The Immunity Reversal

Vaccination is better than natural infection. This isn’t just medical advice — it’s a mathematical claim about epidemic dynamics. Vaccinating a fraction of the population should reach herd immunity more efficiently than letting the disease spread naturally, because vaccination is targeted and controlled while natural infection is random and costly.

Balogh, Odor, and Karsai (arXiv:2602.17360) show this reverses when non-pharmaceutical interventions reshape the contact network. Social distancing measures reduce the average number of contacts per person, changing the network through which both disease and immunity spread. In sparse networks (few contacts per person), uniform vaccination is indeed most effective — it distributes immunity efficiently across the thin network.

But as average contacts increase, a reversal occurs. Naturally acquired immunity — gained through controlled exposure to disease — outperforms vaccination at achieving herd immunity. The crossover happens because vaccination distributes immunity uniformly, ignoring the network’s structure, while natural infection concentrates immunity in the most-connected individuals (who are most likely to get infected). In a dense network, concentrating immunity in hubs is more efficient than distributing it uniformly, because hubs disproportionately transmit disease.

The interaction with non-pharmaceutical interventions creates the paradox. Social distancing measures that reduce contacts make the network sparse, which favors vaccination. Removing social distancing makes the network dense, which favors natural immunity. The optimal immunization strategy depends on the current state of the contact network — which is itself being shaped by policy decisions about distancing.

The structural lesson: the effectiveness of an intervention depends on the system it operates in, and that system is not static. Non-pharmaceutical interventions change the contact network, which changes which immunization strategy is optimal, which should change the immunization policy — but the immunization policy and the contact network are coupled. Optimizing one component (vaccination strategy) without accounting for the other (network-shaping interventions) can produce worse outcomes than not optimizing at all.

Balogh, Odor, & Karsai, “Non-Pharmaceutical Interventions Reshape Network Immunization Outcomes,” arXiv:2602.17360 (2026).