Medicine
Epidemiological Modeling of Vaccine Hesitancy on Herd Immunity Thresholds
Quick fact
When vaccine hesitancy reduces uptake, the herd immunity threshold effectively rises, because some vaccinated individuals remain susceptible (due to incomplete efficacy) and unvaccinated individuals keep transmission alive. For measles, a drop in coverage from 95% to 90% can shift the threshold from R0-based calculations to a level where outbreaks become likely.
Why this is interesting
You’ve probably heard that vaccines protect the herd—but what happens when enough people refuse them? Could a small group of hesitant individuals unravel the entire shield?
Read the full explanation
Understanding Epidemiological Modeling of Vaccine Hesitancy on Herd Immunity Thresholds
Imagine a population as a group of dominoes. If enough people are immune (immune dominoes are ‘immune’ to falling), then even when a disease arrives, it cannot spread far because it keeps hitting immune individuals. This is herd immunity. The proportion needed to be immune is called the herd immunity threshold. For a directly transmitted disease, it depends on the basic reproduction number (R0)—how many people one infected person would infect in a fully susceptible population. The threshold is roughly 1 - 1/R0. For measles (R0 ≈ 12-18), that is about 92-95%. Now, vaccine hesitancy means fewer people get vaccinated. But even among the vaccinated, vaccines are not 100% effective. So the effective proportion of immune people is the product of vaccine efficacy and vaccine coverage. If coverage falls, the proportion immune falls below the threshold, and herd immunity breaks down. Epidemiological models incorporate this by using an effective reproduction number (Re) that accounts for both vaccination and natural immunity. When Re 1, the disease can spread; when Re < 1, it declines. Vaccine hesitancy raises Re by reducing the number of immune individuals, making it harder to reach the threshold.
A deeper explanation
The mechanism lies in the relationship between transmission dynamics and population immunity. In the classic SIR model, the herd immunity threshold (HIT) is derived from R0: HIT = 1 - 1/R0. When a vaccine is introduced, we replace immunity acquired naturally with vaccine-induced immunity. However, not every vaccinated person becomes immune; vaccine efficacy (VE) is the probability that a vaccinated individual becomes protected. Thus, the effective coverage (pc) is VE × vaccination coverage (p). The condition for herd immunity is that the proportion immune, pc, must be at least HIT. Vaccine hesitancy lowers p, which lowers pc, pushing the effective immune proportion below HIT. In models, this is often captured by modifying the susceptible fraction: S = 1 - (VE × p). The effective reproduction number Re = R0 × S. When hesitancy reduces p, S increases, and Re rises. For example, if R0=15, HIT≈0.933. With a vaccine of 90% efficacy, to achieve herd immunity, coverage must be at least HIT/VE = 0.933/0.9 = 1.037, which is impossible (since coverage cannot exceed 100%). This shows that for highly contagious diseases, even a small drop in coverage or efficacy can make herd immunity unattainable. Hesitancy also creates spatial and social clusters of unvaccinated individuals, which models can incorporate by adding heterogeneity: pockets of susceptibility allow transmission to persist even if average coverage is high. This explains why vaccine hesitancy is a critical factor in epidemiological modeling: it not only shifts the threshold but also undermines the reliability of population-level predictions.