The theoretical starting point is one of the oldest ideas in health economics. Vaccination is the canonical positive externality: a vaccinated household protects not only itself but everyone it would otherwise have infected, so the private benefit of vaccinating falls short of the social benefit, and the gap widens as coverage rises. When most of a community is already immune, the residual infection risk that motivates the marginal household is small, while the social value of pushing coverage across the herd threshold remains large. Decades of analytical work have predicted that decentralized vaccination choice should stall strictly below the social optimum, and that disease elimination is not an equilibrium of voluntary behavior. What the literature lacked was direct evidence on the mechanism. The externality argument is fundamentally a statement about dynamics, about how the annual change in coverage should respond to the level of coverage, and no one had estimated that dynamical system on the world’s largest coverage panel.

Yolusever’s framework does exactly that. The analysis draws on the WHO/UNICEF Estimates of National Immunization Coverage, the 2025 revision, an annual country-by-antigen panel of the vaccinated share of each birth cohort covering 195 countries over 1980 to 2025, with UN cohort denominators and World Bank income and health-system capacity controls. Six antigens enter the estimation: the first and third doses of the diphtheria-tetanus-pertussis series, the first and second doses of measles-containing vaccine, and the third doses of hepatitis B and Haemophilus influenzae type b vaccines. First-dose measles coverage is the headline antigen because measles has the highest basic reproduction number among vaccine-preventable diseases, and therefore the most demanding herd threshold. The estimation panel for first-dose measles comprises 8,019 country-year first differences.

The model is built from household choice upward. A household decides whether to complete a vaccination schedule by comparing the expected utility loss from infection, which declines with aggregate coverage because of herd protection, against the full cost of vaccinating, which bundles money, time and travel prices, and the psychological cost documented in the vaccine-hesitancy literature. But households do not re-optimize continuously. In any year, only a fraction actively revise their choice in response to the payoff difference. The remainder is carried by two payoff-blind flows: an institutional enrollment hazard that draws unvaccinated children into the schedule whenever the household touches the health system, and an attrition hazard that removes vaccinated-track households through migration, provider discontinuity, stock-outs, misinformation shocks and administrative failure. Aggregated, the process yields a replicator-mutator equation in which the selection term captures the economics of free riding and the mutation terms carry the institutions. The health system enters at a precise place: workforce density, facility reach and birth-registration linkage govern the contact probability; vaccine supply, default scheduling and provider practice govern the conversion probability; continuity of care and public trust govern attrition.

The identification strategy is the study’s technical heart. The selection term is multiplied by the variance of the two-state population, which vanishes at both boundaries of the coverage range, while the mutation flows remain active there. An exact result shows that the linear turnover coefficient equals the difference between the law of motion’s values at full and at zero coverage, two quantities that contain no payoff parameter. Boundary and near-boundary observations therefore identify the institutional hazards separately from selection, without an instrument. Conversely, in the narrow interior window where 83 percent of the panel lives, the level and slope of the payoff difference are nearly collinear, with a sample correlation of 0.87, so the free-riding signature is weakly identified there and must be sought where the data traverse the entire coverage range: in new-vaccine rollouts.

The results reframe what kind of economic object national vaccination coverage is. In the interior of the coverage range, the dynamics are dominated by a strong linear restoring force. For first-dose measles, the coefficient is −0.248 with a t-statistic above 10 under two-way fixed effects, implying an annual turnover of 15 to 25 percent of the relevant behavioral pool. For the median country, the flow decomposes into an enrollment hazard of about 0.20 per year, the probability that an unvaccinated-track child is pulled into the schedule by institutional contact, and an attrition hazard of about 0.045, the probability that a covered household drifts out. Coverage is high not because households continuously find vaccination optimal, but because the institutional default recruits a fifth of the uncovered pool every year, four and a half times faster than drift erodes the covered pool. The selection terms are statistically weak in the interior, and the author is careful: the estimated hazards are upper bounds on the institutional component, because interior data cannot distinguish payoff-blind institutional flows from a payoff-responsive revision protocol whose switching probability is locally flat in coverage.

Where the data can test free riding, the signature appears sharply. The Hib rollout is the cleanest laboratory, because its national introductions begin at zero within the sample and traverse the whole coverage range, timed by Gavi financing windows and WHO recommendations rather than by household demand. There the payoff difference declines significantly in coverage, and selection alone would have stalled the rollout at 87 percent, below the coverage most programs eventually attained. The first-dose DTP margin shows a weaker version of the same declining payoff, but its implied Nash coverage exceeds one, meaning the private return to first contact remains positive across the range; the persistent DTP1 shortfall in many countries is therefore a contact problem rather than a free-riding problem. Meanwhile, every country’s estimated law of motion has a stable interior rest point, approached with a half-life of about two years. The median rest point for first-dose measles is 87.6 percent, and the gradient across income groups is steep and monotonic: 67.6 percent in low-income countries, where every country rests below the band, 75.4 percent in lower-middle-income, 87.8 percent in upper-middle-income, and 91.7 percent in high-income countries, where 54 percent still rest below the band.

The COVID-era result sharpens the welfare stakes. Interacting the law of motion with an indicator for 2020 onward shows that the post-2019 curve lies below the pre-2020 curve throughout the policy-relevant range, displacing the median country’s rest point from 89.1 to 85.8 percent. The estimates locate the displacement in the contact and conversion probabilities that the pandemic disrupted directly, not in attrition: the value of the law of motion at full coverage, which measures the attrition hazard, moves by only 0.003. This is a sharper statement than the familiar observation that coverage dipped during the pandemic. The dip is not a transitory deviation from an unchanged attractor but a displacement of the attractor itself, so a return to pre-2019 behavior will not occur by relaxation alone.

The policy content is a closed-form leverage result. Because a payoff instrument, such as a subsidy, conditional transfer or risk-information campaign, enters the law of motion multiplied by the vanishing variance factor, while a retention instrument, such as defaults, reminder systems or school-entry verification, enters multiplied by the coverage share itself, the ratio of their steady-state effects is 1/(1 − x*). At the median rest point of 87.6 percent, retention is 8.1 times more powerful per unit, and the ratio grows without bound as coverage approaches one. Calibrated on the estimates, lifting the median country into the herd band requires a payoff shift about twelve times larger than the equivalent improvement in retention. The arithmetic reconciles apparently conflicting intervention evidence: in rural Rajasthan, where full immunization stood near 6 percent, reliable monthly camps and small in-kind incentives carried comparable leverage, whereas in high-coverage settings the systematic review of parental financial incentives finds only weak effects, exactly as a leverage ratio of 7 to 20 in favor of retention implies. The result survives the change of revision protocol: under any smooth, bounded choice probability, the marginal effect of a payoff shift must vanish near the boundary while the effect of a retention shift does not.

The author frames the conclusion structurally rather than rhetorically: herd immunity will not be priced into existence; it must be defaulted and retained into existence. The study also carries caveats. The analysis runs on national aggregates, so subnational heterogeneity, which matters greatly for outbreak risk because herd protection is a local property and outbreaks originate in groups far below the national rest point, is invisible at this resolution. The identification of the institutional hazards is parametric, resting on the affine payoff function and the imitation protocol. Gender enters the model through the caregiver’s time cost and the contact hazard, and the author notes that women’s restricted mobility and time poverty act at the point of contact rather than at the point of valuation, an entry the aggregate panel cannot estimate separately. The immediate extensions are to estimate the same law of motion on subnational, survey-based and surveillance-linked panels, where wealth, residence and caregiver characteristics can be observed, and to decompose the institutional hazards into their supply and confidence components.

Subject of Research: The herd immunity attractor: selection, drift, and the steady-state undersupply of vaccination in 195 countries, 1980–2025

Article Title: The herd immunity attractor: selection, drift, and the steady-state undersupply of vaccination in 195 countries, 1980–2025

Article References: Yolusever, A. (2026). The herd immunity attractor: selection, drift, and the steady-state undersupply of vaccination in 195 countries, 1980–2025. Frontiers in Public Health, 14, Article 1965676. https://doi.org/10.3389/fpubh.2026.1965676

Image Credits: AI Generated

DOI: 10.3389/fpubh.2026.1965676

Keywords: herd, immunity, attractor, selection, drift, steady-state, undersupply, vaccination, countries, scientific research