The herd immunity attractor: selection, drift, and the steady-state undersupply of vaccination in 195 countries, 1980–2025
- 1Department of Economics, Faculty of Economics and Administrative Sciences, Istanbul Kültür University
Abstract
Introduction: Vaccination is the canonical positive externality in health economics: because each vaccination protects others, decentralized choice is predicted to stall below the herd immunity threshold. Yet little evidence exists on the law of motion that governs national coverage. This study estimates it directly.
Methods: I model the vaccinate-or-not decision of a heterogeneous household population as an expected-utility problem whose net payoff declines in the vaccinated share, aggregate it through an explicit revision protocol into a selection-mutation (replicator-mutator) equation in which payoff-responsive switching coexists with health-system contact and attrition hazards, and estimate the resulting equation on the World Health Organization/United Nations Children's Fund (WHO/UNICEF) Estimates of National Immunization Coverage (WUENIC, 2025 revision) for 195 countries over 1980-2025, with UN cohort denominators and World Bank income and health-system capacity controls. An exact identification result shows that the linear turnover coefficient equals the difference between the law of motion at full and at zero coverage, so it is identified from boundary observations independently of the payoff parameters, whereas the payoff slope is identified only where coverage traverses the simplex.
Results: First, in the interior of the coverage range, the dynamics are dominated by a strong linear restoring force, implying an annual turnover of 15%–25% of the relevant pool; the payoff slope is statistically weak there, and interior data cannot distinguish institutional flows from payoff-insensitive revision, so the estimated hazards bound the institutional component from above. Second, the free-riding signature appears where it is identified: sharply in the Hib rollout, which spans the full coverage range, and weakly on the first-dose DTP margin. Third, every country's law of motion has a stable interior rest point; the births-weighted world rest point for first-dose measles vaccination is 78%, below the 92%–94% herd band; 74% of countries rest below it, and a coronavirus disease 2019 (COVID-19) era shift lowered the median rest point by 3.3 points.
Discussion: Because the leverage of retention over payoff instruments equals 1/(1 − x * ) under the replicator protocol and diverges along the last mile under any smooth, bounded choice protocol, closing the gap is a default-and-retention problem rather than a price problem.
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BibTeX
@article{yolusever2026herd,
title = {{The herd immunity attractor: selection, drift, and the steady-state undersupply of vaccination in 195 countries, 1980–2025}},
author = {Aras Yolusever},
journal = {Frontiers in Public Health},
year = {2026},
month = oct,
doi = {10.3389/fpubh.2026.1965676},
url = {https://www.frontiersin.org/articles/10.3389/fpubh.2026.1965676/full},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - The herd immunity attractor: selection, drift, and the steady-state undersupply of vaccination in 195 countries, 1980–2025
AU - Aras Yolusever
PY - 2026
DA - 2026/10/22
JO - Frontiers in Public Health
DO - 10.3389/fpubh.2026.1965676
UR - https://www.frontiersin.org/articles/10.3389/fpubh.2026.1965676/full
AB - Introduction: Vaccination is the canonical positive externality in health economics: because each vaccination protects others, decentralized choice is predicted to stall below the herd immunity threshold. Yet little evidence exists on the law of motion that governs national coverage. This study estimates it directly. Methods: I model the vaccinate-or-not decision of a heterogeneous household population as an expected-utility problem whose net payoff declines in the vaccinated share, aggregate it through an explicit revision protocol into a selection-mutation (replicator-mutator) equation in which payoff-responsive switching coexists with health-system contact and attrition hazards, and estimate the resulting equation on the World Health Organization/United Nations Children's Fund (WHO/UNICEF) Estimates of National Immunization Coverage (WUENIC, 2025 revision) for 195 countries over 1980-2025, with UN cohort denominators and World Bank income and health-system capacity controls. An exact identification result shows that the linear turnover coefficient equals the difference between the law of motion at full and at zero coverage, so it is identified from boundary observations independently of the payoff parameters, whereas the payoff slope is identified only where coverage traverses the simplex. Results: First, in the interior of the coverage range, the dynamics are dominated by a strong linear restoring force, implying an annual turnover of 15%–25% of the relevant pool; the payoff slope is statistically weak there, and interior data cannot distinguish institutional flows from payoff-insensitive revision, so the estimated hazards bound the institutional component from above. Second, the free-riding signature appears where it is identified: sharply in the Hib rollout, which spans the full coverage range, and weakly on the first-dose DTP margin. Third, every country's law of motion has a stable interior rest point; the births-weighted world rest point for first-dose measles vaccination is 78%, below the 92%–94% herd band; 74% of countries rest below it, and a coronavirus disease 2019 (COVID-19) era shift lowered the median rest point by 3.3 points. Discussion: Because the leverage of retention over payoff instruments equals 1/(1 − x * ) under the replicator protocol and diverges along the last mile under any smooth, bounded choice protocol, closing the gap is a default-and-retention problem rather than a price problem.
SN - 2296-2565
ER -