Wearing face masks to protect oneself and/or others: Counter-intuitive results from a simple epidemic model accounting for selfish and altruistic human behaviour
Résumé
We study a simple SIS epidemic model accounting for human behaviour. 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 disease. We consider a situation in which individuals are unaware of their health status (infected or not), but can perceive disease prevalence at the population level. This assumption fits situations in which asymptomatic people can be numerous and tests are not widely available. Individual decision dynamics depend both on disease prevalence, as a proxy for the risk of being infected or infecting others, and/or the fraction of the population complying to mask-wearing, which people can observe in their everyday life. Specifically, human behaviour is assumed to be driven by imitation dynamics. When the disease 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 effectiveness of mask-wearing is positively correlated to its cost at the individual level. Increasing mask effectiveness and therefore its individual cost can make the system switch from full-compliance to partial-compliance. This way, increasing mask effectiveness may increase disease prevalence at equilibrium. In other words, disease prevalence is minimized for intermediate mask effectiveness 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 behaviour may lead to counter-intuitive but nevertheless intelligible outcomes, which should be anticipated when designing public health policies.
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