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In this study, we discuss the impacts of assortative mixing by mask-wearingon the effectiveness of mask use in suppressing the propagation of epidemics.We employ the mask model, which is an epidemic model involving mask wearers andnon-mask wearers. We derive the occurrence probability and mean size of largeoutbreaks, epidemic threshold, and average epidemic size for the mask model inan assortatively mixed random network that follows an arbitrary degreedistribution. Applying our analysis to the Poisson random networks, we findthat the assortative (disassortative) mixing by mask-wearing decreases(increases) the epidemic threshold. Assortative mixing, the tendency for(non-)mask wearers to prefer to connect with (non-)mask wearers, is noteffective in containing epidemics in that the transmissibility required forlarge outbreaks to occur is small. On the other hand, in high-transmissibilitycases, mask use is most effective in decreasing the occurrence probability andmean size of large outbreaks, as well as the average epidemic size, when themixing pattern is strongly assortative. Strongly assortative mixing, resultingin the separation of mask wearers and non-mask wearers, reduces the probabilityand degree of a large outbreak in high-transmissibility cases, although itallows a large outbreak to occur even in low-transmissibility cases. Inscale-free networks, mask use is most effective when the mixing pattern isstrongly assortative and when it is maximally disassortative, provided that themask coverage is not low. Both for the Poisson random and scale-free networks,all analytical treatments are in good agreement with simulation results.

Impact of assortative mixing by mask-wearing on the propagation of epidemics in networks