The Risk of SARS-CoV-2 Infection in Non-Immune Persons

To date, the 7-day incidence has been considered the key indicator for the prevailing risk of infection and pandemic control status. It is calculated as the number of newly infected persons per 100 000 inhabitants. As the epidemic progresses and the vaccination rate increases, however, the number of persons at risk of new infection goes down as the number of those vaccinated or recovered goes up. Nevertheless, the residual group at risk (the “susceptibles”) is still in need of protection. The Table shows how the incidence rate among susceptibles changes in relation to the rate reported for the total population as the proportion of susceptibles decreases. If susceptibles account for only 50% of the population, their incidence is twice as high (relative increase 100%) as that reported for the population as a whole.

Table. Incidence rates based on the total population and corresponding incidence rates in the group of persons not yet immune (susceptibles) as the proportion of susceptibles decreases.

Population	Seven-day incidence per 100 000 persons								Relative increase
Total population	5	10	25	35	50	100	150	200	0.0 %
Population at risk
90% susceptibles	6	11	28	39	56	111	167	222	11.1 %
80% susceptibles	6	13	31	44	63	125	188	250	25.0 %
70% susceptibles	7	15	36	50	71	143	214	286	42.9 %
60% susceptibles	8	17	42	58	83	167	250	333	66.7 %
50% susceptibles	10	20	50	70	100	200	300	400	100 %
40% susceptibles	13	25	63	88	125	250	375	500	150 %
30% susceptibles	17	33	83	117	167	333	500	667	233 %
20% susceptibles	25	50	125	175	250	500	750	1 000	400 %
10% susceptibles	50	100	250	350	500	1 000	1 500	2 000	900 %

Method

We calculated the constantly decreasing susceptible proportion of the population, which is complementary to those already infected or vaccinated. To this end, we shifted the cumulative time series of documented infections back by 10 days from the day of reporting (incubation time with delayed testing and reporting). The cumulative numbers of vaccinated persons were shifted forward by 14 days (latency period before effective immunity). Regarding vaccine effectiveness, it was assumed that a first vaccination offers 60% protection, a second vaccination, 90% (1). The possibility of vaccination breakthroughs was thus factored in.

Results

The Figure presents the cumulative proportions of the population accounted for by the registered (nominal) SARS-CoV-2 infections and numbers of persons receiving their first and second vaccinations as regularly reported by the Robert Koch Institute (RKI) (2). Because the effectiveness of the vaccinations in avoiding SARS-CoV-2 infection is accounted for in these figures, the complement is an estimate of the remaining proportion of susceptibles.

Figure.

Effective proportions of the population made up by infected persons, those with two vaccinations, and those with only one vaccination, weighted by their respective protective factor (infected 1, double vaccinated 0.9, only single vaccinated 0.6), and the proportion effectively not yet protected (descending curve), Germany 2021 (all data from RKI, status as of 25 August 2021)

The proportion of the population without adequate immunity became smaller than that with immunity on 25 July 2021. By the beginning of August the figure was 46%. This subgroup supplied the newly infected persons who made up the 7-day incidence reported for the total population. Therefore, the incidence of 25.1 per 100 000 reported on 11 August 2021 corresponds to an incidence of 54.6 per 100 000 in the non-immune group (table).

The proportion of susceptibles varies across age groups, particularly because the vaccination coverage is age dependent. Nominally the age-specific 7-day incidence is reported as 8.9 cases per 100 000 in those aged 60 years or over, 45.9 in those aged 20–59 years, and 78.2 in 10- to 19-year-olds (calendar week 32, RKI). However, these age-specific incidences must be viewed together with the age-specific vaccination rates. As of 19 August 2021, the rate of complete vaccination (in parentheses: first vaccination) was 82.9% (86%) for persons aged 60 years or more, 61.7% (64.7%) in 18- to 59-year-olds, and 17% (26.2%) in those aged 12 to 17 years (1). The nominal incidence in the age group 60 years and above therefore underestimates the incidence among the non-immune by a factor of 5.28, corresponding to a corrected incidence of 47 per 100 000. The nominal incidence in the intermediate age group has to be corrected by a factor of 2.65, resulting in a true incidence of 122 per 100 000 for those without immunity.

Discussion

The incidence rates in the total population are important when assessing the course of the epidemic and deciding on control measures. However, they underestimate the infection dynamics in the non-immune segment of the population considerably and to a growing extent as the proportion of susceptibles decreases. Infection fatality rate, case fatality rate, and the R number are not affected by changes in the population denominator.

The calculation presented here is based on simplifying assumptions and thus can only serve as an example. One quantitatively important assumption concerns the extent to which the number of persons infected is undercounted. On the basis of serological studies in Germany, the RKI estimates that the true infection rate is twice as high as the reported figure (3). Doubling the proportion of those previously infected (most recently 4.7%) would lower the proportion of persons without adequate immunity correspondingly in the graph. Changes in proportions also result from variations in vaccine effectiveness. A small fraction of vaccinations are given to persons already infected earlier, but this double counting cannot yet be quantified.

The present picture will be complicated by partial or complete loss of the immunity acquired. New variants may emerge against which theimmunity acquired up to that point offers no protection. Because, as demonstrated, the incidence rate for the total population is increasingly unsuitable for evaluation of the risk of infection among those who do not yet have immunity, preventive measures taken to protect the remaining susceptibles have to be adapted to their elevated risk of infection based on corrected (age-specific) incidence rates. It must also be assumed that the significance of incidence as an advance signal of disease severity and its consequences, particularly hospitalization and death, decreases with expanding vaccination coverage of especially vulnerable groups. Both of these aspects are important in assessing the role of the incidence rate as pandemic indicator.