The basic reproduction number R₀ — how many people one infected person infects in a fully susceptible population — is the headline number in any epidemic. In a well-mixed population, R₀ is a simple ratio of transmission and recovery rates. The effective reproduction number Rₑ declines exponentially as susceptibles are consumed.
The authors (arXiv:2603.22150) show that spatial structure changes both numbers. In networks with spatial topology, R₀ is smaller than in the well-mixed case because infected nodes compete with each other for nearby susceptibles. Two infected neighbors can't both transmit to the same person. This competition reduces the effective rate of spread.
More subtly, the dynamics of Rₑ change. In well-mixed populations, Rₑ declines exponentially and smoothly toward 1. In spatial networks, Rₑ drops faster initially — nearby susceptibles are consumed quickly — but then the decline slows as the epidemic reaches regions where competition between infected nodes is lower. The trajectory eventually converges to unity, but through a different path.
The through-claim: the reproduction number isn't a property of the pathogen — it's a property of the pathogen-network pair. The same virus in the same population produces a different R₀ depending on whether people interact locally or globally. Spatial structure doesn't just slow transmission; it changes the shape of the epidemic curve by introducing competition between infections for finite local resources.