  Masks have remained an important mitigation strategy in the fight against
COVID-19 due to their ability to prevent the transmission of respiratory
droplets between individuals. In this work, we provide a comprehensive
quantitative analysis of the impact of mask-wearing. To this end, we propose a
novel agent-based model of viral spread on networks where agents may either
wear no mask or wear one of several types of masks with different properties
(e.g., cloth or surgical). 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 contact network, viral
transmission dynamics, and the distribution of the different types of masks
within the population. Through extensive simulations, we then investigate the
impact of different allocations of masks within the population and trade-offs
between the outward efficiency and inward efficiency of the masks.
Interestingly, we find that masks with high outward efficiency and low inward
efficiency are most useful for controlling the spread in the early stages of an
epidemic, while masks with high inward efficiency but low outward efficiency
are most useful in reducing the size of an already large spread. Lastly, we
study whether degree-based mask allocation is more effective in reducing the
probability of epidemic as well as epidemic size compared to random allocation.
The result echoes the previous findings that mitigation strategies should
differ based on the stage of the spreading process, focusing on source control
before the epidemic emerges and on self-protection after the emergence.
