key: cord-1028799-dt2pew66
authors: Fisman, David N.; Greer, Amy L.; Tuite, Ashleigh R.
title: Brief research report: Bidirectional impact of imperfect mask use on reproduction number of COVID-19: A next generation matrix approach()
date: 2020-07-04
journal: Infect Dis Model
DOI: 10.1016/j.idm.2020.06.004
sha: 439a6ffc1d3b514b3e5a5d2a298e79637cc85bb2
doc_id: 1028799
cord_uid: dt2pew66

The use of masks as a means of reducing transmission of COVID-19 outside healthcare settings has proved controversial. Masks are thought to have two modes of effect: they prevent infection with COVID-19 in wearers; and prevent transmission by individuals with subclinical infection. We used a simple next-generation matrix approach to estimate the conditions under which masks would reduce the reproduction number of COVID-19 under a threshold of 1. Our model takes into account the possibility of assortative mixing, where mask users interact preferentially with other mask users. We make 3 key observations: 1. Masks, even with suboptimal efficacy in both prevention of acquisition and transmission of infection, could substantially decrease the reproduction number for COVID-19 if widely used. 2. Widespread masking may be sufficient to suppress epidemics where R has been brought close to 1 via other measures (e.g., distancing). 3. “Assortment” within populations (the tendency for interactions between masked individuals to be more likely than interactions between masked and unmasked individuals) would rapidly erode the impact of masks. As such, mask uptake needs to be fairly universal to have an effect. This simple model suggests that widespread uptake of masking could be determinative in suppressing COVID-19 epidemics in regions with R(t) at or near 1.

The use of masks as a means of reducing transmission of COVID-19 outside healthcare settings has proved controversial. Masks are thought to have two modes of effect: they prevent infection with COVID-19 in wearers; and prevent transmission by individuals with subclinical infection. We used a simple next-generation matrix approach to estimate the conditions under which masks would reduce the reproduction number of COVID-19 under a threshold of 1. Our model takes into account the possibility of assortative mixing, where mask users interact preferentially with other mask users. We make 3 key observations:

1.

Masks, even with suboptimal efficacy in both prevention of acquisition and transmission of infection, could substantially decrease the reproduction number for COVID-19 if widely used.

Widespread masking may be sufficient to suppress epidemics where R has been brought close to 1 via other measures (e.g., distancing).

3. "Assortment" within populations (the tendency for interactions between masked individuals to be more likely than interactions between masked and unmasked individuals) would rapidly erode the impact of masks. As such, mask uptake needs to be fairly universal to have an effect.

This simple model suggests that widespread uptake of masking could be determinative in suppressing COVID-19 epidemics in regions with R(t) at or near 1.

The use of masks as a means of reducing transmission of COVID-19 outside healthcare settings has proved controversial. Available evidence suggests that masks and other face coverings reduce both transmission and acquisition of droplet-borne respiratory viruses in healthcare settings (1-3) but evidence outside healthcare is limited . Ecological evidence suggests that countries where mask use is widespread have controlled COVID-19 epidemics more rapidly (4), and models suggest that even imperfect use of masks and other face coverings could be a potent disease control intervention, due to the bidirectional effects of masks on disease transmission (5) .

To use a simple, "next generation matrix" approach to explore the impact of masks on epidemic reproduction numbers under varying assumptions around effectiveness, uptake, and population mixing patterns.

We can represent mask use in a population using a simple mixing approach whereby the "force of infection" (rate of infection of susceptibles) in masked (λm) and unmasked (λu) individuals is:

Here Im and Iu represent prevalent infections among masked and unmasked individuals. Each βij represents the product of contact rate and transmission probability from an infectious individual with mask use status i, acting on a susceptible person with mask use status j.

Population mixing may be random, but assortativity is also possible, in which case masked individuals would interact predominantly with other masked individuals, and vice versa.

Assortativity would manifest as zeroes in the anti-diagonal of the matrix (6) (Figure 1, bottom panels) . If R is closer to 1 (e.g., 1.5) as may be the case following social distancing, limited mask uptake with effects limited entirely to reduced transmission may be sufficient to drive R to values below 1 (Figure 1, top   panels) .

Assortative mixing diminishes the impact of masking (Figure 2) , concentrating the epidemic in non-masked segments of the population. Assortativity is modeled using the approach of Garnett and Anderson (6), by adding an assortativity constant (η) to the matrix; values of η closer to 0 approximate random mixing while values closer to 1 represent extreme assortativity. Our analysis has several limitations, including the model's simplicity and the lack of precise estimates for mask effectiveness in the context of COVID-19. However, it should be noted that our model is likely conservative; a recent systematic review suggested, based on the best available evidence, that face masks reduce the risk of acquisition of viral infection by 85% (95% CI 66-93%) (3); as we note here, the impact of masking is markedly enhanced if both acquisition and transmission are reduced. In a health emergency like the current pandemic, decisions may need to be made on the basis of best available information, even if that information is imperfect.

In the absence of evidence of harms done by masking, and with even preliminary evidence that they could influence epidemic growth, we suggest that their more widespread use be considered by jurisdictions which have not yet advocated this intervention.

Effective reproduction number (R) is plotted on the Y-axis and increasing mask effectiveness is plotted on the X-axis in both figures. Curves represent 50% (light), 75% (medium) or 90%

(dark) uptake of masks in the population. Top panels represent a scenario with baseline R = 1.5;

and masks reducing transmission only (left), or both transmission and acquisition of infection with equal effectiveness (right). Bottom panels are identical, but use a baseline R = 3.

Baseline effective reproduction number (R) is plotted on the Y-axis and increasing mask effectiveness is plotted on the X-axis, across four different scenarios with respect to assortativity. Left handed panels show random mixing, while the three right hand panels show progressive increases in assortativity (coefficients of 0.25, 0.5 and 0.9, based on the approach of Garnett and Anderson (6)). The effective reproduction number, R, in each scenario is represented by color coding, with red areas signifying R > 1, white signifying R = 1, and blue areas signifying R < 1. It can be seen that R falls below 1 more easily with random mixing than with assortative mixing; when assortativity is extreme (far right panel), R cannot be brought below 1, even when R0 is low, mask use is widespread, and masks are highly efficacious. Note that simulations in this figure consider only reduction of transmission risk, and assume that masks do not prevent acquisition of infection.

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The research was supported by a grant to DNF from the Canadians Institutes for Health Research (2019 COVID-19 rapid researching funding OV4-170360). None of the authors has any conflict of interest to declare.