13 Oct 2026 · Medicine & Epidemiology

Who should get the vaccine first?

Most vaccines don't make you immune outright: they cut your chance of infection each time you're exposed. That "leaky" protection changes whether it's better to vaccinate the busiest spreaders or the oldest people first, and the answer flips with how fast the disease spreads.

Why it matters

Health agencies often decide who to vaccinate first, the people who spread the most or the oldest, without considering that a vaccine might only reduce the risk from each exposure rather than block infection completely. This study shows that under that kind of leaky protection, the better choice depends on how intensely the disease is spreading, so a priority list that works for a mild outbreak can be the wrong one for an intense one.

The paper

Leaky protection reveals three patterns in the relative advantages of vaccination strategies across transmission intensity

Yiwen Xing, Jianyi Zhang, Haoliang Cui, Zijie Yang, Qianning Wang, Lang Qin, Zheqi Wang, Zhongwei Jia. arXiv:2610.13567 [q-bio.PE], submitted 9 Oct 2026. Read on arXiv · PDF

In plain language: the authors used a survey of 2,279 residents to estimate how much each person is exposed to others, then simulated epidemics at many levels of transmission and vaccine efficacy. They compared vaccinating the most-exposed people first with vaccinating the oldest first. At low transmission, targeting the most exposed wins on both the epidemic peak and total infections; at intermediate transmission it lowers the peak but leaves more people infected overall; at high transmission the two strategies converge and oldest-first is slightly ahead on both.

Try it

Transmission intensity R₀

Vaccine efficacy per exposure

Share of people vaccinated

Peak infected, high-exposure first

Peak infected, oldest first

Ever infected, high-exposure first

Ever infected, oldest first

Share currently infected over time

High-exposure firstOldest first

Advantage of high-exposure first, across R₀

Peak reduction (points)Total-infection reduction (points)Your R₀

The maths in this page

The demo uses a simplified stand-in for the paper's survey population: 30 groups (6 age bands × 5 exposure levels), with younger working-age adults more exposed. Each group i has exposure a_i, and infection spreads by proportionate mixing:

λ_i = β a_i · Σ_j a_j I_j / Σ_j a_j N_j, β = R₀ γ Σa N / Σa² N

Leaky vaccine: vaccinated people stay susceptible but are infected at rate (1 − VE) λ_i at every exposure, so heavy exposure can still wear through protection. (An "all-or-nothing" vaccine would instead fully protect a fraction VE.)
Unvaccinated: dS/dt = −λS; vaccinated: dS_v/dt = −(1−VE)λS_v; dI/dt = new infections − γI, with γ = 1/5 per day.
Strategies: give the doses either to the highest-exposure groups first or to the oldest age bands first.

This is an illustrative toy model, not the authors' code or data, so the exact R₀ at which the patterns switch differs from the paper. It shows the low-transmission win and the intermediate trade-off clearly, and the narrowing gap at high transmission.

How to use it

Start with R₀ low (about 1.5) and see that vaccinating the most-exposed people almost stops the outbreak. Raise R₀ toward 4–5 and watch the right plot: the blue line (peak) stays above zero while the green line (total infections) drops below it, which is the trade-off the paper reports. At high R₀ the gaps shrink and oldest-first keeps the edge on total infections; in this toy the peak gap narrows but doesn't fully flip as it does in the paper. Lower the efficacy to make the vaccine leakier and see how the switch points move. For real policy, this is a reminder to ask how a vaccine fails before choosing who gets it first.