A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2

Abstract

Despite various levels of preventive measures, in 2020, many countries have suffered severely from the coronavirus disease 2019 (COVID-19) pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Using a model, we show that population heterogeneity can affect disease-induced immunity considerably because the proportion of infected individuals in groups with the highest contact rates is greater than that in groups with low contact rates. We estimate that if R ₀ = 2.5 in an age-structured community with mixing rates fitted to social activity, then the disease-induced herd immunity level can be ~43%, which is substantially less than the classical herd immunity level of 60% obtained through homogeneous immunization of the population. Our estimates should be interpreted as an illustration of how population heterogeneity affects herd immunity rather than as an exact value or even a best estimate.

Fig. 1. Overall fraction infected over time.

Shown is a plot of the overall fraction infected over time for the age and activity structured community with R₀ = 2.5 for four different preventive levels inserted 15 March (day 30) and lifted 30 June (day 135). The blue, red, yellow, and purple curves correspond to no, light, moderate, and severe preventive measures, respectively.

Fig. 2. Cumulative fraction infected over time.

Shown is a plot of the cumulative fraction infected over time for the age and activity structured community and R₀ = 2.5 for four different preventive levels inserted 15 March (day 30) and lifted 30 June (day 135). The blue, red, yellow, and purple curves correspond to no, light, moderate, and severe preventive measures, respectively.