Wearing face masks to protect oneself and/or others: Counter-intuitive results from a simple epidemic model accounting for selfish and altruistic human behavior

We study a simple SIS epidemic model accounting for human behavior. Individuals can decide at each instant of time whether or not they wear a face mask. Mask wearing decreases susceptibility to and/or transmission of the pathogen. We consider a situation in which individuals are unaware of their health status (infected or not), but they can perceive the prevalence of infection at the population level. This assumption fits situations in which most infected individuals are asymptomatic. Individual decision dynamics depends both on prevalence, as a proxy for the risk of being infected or infecting others, and on the fraction of the population complying to mask-wearing, which people can observe in their everyday life. Specifically, human behavior is assumed to be driven by imitation dynamics. When the epidemic does not naturally die out, the model has three types of endemic equilibria: no-compliance, partial-compliance, and full-compliance. Only one of these equilibria can be stable at a time. We assume that the efficacy of mask-wearing is positively correlated to its cost at the individual level. Increasing mask efficacy and therefore its individual cost can make the system switch from full-compliance to partial-compliance. This way, increasing mask efficacy may increase the prevalence of infection at equilibrium. In other words, prevalence is minimized for intermediate mask efficacy and cost. This is because, when mask-wearing is too effective and therefore costly, part of the population free-rides on the effort of others and drops mask, resulting in increased prevalence. Altogether, our results show that the interplay between epidemiology and human behavior may lead to counter-intuitive but nevertheless intelligible outcomes, which should be anticipated when designing public health policies.