key: cord-0783394-7cnqz1ee
authors: Catching, A.; Capponi, S.; Yeh, M. T.; Bianco, S.; Andino, R.
title: Examining face-mask usage as an effective strategy to control COVID-19 spread
date: 2020-08-14
journal: nan
DOI: 10.1101/2020.08.12.20173047
sha: 2e66c4cf30c64aa275f857ab96fd71b9c43133b3
doc_id: 783394
cord_uid: 7cnqz1ee

The COVID-19 global crisis is facilitated by high virus transmission rates and high percentages of asymptomatic and presymptomatic infected individuals. Containing the pandemic hinged on combinations of social distancing and face mask use. Here we examine the efficacy of these measures, using an agent-based modeling approach that evaluates face masks and social distancing in realistic confined spaces scenarios. We find face masks are more effective than social distancing. Importantly, combining face masks with even moderate social distancing provides optimal protection. The finding that widespread usage of face masks limits COVID-19 outbreaks can inform policies to reopening of social functions.

The COVID-19 outbreak has caused a catastrophic mortality and economic damage around the world. The 52 causative agent of COVID-19, SARS-CoV-2, is an airborne pathogen that can be transmitted between 53 humans through droplets and aerosols that can travel 1-8 meters 1 . The virus is transmitted by both 54 symptomatic and asymptomatic individuals. COVID-19 causes severe symptoms that require 55 hospitalization, as well as severe long-term sequels and death. Accordingly, the outbreak has seriously 56 impacted healthcare systems around the world 2 . One of the major difficulties to contain the COVID-19 57 pandemic has been detection of infected asymptomatic or pre-symptomatic individuals, who are estimated 58 to be responsible for as much as 95% of all transmissions 3 4 . As these individuals carry and spread the 59 virus without manifesting any sign of the disease, they represent a crucial variable in managing the 60 outbreak.

In the absence of an effective vaccine or antiviral, most countries have implemented non- 

Face masks covering the nose and mouth area also provide a level of filtration that blocks virus 73 transmission to certain extend 6-8 . Masks prevent the spread of droplets and aerosols generated by an 74 infected individual 1 , reducing viral transmission by 95%. Uninfected individuals wearing a mask are 75 about 85% protected against infection 9 . Masks may be more effective to control the source of infectious 76 virus because they prevent the larger expelled droplets from being converted into smaller droplets that can 77 travel farther. Accordingly, face masks reduce the spread of influenza 10 and coronaviruses 11, 12 .

In our current study, we analyzed the relative efficacy of wearing face masks and/or exercising SD 79 to reducing the spread of COVID-19. Through stochastic computer simulations of infection spread, we 80 modeled realistic outbreak scenarios and found that SD only yields beneficial effects if accompanied by a 81 widespread population lockdown. In contrast, wearing face masks is a highly effective strategy to reduce 82 the spread of infection. Our results suggest that, even when a large fraction of infected individuals is 83 asymptomatic, mask wearing is the most effective strategy to control virus spread and alleviate the impact 84 of COVID-19 outbreak, particularly when combined with conditions of partial SD compatible with the 85 function of society.

who resolve the infection, cannot be re-infected or infect others, which is a reasonable assumption for the 102 duration of our models (45 days).

To define the probabilities of infection, we used reported COVID-19 parameters 17 . The probability 104 of transmission follows a G (gamma) distribution (see Methods) whose shape is described by a constant 105 (a), estimated to be 0.25. Wearing masks reduces this probability (Fig. 1 , probability of infection). To 106 estimate the protective effect of masks, we used parameters determined for FDA-approved surgical masks, 107 whose efficacy has been experimentally verified to inhibit virus transmission 10 . Based on previous studies 108 (Ferguson et al.) , we assumed that, if an infectious individual wears a mask, the effective probability of 109 transmission is reduced by a factor of 0.05. If a susceptible individual wears a mask, a is reduced by a 110 factor of 0.15 (Fig. 1A) . Our assumption that wearing masks is more effective to reduce transmission than 111 to prevent getting infected is supported by experimental data 18 . However, if both infectious and susceptible 112 individuals wear masks the probability of transmission is the product of these probabilities (0.0075) and, 113 thus, sufficiently low such that transmission is effectively null. We calibrated our model by running 114 simulations without any individuals wearing a face mask or practicing SD and considering that 50% of 115 infected individuals are asymptomatic (Movie 1). In this way, we determined the simulation parameters, 116 such as velocity and density of individuals, to obtain a value of R0 = 2.5, consistent with what was reported 117 early on as the infection rate of the epidemic in Wuhan 9 .

Percentage of population wearing masks determines the daily infection incidence and cumulative 119 number of cases. We started each simulation with one individual being infected and all others susceptible 120 and assuming that 50% of COVID-19 infections are asymptomatic (or pre-symptomatic). Non-infected and 121 asymptomatic individuals circulate in the population without any restriction (i.e., they do not isolate 122 themselves or become hospitalized) (see Methods). In contrast, symptomatic individuals no longer move 123 after 12 hours of the symptom onset, simulating hospitalization or self-isolation. Thus, symptoms are 124 assumed to manifest after the incubation time of 5.1 days plus 12 hours (Fig. 2B ). Using these assumptions 

If the daily incidence surpasses the treatment capacity, it will overwhelm the healthcare system none of the individuals is infectious or exposed any longer. Even more significantly, if 80% of the population 150 wear masks, we observed a significant flattening of the curve, with a substantial reduction in the maximum 151 number of infected individuals per day, 5.9 ± 6.8 ( Fig. 2A, green line) , and the number of new infected 152 individuals reached zero by day 57.8 ± 35.0. Thus, the shape of the outbreak changes from a curve 153 characterized by a sharp peak when no intervention is considered to a broader peak when 80% of the 154 individuals wear masks. By increasing the percentage of the individuals wearing masks, the number of newly infected individuals per day substantially decreases, which will reduce mortality and morbidity.

Moreover, since the use of masks eliminates the sharp peak that characterizes SARS CoV2 epidemics, the 157 overall impact of the outbreak on the health system is alleviated. These results highlight the importance of 158 widespread mask wearing as an effective intervention that can be implemented as soon as the first cases 159 are reported. 

In contrast, SD was only effective in populations with high incidence of asymptomatic infections 216 when a very high fraction of the population practice SD (more than 60%) (Fig. 3C) . Furthermore, the low 217 efficacy of SD as a containment strategy is more pronounced when the proportion of asymptomatic 

Our analysis uncovers a linear relationship between the fraction of a population wearing masks and 225 the reduction in infection rate. In contrast, we find SD requires a high fraction of compliance to be effective.

These findings indicate that having a high percentage of individuals wearing face masks is more beneficial 

To gain additional insights into the characteristics of the epidemic in response to these mitigation 243 strategies, we studied the shape of the epidemic curve by calculating the peak and full-width half-maximum increases dramatically to 85.5 when 80% of the population wears masks (Fig. 2B) . Our data indicate that 253 wearing masks has a more profound effect than SD on flattening the epidemic curve. For instance, when 254 80% of the population wears masks, the epidemic curve is eight times flatter than without any non-255 pharmacological intervention (Fig. 4B) . In contrast, if 80% of the population practices SD, the flattening of 256 the curve is less than threefold. The most dramatic effect on flattening of the curve is observed when 257 wearing masks is combined with SD; for instance, if 80% of the population wears masks and 80% practices 258 SD, the curve is flattened over 10-fold, compared to no intervention. the extinction time increases from ~39.0 to ~53 days (Fig. 4C) . Similarly, as a higher proportion of 263 individuals practice SD, the time to extinction of the infection also increases (Fig. 4C, ~39 to 51 days for 264 0% to 80% of SD). Importantly, even though the time to epidemic extinction is extended, the total number 265 of infected individuals dramatically decreases (Fig. 4A) . However, if a higher proportion of the population 266 (80%) wears face masks and practices SD, the time to epidemic extinction is reduced because the total 267 number of infected individuals is dramatically reduced (Fig. 4A ).

To relate the impact of these interventions to their societal impact, we determined the number of 269 deaths per million after each mitigation strategy, assuming a mortality rate of ~3% 31 . This analysis illustrates 270 the heavy cost of lives of the virus, but also demonstrates that a high level of mask wearing compliance is 271 the most effective non-pharmacological approach to protect human lives, particularly when combined with 272 even moderate SD measures (Fig. 4D) . In contrast, SD, without masks wearing is not effective to reduce 273 mortality (Fig. 4E) . Finally, our simulations predict that increasing the proportion of the population wearing 274 masks will increase the time to outbreak extinction (from ~40 to ~60 days) (Fig. 4F) . Together with the 275 broadening of the peak (Fig. 4C) , this shows an effective flattening of the curve. Importantly, with 80% mask 276 wearing, we observed an increase in the statistical distribution from the average time to extinction (Fig. 4F , 277 see 95% confidence intervals). Thus, a generally low disease incidence triggers stochastic events leading 278 to extinction of the infection. Our simulations represent real outbreak scenarios and reveal that as the 279 outbreak approaches its extinction there is an increase in the uncertainty of whether or not the infection has 280 been completed eliminated, which argue to be prudent before society reopening can be done safety.

Here we use realistic simulations rooted in experimentally measured parameters of SARS-Cov2 spread, 284 contagion mode and mortality, to evaluate two available NPIs that reduce the spread of a respiratory 285 infection, such as COVID-19. In our simulation, we assumed proper use of FDA-approved face masks. We Fig. 2A and 4A ). These two effects should reduce mortality and morbidity, alleviate the current 291 stress on healthcare systems, and enable a more effective management of severe cases. However, solely 292 wearing masks cannot entirely prevent an outbreak from occurring. It cannot by itself extinguish the virus, 293 since as long as a small fraction of the population is non-compliant, the virus can persist in the population.

Our models show that combining proper use of masks with practices such as SD, indisputably decreases 295 the number of new infected individuals per day (Fig. 2) . This conclusion is in agreement with that of ODE 296 models 32 .

Our analysis provides guidance for policies to protect the population from COVID-19. Optimizing 298 the use of masks with SD practices effectively limits the virus spread and reduces several parameters in 299 the epidemic, including cumulative incidence, shape of the peak, and the extinction rate (Fig. 3) . In 300 particular, we observed that wearing masks is more important than SD. Even in a population with a high 301 number of asymptomatic infections, increasing the use of masks up to 80% results in a significant reduction 302 in infection (Fig. 4A) . Meanwhile, even 80% of individuals practicing SD has only a marginal effect (Fig.   303   4D ). This result can be understood in terms of contact rate, since we assume that asymptomatic infectious 304 individuals have higher mobility than symptomatic infectious ones. If the vast majority of the population is 305 asymptomatic, then high compliance with face mask use is a key factor for curbing the epidemic.

Our simulations also provide insights into how enforcing different mitigation practices affects the 307 length of the epidemic. Assuming a homogenous population, the trajectory of epidemic extinction lasts 50-308 60 days, when 80% of the population either wears masks or practices SD (Fig. 4C) . However, when 80% 309 of the population is wearing masks and 0% of the population is practicing SD, the cumulative incidence is 310 reduced three times (~35%), and the peak is very broad (FWHM of ~ 85 days). In contrast, when the 311 population solely practices SD (80%), the majority of the population (93%) will end up infected, and the 312 peak of daily infected individuals will be sharper (FWHM of ~ 20 days).

Our model indicates that the synergistic utilization of face masks wearing and social distancing 314 practice is most effective controlling SARS-CoV-2 spread. We observed that wearing masks in combination 315 with some degree of SD relaxes the need for a complete lockout, leading to a partial reopening of the 316 society. The effectiveness masks wearing to control virus spread is not reduced if a large fraction of the 317 population is asymptomatic. This suggests that, in the absence of universal testing, widespread use of face 318 masks is necessary and sufficient to prevent a large outbreak. Our results are supported by the real data 319 of Korea 33 and Taiwan 34 , where an early mandate to requiring face mask usage, in combination with SD, 320 severely limited the spread of the virus. While more work is necessary to specifically assess the impact of 321 other variables shaping COVID-19 outbreaks, such as increased mobility, age stratification, testing a 322 fraction of the population, our study can accurately inform strategies to reduce the spread of the virus. In 

For the interaction between symptomatic infected and susceptible individuals, the infection probability was 350 randomly sampled from a gamma distribution with a mean of 1 and a shape of 2.5, whereas for that between 351 asymptomatic infected and susceptible individuals, the infection probability is reduced by 33 %. We assume 352 this reduction of infectivity for the asymptomatic, based on the absence of transmission-aiding symptoms, 353 such as coughing, sneezing, and a runny nose 17 . The time between a susceptible individual being exposed 354 to being in the infectious infected state is 5.1 days 17 . Symptomatic infected individuals are infectious for 12 355 hours before self-isolating. After this time, we assume that these individuals no longer infect those around 356 them because they are hospitalized or self-isolating. Asymptomatic infected individuals are infectious for 7 357 days, and the infectivity linearly declines until the individual is no longer infectious on day 7 37 . If an infected, 

Then, we carried out four more sets of simulations in which we increased the percentage of individuals Simulations are stochastic, and we simulated each condition 100 times to increase the statistical power of 368 the analysis. In total, we simulated 25 different conditions for a total of 2500 simulations, 100 for each 369 condition. In all these simulations, the probability of a new infection being asymptomatic was 50%.

Simulations were run until there were no individuals either infected or exposed. Summary values were 371 computed by methods in the NumPy module. Error bars were calculated by the standard deviation method 372 in NumPy. The full-width half-maximum (FWHM) was calculated for each simulation from the newly infected 373 per day data by taking the maximum and using it to find the days that intersect the value of half the maximum 374 value. The first and last days of this intersection were then used to calculate the number of days of the 375 FWHM. From the set of FWHM for each simulation, an average and standard deviation were calculated 376 using the NumPy module. FWHM error bars are large due to a large variation in how flat the curves are.

Graphs were created by using the Matplotlib 38 and Seaborn 39 modules in python.

We followed the same protocol described above to perform simulations, varying the probability of 

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