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

Abstract

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. In high-transmissibility cases, we establish that 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. 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.

Herd immunity and epidemic size in networks with vaccination homophily

“…Recently, we became aware of two other research works [31,32] that report results in line with what we have described here. They found qualitatively similar effects of homophily on epidemic size for scale-free networks [31] and empirical contact networks [32].…”

“…Recently, we became aware of two other research works [31,32] that report results in line with what we have described here. They found qualitatively similar effects of homophily on epidemic size for scale-free networks [31] and empirical contact networks [32]. This further corroborates the generalizability of our theoretical findings to networks with heterogeneous degree distributions [33].…”

Herd Immunity and Epidemic Size in Networks with Vaccination Homophily

“…After the completion of this manuscript, we became aware of two other research works [29,30] that report results in line with what we have described here. They found qualitatively similar effects of homophily on epidemic size for scale-free networks [29] and empirical contact networks [30]. This corroborates the generalizability of our theoretical findings to networks with inhomogeneous degree distributions.…”

“…As a final remark, we note that our approach has a broader scope. In this Letter, we focused on homophily by vaccination status; however, our framework is general enough to account for homophily by adherence to other epidemic interventions that reduce the susceptibility or infectiousness of individuals, such as the practice of social distancing, use of protective equipment [29], and adoption of digital contact tracing [31,32]. It can also be applied to the analysis of herd immunity in the case where the past infection (and consequent disease-induced immunity) is localized to a subpopulation [33] and in the case where the mixing pattern is assortative by risk factors of the disease [34].…”

The advantage of self-protecting interventions in mitigating epidemic circulation at the community level

“…As one of the most widely adopted means to fight the current pandemic, mask wearing is the paradigmatic example of these types of interventions. Given the evidence for the airborne transmission of SARS-CoV-2 by means of droplets and aerosols [18], recent research has shown that face masks are a very effective way to reduce the spread of COVID-19 [19][20][21][22][23][24][25][26]. Different types of masks exist, characterized by very different protecting performance, both qualitatively and quantitatively.…”