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The effectiveness of non-pharmaceutical interventions to curb the spread ofSARS-CoV-2 is determined by numerous contextual factors, including adherence.Conventional wisdom holds that the effectiveness of protective behaviour suchas wearing masks always increases with the number of people adopting it. Herewe show in a simulation study that this is not true in general. We employ aparsimonious network model based on the well-established empirical facts that(i) adherence to such interventions wanes over time and (ii) individuals tendto align their adoption strategies with their close social ties (homophily).When combining these assumptions, a broad dynamical regime emerges where theindividual-level infection risk reduction for those adopting protectivebehaviour increases as the adherence to protective behavior decreases. Forinstance, for a protective coverage of 10% we find the infection risk foradopting individuals can be reduced by close to 30% compared to situationswhere the coverage is 60%. Using estimates for the effectiveness of surgicalmasks, we find that reductions in relative risk of masking versus non-maskingindividuals range between 5% and 15%, i.e., vary by a factor of three. Thissmall coverage effect originates from system-dynamical network properties thatconspire to increase the chance that an outbreak will be over before thepathogen is able to invade small but tightly connected groups of individualsthat protect themselves. Our results contradict the popular belief that maskingbecomes ineffectual as more people drop their masks and might have far-reachingimplications for the protection of vulnerable population groups under resurgentinfection waves.

Small coverage effect in epidemic network models shows that masks can become more effective with less people wearing them