Picture a crowd of pedestrians, each going their own way but occasionally bumping into others. If every third person wears a protective suit that blocks the infection, the disease spreads quite differently. Scientists built a computer model of such a crowd: 3000 particles that move on their own, repel each other, and get infected upon close contact.

Previously, epidemics were calculated using equations where all people are uniformly mixed, like sugar in tea. But in real life, people walk and cluster. In the new model, each particle is a person with their own speed and random turns. A susceptible agent gets infected if it stays near an infected one long enough, while a protected agent never gets infected. The scientists varied the fraction of protected particles from 0% to 50% and the crowd density by changing the area size.

Why is that? In a sparse crowd, people meet less often, so each protected individual has a stronger effect. In a dense crowd, frequent encounters partially offset the benefit of protection. Previously, it was unclear how protection and density interact, because old models ignored movement. Now it's clear: in sparsely populated areas, vaccination or masks have a greater impact than in dense ones. This could help plan interventions in cities and on farms, where density and protection vary from place to place.

The crowd disperses again, but now it's clear: one in three in a protective suit changes not just the number of infections, but the very law by which the epidemic spreads.