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Calculating a Population’s Live IFR and Live Herd Immunity

CoronaSim.eu now includes “Live IFR” and “Live Herd Immunity” columns who provide estimates on the current, forward-looking IFR and the current herd immunity level of the total population. These calculations use an individual-based IFR model and adds achieved immunity and vaccines into the equation.

The following text describes which assumptions are being made. Please feel free to suggest improvements or correct mistakes, but please document any specific claims by referring to research from reliable sources.

Individual Infection Fatality Rates

Most IFR tables simplify the IFRs by assigning a specific rate to a specific year of age (or a range of years) which then is the average IFR for that year of age. Obviously, not all people at a specific year of age have the exact same IFR. Covid-19 deaths will tend to be biased towards those with higher fatality risks, caused by, for example, other diseases. Due to this bias, the IFR for each year of age will decline as time passes when many people die during a relatively short period of time.

This bias is now modeled by using individual IFRs. The IFR of the most vulnerable 20% of the population is set to be 50% higher than that year of age’s average. In other words, the population at that year of age is given IFRs distributed using a linear function which ensures that the average IFR still match up to the previously assumed average.

Vaccinations

Vaccinations affect the forward-looking IFR. To simplify the calculation of the vaccinations' impact, we assume that EU and most other countries in general prioritize those that have the highest risk of dying from covid-19 ( Overview of the implementation of COVID-19 vaccination strategies and vaccine deployment plans in the EU/EEA ). Thus, calculations distribute the vaccine doses from older to younger age groups. Within each year of age, vaccines are distributed without any prioritization.

The two most used vaccines so far in Europe and many other countries are those from Pfizer and Moderna. Due to this, we base the calculations on these two, until further detailed knowledge about vaccine distributions can be obtained.

Pfizer claims 95% efficacy in general and 94% efficacy for those older than 65 years ( COVID-19 vaccine hope for older adults: following release of AstraZeneca, Pfizer, Moderna clinical trial data ).

Moderna claims 94.1% efficacy in general, while their figure in the 65+ age group is estimated to 86.4% ( Efficacy and Safety of the mRNA-1273 SARS-CoV-2 Vaccine ).

Since the oldest age groups in general get the largest quantities of vaccine doses first, we set the efficacy of those over 65 years of age to the approximate average of the Pfizer and Moderna vaccine; 90%.

The percentages represent the reduction in serious illness caused by covid-19, and not the reduction of the fatality rate. We assume that since the number of serious cases will be reduced by 90%, the number of very serious cases will be reduced even somewhat more, since case seriosity is 'shifted' towards less serious. Therefore, we assume that the fatality rate of those who are classified as with serious illness after having had the vaccine is also reduced by ⅓ compared to a non-vaccinated population, meaning that the overall fatality reduction for the oldest age group is assumed to be 93.33%.

For those under 65 years of age, we assume the same principle, resulting in a reduced chance of death of approx. 96.5%.

For simplicity, we assume that one dose reduces the fatality risk by half of the rate for a fully vaccinated (two doses) person.

Immunity

After having recovered from covid-19, antibodies develop and provide immunity against new infections. It is known that the antibody level starts to wane after some time. Various research reports slightly disagreeing rates of decline. ( Chinese study: Antibodies in COVID-19 patients fade quickly , Sero survey: Only 54% Covid-19 infected in Ahmedabad have antibodies , COVID-19 - Immunity after recovery from COVID-19 , UK Biobank SARS-CoV-2 Serology Study ) The reduction of the antibody level results in decreasing protection against a new infection.

The calculation uses an average immunity period of 6 months from infection.

Research shows that those with a serious infection get a longer-lasting protection ( Immune responses and immunity to SARS-CoV-2 ). The vaccines are claimed to create a strong immune response. (E.g. PFIZER AND BIONTECH PROVIDE DATA FROM GERMAN PHASE 1/2 STUDY FURTHER CHARACTERIZING IMMUNE RESPONSE FOLLOWING IMMUNIZATION WITH LEAD COVID-19 VACCINE CANDIDATE BNT162B2 ). Therefore, we assume that the average immunity period following a vaccination is longer than from getting the virus “naturally” and set it to 9 months.

When both immunity periods ends (whether was caused by getting the virus or the vaccine), we assume that the body has developed memory cells ( T cell immunity: What is it and how does it help to protect us from COVID-19? , Covid-19 vaccines: delivering protective immunity ) who will help with fighting subsequent infections more efficient than the very first one. The calculation assumes a 40% reduction of the individual IFR after the immunity period of the first infection or the vaccine. Due to the current time scale of the ongoing pandemic, we do not calculate any time-dependent reduction of this cell immunity.

Vaccination Support

We assume that vaccination support is high for the age groups that have received the possibility of vaccination and who are most at risk. At present, the levels are generic and not country-specific. These figures are used:

From (year of age)To (year of age)Vaccination participation (%)
0180
193030
314550
466570
667580
76-90

If a country reports more vaccinations than are possible to preform with the percentages above, the calculation will perform additional vaccinations beyond the levels above by closing the gap up to 100% in steps of 25% of the non-vaccinated population for each level. The calculations will not give a (double-dose) vaccine twice to the same person.

Other Simplifications and Assumptions

We estimate a delay of 25 days from infection until death when calculating the infection numbers.

As explained, we assume “static” immunity periods when being infected and vaccinated. Since these periods are meant to be the average values, they will not affect the calculations considerably.

The population does not age. If it did, it would add some few more deaths.

Improvements in treatment are not considered. This would reduce the IFRs. ( Trends in COVID-19 Risk-Adjusted Mortality Rates )

Possible changes in the IFRs for mutants of the virus are not considered. These could affect the IFRs. Apparently, some mutants like the “British” might have higher fatality rates. ( NERVTAG note on B.1.1.7 severity for SAGE )

Due to the computation time for the “live” data, calculations are performed on a reduced population count for most countries and then upscaled. This introduces some inaccuracy in the “live” numbers, especially for populations of several tens of millions.

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