COVID-19, caused by SARS-CoV-2 is a rapidly spreading global pandemic. Although precise
transmission routes and dynamics are unknown, SARS-CoV-2 is thought primarily to spread
via contagious respiratory droplets.
1
Unlike with SARS-CoV, maximal viral shedding occurs in the early phase of illness,
1,2
and this is supported by models that suggest 40–80% of transmission events occur from
pre- and asymptomatic individuals.
3,4
One widely-discussed strategy to limit transmission of SARS-CoV-2, particularly from
presymptomatic individuals, has been population-level wearing of masks. Modelling
for pandemic influenza suggests some benefit in reducing total numbers infected with
even 50% mask-use.
5
COVID-19 has a higher hospitalization and mortality rate than influenza,
6
and the impacts on these parameters, and critically, at what point in the pandemic
trajectory mask-use might exert maximal benefit are completely unknown.
We derived a simplified SIR model based on the population of Israel as proof of principle
(population 8 million) to investigate the effects of near-universal mask-use on COVID-19
assuming 8 or 16% mask efficacy (see Methods for relevant parameters). We decided
to model, in particular, the impact of masks on numbers of critically-ill patients
and cumulative mortality, since these are parameters that are likely to have the most
severe consequences in the COVID-19 pandemic. Whereas mask use had a relatively minor
benefit on critical-care and mortality rates when transmissibility (Reff) was high
(Fig. 1A), the reduction on deaths was dramatic as the effective R approached 1 (Fig.
1B), as might be expected after aggressive social-distancing measures such as wide-spread
lockdowns.
6
One major concern with COVID-19 is its potential to overwhelm healthcare infrastructures,
even in resource-rich settings, with one third of hospitalized patients requiring
critical-care. We incorporated this into our model, increasing death rates for when
critical-care resources have been exhausted, however, we also modelled the same parameters
for scenarios in which critical care capacity was unrestricted (Fig. 1C-D). Our simple
model shows that modest efficacy of masks could avert substantial mortality when critical
care capacity is limiting, but also derives benefit when it is unrestricted. Importantly,
the effects on mortality became hyper-sensitive to mask-wearing as the effective R
approaches 1, i.e. near the tipping point of when the infection trajectory is expected
to revert to exponential growth, as would be expected after effective lockdown.
Figure 1
Mask effectiveness on mortality varies by R
eff
(A) Number of critically ill patients (red) and total deaths (black) for an epidemic
spreading with R of 2.2 (see Methods for parameters) in a simple SIR model, x-axis
represents time in days. The different curves are computed for a reduction of infectivity
of 0, 8 and 16% by mask-wearing. (B) Same as A, but for an epidemic spreading with
R of 1.3. Note that the reduction in infectivity by mask wearing has a larger effect.
(C-D) Same as A-B but taking into account decrease in death when beds are unrestricted
for critically-ill patients (see Methods). (E-F) Analysis of the data of Ferguson
et al (ref 5, Table 4). Assuming a 10% reduction in infectivity, mask wearing may
be at least as effective as home confinement at reducing deaths (E) or preventing
overwhelming icu beds (F). The different bars (1–5) are different thresholds (“triggers”)
for implementing social measures in the Ferguson et al model.
In order to understand the generality of the effect of mask wearing upon home confinement
removal, we also analysed the potential effects of mask-wearing for data provided
by a more comprehensive and realistic model of the COVID-19 infection, which included
modelling of different levels of social-distancing measures on infection and likely
deaths.
6
When home-confinement is lifted but other social-distancing measures are in place,
such as school closure and case isolation, wearing masks can maintain the benefits
of home-confinement, both in terms of deaths (Fig. 1E) and critical-care bed use (Fig.
1F).
Limitations of our study include the relatively straightforward model we employed,
as well as assumptions of high compliance with mask-wearing and their potential efficacy,
for which definitive evidence in pandemics is lacking.
7,8
Another recent modelling study of mask use came to similar conclusions as ours despite
slightly different input parameters.
9
However, that model mostly considered scenarios where the effective transmissibility
of SARS-CoV-2 remained high. Despite the limitations of our study, our model suggests
that mask-wearing might exert maximal benefit as nations plan their ‘post-lockdown’
strategies and suggests that mask-wearing should be included in further more sophisticated
models of the current pandemic. Since otherwise similar countries are currently devising
different mask-wearing scenarios, the current situation offers an unprecedented opportunity
to gather evidence on the real-world utility of population mask-wearing for implementation
in this and future pandemics.
Methods
Infection dynamics model (Figure 1a-c)
To demonstrate the effect of masks, we used a simple SIR model of the dynamics of
infection taking several populations into account: S: susceptible individuals, I:
infected, R: resistant, CI: critically ill, D: dead. The goal of the model is not
to predict any particular infection in a completely realistic way, but rather to illustrate
the impact of reducing infectivity at high versus low Reff values.
Where the Heaviside function is used for changing the death rate when the critically
ill number saturates ICU beds. Parameters are defined in the following Table. The
model was run using Matlab R2017a (MathsWorks,USA) ODE solver (‘ode23s’).
Wearing of masks was implemented in the model as a reduction of infectivity between
8–16%.
5,8,10–15
Total population size was taken as 8x106
In the absence of ICU beds, 86% of the critical care patients die, whereas if ICU
beds are not limiting, only 40% of critical care patients would die. The total fraction
of critical care patients is 1.8% of the total number of infected cases
6
.
Data for (Figure 1E and 1F) was adapted from Ferguson et al
6
(16/3/2020- Table 4) The wearing of masks is assumed to reduce transmissibility by
10%. We, therefore, compared the results of Fergusson et al (Table 4) at different
R and for different social-distancing policy measures.