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

The ideas of R0 and herd immunity can take multiple definitions that may not always coincide in models of non-homogenous or unmixed populations. R0 is the mean number of individuals infected by a typical individual, and in a structured population (where individuals have different characteristics), it is necessary to define “typical." Herd immunity is the proportion of individuals who need to reduce the growth rate of an epidemic (R0 less than 1), due to a lack of susceptible individuals in the population. In a structured population, the distribution of different types of individuals within the population who have immunity is an important aspect of this question.

Historically, herd immunity is defined as the proportion of individuals who must be randomly immunized by vaccination. Disease-induced herd immunity level, on the other hand, is the proportion of individuals immunized in the course of the epidemic (infected individuals who have recovered) that must be attained for the epidemic to slow down, if it were allowed to continue unobstructed (and assuming that there is not a second wave). If the population is not structured (susceptible individuals are identical), the definitions and proportions of herd immunity and disease-induced herd immunity coincide. Here, the authors look at the effect of structuring the population by age and/or level of inactivity, which influence the number of person-to-person contacts, and verify that the level of disease-induced herd immunity (derived directly from R0) is lower than immunity attained by random, uniform vaccination. This confirms both other researchers’ work and the intuition that the disease first affects those individuals with the greatest exposure to the pathogen (and thus who expose the greatest number of people). Likewise, the authors show that the level of inactivity plays a larger role than age. They provide examples of their findings with COVID-19. The definition that the authors give for disease-induced herd immunity is a little more complex and subtle, because it incorporates the effect of first-phase measures to control the epidemic and the immunity achieved when relaxing these measures does not result in a second wave of infections. This definition and the use of deterministic approximations for the first wave of the epidemic could be clarified and further explained.