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

Our take —

Herd immunity is the threshold of population immunity to a disease that must be achieved in order to bring an epidemic under control and limit onward transmission in the population. In this paper, researchers demonstrated the importance of real-world assumptions like age-dependent susceptibility to infection, age-dependent probability of transmission, and age-specific contact patterns on the calculation of herd immunity thresholds. After accounting for realistic variation in age and contact patterns, they conclude that the herd immunity threshold that must be achieved to prevent a second large wave of COVID-19 may be lower than projections from models that do not account for this age-specific variability in disease transmission. However, results are not meant to be interpreted as exact values, and should be interpreted qualitatively.

Study design


Study population and setting

Authors used a Susceptible-Exposed-Infectious-Recovered (SEIR) mathematical model in a generic population that included six age cohorts, three social activity levels (high, normal, low), and “preventive measures” to 1) demonstrate the effectiveness of the interventions; and 2) how herd immunity to SARS-CoV-2 is affected by different population structures. Authors varied the effectiveness of the preventive measures, but did not specify explicit interventions. Assuming an R0 (basic reproductive number) of 2.5 and introduction of the virus on February 15, 2020, authors modeled differences in effectiveness and disease-induced herd immunity assuming homogenous and heterogenous (varying population mixing by age only, activity levels only, or both) populations.

Summary of Main Findings

Models demonstrated that herd immunity levels were lower among a non-homogenous population (i.e., one of the mixed population structures described above) compared to a homogenous population; mixing both age and activity levels decreased the herd immunity level by 17 percentage points (60% vs 43%). Mixing only activity levels resulted in a greater reduction in disease-induced herd immunity levels compared to mixing age groups only (46.3% vs 55.8%). Assuming preventive measures are put in place one month after virus introduction (March 15, 2020) and lifted almost two months later (June 30, 2020), preventive measures reduced the size and delayed the timing of the peak. In the scenario with the most restrictive preventive measures, lifting these resulted in a clear second wave of infections.

Study Strengths

Authors explored different types of heterogeneous mixing, making the model adaptable to regions or locations with known age structures and activity levels.


Although authors considered age structures and varying activity levels in their models, they did not consider more complex parameters, such as contact matrices and differences in daily contacts based on location (e.g., household vs work). Authors made several assumptions in the model that contribute to uncertainty. First, authors assumed that preventive measures would decrease all contact rates proportionally, however, most interventions target older adults and persons at highest risk. Furthermore, they assumed that these measures would be lifted simultaneously, when in reality most countries have been lifting restrictions in stages. Authors also assumed immunity to SARS-CoV-2 after infection for an “extended period of time”. However, the true duration of infection-acquired immunity is not currently known, and more work is needed in this area.

Value added

This study estimates the impact population heterogeneity can have on disease parameters, such as herd immunity, and illustrates the importance of incorporating real-world assumptions (i.e., that populations are not homogenous) when developing mathematical models.

This review was posted on: 16 July 2020