by_age.items()):
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# place the marker at the middle (mean) of the age group
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x.append(np.mean(age_group))
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y.append(ifr_val)
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ax.plot(x, y, color=col(is_covid, i), label=name, lw=1, alpha=.8,
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marker=markers[i % len(markers)], ms=4,
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ls=lstyles[i % len(lstyles)])
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i += 1
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def interpolate(age, x1, y1, x2, y2):
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def func_exp(x, a, b):
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return a * (b ** x)
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popt, pcov = curve_fit(func_exp, [x1, x2], [y1, y2])
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return func_exp(age, *popt)
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def ifr_for_model(age, ifr_model):
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# calculate IFR for age <age>
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m_prev = ifr_prev = None
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# iterate over the age groups in order
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for age_group, ifr in sorted(ifr_model[1].items()):
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m = np.mean(age_group)
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if m == age:
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return ifr
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if m > age:
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if ifr_prev == None:
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sys.stderr.write(f'{ifr_model[0]}: no data, age {age} too young\n')
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return None
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if ifr_prev == 0 or ifr == 0:
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sys.stderr.write(f'{ifr_model[0]}: ignoring IFR zero for age {age}\n')
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return None
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return interpolate(age, m_prev, ifr_prev, m, ifr)
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m_prev, ifr_prev = m, ifr
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sys.stderr.write(f'{ifr_model[0]}: no data, age {age} too old\n')
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return None
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def mean_ifr(age, ifr_models):
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# calculate the geometric mean of IFR estimates in <ifr_models> for age <age>
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values = []
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for ifr_model in ifr_models:
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ifr = ifr_for_model(age, ifr_model)
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if ifr != None:
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values.append(ifr)
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return scipy.stats.gmean(values)
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def plot_comp(ax):
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for age in np.arange(30, 90, 10):
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y1 = mean_ifr(age, ifrs_flu)
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y2 = mean_ifr(age, ifrs_covid)
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assert not np.isnan(y1) and not np.isnan(y2)
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ax.annotate(s='', xy=(age, y1), xytext=(age, y2),
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arrowprops=dict(arrowstyle='|-|', shrinkA=0, shrinkB=0,
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alpha=.7))
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ax.text(age, y1 * .6, f'{y2/y1:.1f}×', ha='center', va='top',
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weight='bold', size=12, alpha=.7)
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def main():
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(fig, ax) = plt.subplots(dpi=300, figsize=(8,6))
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# plot ifrs_covid
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plot(ax, ifrs_covid, True)
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ax.text(3, 35, 'COVID-19:')
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handles, labels = fig.gca().get_legend_handles_labels()
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first_legend = ax.legend(handles=handles, labels=labels, loc='upper left',
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frameon=False, fontsize='x-small', handlelength=5)
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fig.gca().add_artist(first_legend)
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# plot ifrs_flu
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plot(ax, ifrs_flu, False)
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# plot vertical comparison bars
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plot_comp(ax)
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ax.semilogy()
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ax.grid(True, which='minor', linewidth=0.1)
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ax.grid(True, which='major', linewidth=0.3)
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ax.spines['top'].set_visible(False)
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ax.spines['bottom'].set_visible(True)
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ax.spines['left'].set_visible(True)
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ax.spines['right'].set_visible(False)
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ax.set_ylabel('IFR (%)')
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ax.set_xlabel('Age')
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ax.set_xlim(left=0)
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ax.xaxis.set_minor_locator(ticker.MultipleLocator(base=5))
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ax.xaxis.set_major_locator(ticker.MultipleLocator(base=10))
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ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g'))
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ax.text(75, .0016, 'Seasonal Influenza:')
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handles, labels = fig.gca().get_legend_handles_labels()
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x = len(ifrs_flu)
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ax.legend(handles=handles[-x:], labels=labels[-x:], loc='lower right',
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frameon=False, fontsize='x-small', handlelength=5)
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fig.suptitle('Infection Fatality Ratio of COVID-19 vs. Seasonal Influenza')
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ax.text(0, -0.11,
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'Source: https://github.com/mbevand/covid19-age-stratified-ifr\n'
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'Note: the vertical lines on two COVID-19 IFR curves (Poletti and O’Driscoll) are caused by the IFR being\n'
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'estimated to be zero by Poletti for age groups 0-19 and 20-49, and by O’Driscoll for 5-9 and 10-14.\n',
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transform=ax.transAxes, fontsize='small', verticalalignment='top',
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)
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ax.text(1, 1, 'Created by: Marc Bevand — @zorinaq',
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transform=ax.transAxes, fontsize='xx-small', va='top', ha='right')
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fig.savefig('covid_vs_flu.png', bbox_inches='tight')
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plt.close()
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if __name__ == '__main__':
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main()
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