A naive estimate in the reduction in IFR you get from vaccinating the most vulnerable fraction of the population

vaccinated_ifrs.py

import numpy as np 
import matplotlib.pyplot as plt
import pandas as pd
from io import StringIO
import matplotlib.ticker as mtick

# Source: p11, https://www.imperial.ac.uk/media/imperial-college/medicine/mrc-gida/2020-10-29-COVID19-Report-34.pdf 
IFR = """
0-4 0.00 (0.00, 0.03) 0.00 (0.00, 0.03)
5-9 0.01 (0.00, 0.06) 0.01 (0.00, 0.06)
10-14 0.01 (0.00, 0.11) 0.01 (0.00, 0.10)
15-19 0.02 (0.00, 0.18) 0.02 (0.00, 0.17)
20-24 0.03 (0.00, 0.3) 0.02 (0.00, 0.28)
25-29 0.04 (0.00, 0.46) 0.04 (0.00, 0.44)
30-34 0.06 (0.01, 0.71) 0.06 (0.01, 0.67)
35-39 0.10 (0.01, 1.03) 0.09 (0.01, 0.98)
40-44 0.16 (0.02, 1.47) 0.15 (0.02, 1.37)
45-49 0.24 (0.03, 2.03) 0.23 (0.03, 1.88)
50-54 0.38 (0.05, 2.74) 0.36 (0.05, 2.52)
55-59 0.60 (0.10, 3.64) 0.57 (0.10, 3.32)
60-64 0.94 (0.18, 4.79) 0.89 (0.18, 4.34)
65-69 1.47 (0.35, 6.27) 1.39 (0.34, 5.64)
70-74 2.31 (0.65, 8.21) 2.17 (0.64, 7.35)
75-79 3.61 (1.21, 10.81) 3.39 (1.19, 9.65)
80-84 5.66 (2.23, 14.37) 5.3 (2.19, 12.81)
85-89 8.86 (4.06, 19.36) 8.28 (3.98, 17.25)
90+ 17.37 (9.7, 31.12) 16.19 (9.44, 27.78)"""

# Source: https://www.ons.gov.uk/peoplepopulationandcommunity/populationandmigration/populationprojections/datasets/tablea21principalprojectionukpopulationinagegroups
AGE = """
 0-4	3,914	3,854	3,801
 5-9	4,139	4,153	4,153
10-14	3,859	3,956	4,049
15-19	3,669	3,653	3,676
20-24	4,185	4,155	4,118
25-29	4,527	4,525	4,490
30-34	4,463	4,505	4,535
35-39	4,372	4,402	4,418
40-44	3,993	4,021	4,099
45-49	4,507	4,405	4,312
50-54	4,674	4,662	4,618
55-59	4,294	4,408	4,514
60-64	3,673	3,758	3,862
65-69	3,396	3,371	3,363
70-74	3,252	3,320	3,369
75-79	2,236	2,327	2,412
80-84	1,673	1,716	1,738
85-89	1,024	1,041	1,058
90-94	448	459	469
95-99	123	128	128
100 & over	13	13	15"""

VACCINATED = .2

def load_ifr():
    return (pd.read_csv(StringIO(IFR), sep=' ', header=None)
        .rename(columns={0: 'age', 1: 'ifr'})
        .set_index('age')['ifr']
        .div(100)
        .pipe(pd.to_numeric))

def load_age():
    age = (pd.read_csv(StringIO(AGE), sep='\t', header=None)
           .rename(columns={0: 'age', 3: 'pop'})
           .set_index('age')['pop']
           .str.replace(',', '').pipe(pd.to_numeric)
           .rename(index=lambda s: s.strip()))
    age['90+'] = age['90-94'] + age['95-99'] + age['100 & over']
    age = age.drop(['90-94', '95-99', '100 & over'])
    return age/age.sum()

def vaccinated_ifrs(age, ifr):
    rates = {}
    cumulants = age[::-1].cumsum()
    for v in [0.] + cumulants.values.tolist():
        rates[v] = (cumulants > v).mul(ifr).mul(age).sum()
    return pd.Series(rates)

def plot(rates):
    with plt.style.context('seaborn-poster'):
        ax = rates.mul(100).rename(lambda i: 100*i).plot()
        ax.set_ylim(0, 100*rates.max())
        ax.set_xlim(0, 100)
        ax.axvspan(0, 20, color='k', alpha=.2)
        ax.grid(True)
        ax.yaxis.set_major_formatter(mtick.PercentFormatter())
        ax.xaxis.set_major_formatter(mtick.PercentFormatter())
        ax.set_ylabel('population ifr')
        ax.set_xlabel('fraction of population vaccinated, starting with eldest')
        ax.set_title('a naive estimate of IFR based on UK vaccination strategy;\n20% vaccinated means ~80% reduction in IFR')

if __name__ == '__main__':
    ifr = load_ifr()
    age = load_age()

    rates = vaccinated_ifrs(age, ifr)

    plot(rates)