Spreading processes with population heterogeneity over multi-layer networks

It's been controversial whether re-opening school will facilitate viral spread among household communities with mitigation strategies such as mask-wearing in place. In this work, we propose an epidemiological model that explores the viral transmission over the multi-layer contact network composed of the school layer and community layer with population heterogeneity on mask-wearing behavior. We derive analytical expressions for three key epidemiological quantities: the probability of emergence, the epidemic threshold, and the expected epidemic size. In particular, we show how the aforementioned quantities depend on the structure of the multi-layer contact network, viral transmission dynamics, and the distribution of the different types of masks within the population. Through extensive simulations, our analytical results show near-perfect agreement with the simulation results with a limited number of nodes. Utilizing the model, we study the impact of the opening/closure of the school layer on the viral transmission dynamics with various mask-wearing scenarios. Interestingly, we found that it's safe to open the school layer with the proper proportion of good-quality masks in the population. Moreover, we validate the theory of the trade-off between source-control and self-protection over a single layer by Tian et al on our multi-layer setting. We conclude that even on a multi-layer network, it's of great significance to treat the spreading process as two distinct phases in mind when considering mitigation strategies. Besides, we would like to remark that our model of spreading process over multi-layer networks with population heterogeneity can also be applied to various other domains, such as misinformation control.