Critical levels of mask efficiency and of mask adoption that theoretically extinguish respiratory virus epidemics
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Abstract
Using a respiratory virus epidemiological model we derive equations for the critical levels of mask efficiency (fraction blocked) and of mask adoption (fraction of population wearing masks) that lower the effective reproduction number to unity. The model extends a basic epidemiological model and assumes that a specified fraction of a population dons masks at a given initial number of infections. The model includes a contribution from the ocular (nasolacrimal duct) route, and does not include contributions from contact (fomite) routes. The model accommodates dose-response (probability of infection) functions that are linear or non-linear. Our motivation to study near-population-wide mask wearing arises from the concept that, between two mask wearers, the concentration of particles at inhalation should be the square of the mask penetration fraction. This combination, or team, of masks can provide a strong dose-lowering squaring effect, which enables the use of lower-efficiency, lower-cost, lower pressure-drop (easier breathing) masks.
For an epidemic with basic reproduction number R 0 = 2.5 and with a linear dose-response, the critical mask efficiency is calculated to be 0.5 for a mask adoption level of 0.8 of the population. Importantly, this efficiency is well below that of a N95 mask, and well above that of some fabric masks. Numerical solutions of the model at near-critical levels of mask efficiency and mask adoption demonstrate avoidance of epidemics. To be conservative we use mask efficiencies measured with the most-penetrating viral-particle sizes. The critical mask adoption level for surgical masks with an efficiency of 0.58 is computed to be 0.73. With surgical masks (or equally efficient substitutes) and 80% and 90% adoption levels, respiratory epidemics with R 0 of about 3 and 4, respectively, would be theoretically extinguished.
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SciScore for 10.1101/2020.05.09.20096644: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:Limitations: Deterministic SIR models implicitly assume that the population has homogeneous mixing, with a fixed product of the number of contacts per day and of the probability of infection per contact. However, in some situations, for example at home, one would not normally expect people to wear masks. (Such limitations also apply to …
SciScore for 10.1101/2020.05.09.20096644: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:Limitations: Deterministic SIR models implicitly assume that the population has homogeneous mixing, with a fixed product of the number of contacts per day and of the probability of infection per contact. However, in some situations, for example at home, one would not normally expect people to wear masks. (Such limitations also apply to physical distancing.) Since the basic reproduction number R0 is not a constant determined solely by viral characteristics, one might consider a range of R0 in a population in order to accommodate higher-density higher-contact regions. For example, regions with busy subways would be expected to have higher R0. The critical mask efficiency calculated herein may be insufficient in environments with exposure higher than the average expected in simple SIR modelling. One such environment would be hospitals. Another such environment would be long-term-care facilities, where the duration and closeness of the contacts between personal care workers and residents are significant. Additionally, mask wearing by residents would not be practical, so the advantages of combined mask wearing would not exist. Finally, such residents have a high death rate once infected. Given all of these factors, higher efficiency masks worn by personal care workers deserves consideration. Other situations of higher-exposure than average might include those with tight-spacing and/or longer-duration, including public transportation and air travel. Many situations may have average...
Results from TrialIdentifier: No clinical trial numbers were referenced.
Results from Barzooka: We did not find any issues relating to the usage of bar graphs.
Results from JetFighter: We did not find any issues relating to colormaps.
Results from rtransparent:- Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
- Thank you for including a funding statement. Authors are encouraged to include this statement when submitting to a journal.
- No protocol registration statement was detected.
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