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

In this study, we discuss the impacts of assortative mixing by mask-wearing on the effectiveness of mask use in suppressing the propagation of epidemics. We employ the mask model, which is an epidemic model involving mask wearers and non-mask wearers. We derive the occurrence probability and mean size of large outbreaks, epidemic threshold, and average epidemic size for the mask model in an assortatively mixed random network that follows an arbitrary degree distribution. Applying our analysis to the Poisson random networks, we find that 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 not effective in containing epidemics in that the transmissibility required for large outbreaks to occur is small. On the other hand, in high-transmissibility cases, mask use is most effective in decreasing the occurrence probability and mean size of large outbreaks, as well as the average epidemic size, when the mixing pattern is strongly assortative. Strongly assortative mixing, resulting in the separation of mask wearers and non-mask wearers, reduces the probability and degree of a large outbreak in high-transmissibility cases, although it allows a large outbreak to occur even in low-transmissibility cases. In scale-free networks, mask use is most effective when the mixing pattern is strongly assortative and when it is maximally disassortative, provided that the mask coverage is not low. Both for the Poisson random and scale-free networks, all analytical treatments are in good agreement with simulation results.