A crowd of pedestrians in a square moves chaotically: each person goes their own way, occasionally bumping into others. If every third person in that crowd wears a protective suit that blocks the pathogen, the rhythm of disease spread changes abruptly. That is exactly the scenario scientists reproduced by simulating 3000 self-propelled particles that repel each other and become infected upon close contact.

Until now, epidemics have been described by equations that assume people are uniformly mixed, like sugar in tea. But real cities are different: people walk, cluster, and disperse. The authors of the new study took a different approach and built a microscopic model in which each particle is a person with their own speed and random turns. A susceptible agent becomes infected if they stay near an infected one for a certain time, while a protected agent never gets infected.

The result was unexpected. When fewer than 30% are protected, infection curves for different densities collapse onto a single universal line, and the maximum epidemic rate grows as the square root of density. This follows from simple geometry: the distance between particles is inversely proportional to the square root of density, so the encounter frequency scales the same way. But once the protected fraction exceeds 30%, universality vanishes. The curves diverge, and protection begins to dominate, suppressing the epidemic most strongly in sparse populations where encounters are already rare.

This work is the first to systematically introduce protected agents into a microscopic model of active matter and reveals a clear crossover between two regimes. Previously, it was unclear how individual protection and population density jointly affect infection dynamics, because classical models ignore movement. Now it is clear: in sparsely populated areas, vaccination or masks have a stronger effect than in dense ones, where high encounter rates partially offset protection. This could inform planning of anti-epidemic measures in cities and on farms, where population density and protection levels vary from area to area.

The crowd in the square disperses again, but now it is evident that one in three in protective suits changes not just the number of infected, but the very law by which the epidemic spreads.