Development of contagion contours
Literature shows opposing conditions for transmission of viruses in general; low relative humidity (RH) and high RH[
5,
25,
26] with temperature a secondary factor. Theory predicts osmotic forces should affect enveloped viruses such as influenza, while icosahedral viruses (e.g. polio, norovirus) would not be so sensitive for structural reasons. Enveloped viruses generally have highest infective stability at RH somewhat below 50%[
5], and non-enveloped icosahedral viruses usually show greatest infective stability in aerosol in high humidity conditions[
25,
26].
Data of Lowen et al.[
16,
17] at 20°C show optimal transmission of influenza by aerosol at a first RH range from 20-40%, and at a second from 60-70%. Lower temperatures improve transmission, with temperatures above 30°C reducing transmission to zero. These data correlate with other
in-vitro studies[
5,
25‐
27].
Influenza is an enveloped virus. Enveloped viruses bud from the cell membrane, so the virus envelope is host cell (or golgi) membrane acquired in the budding process. Inside the envelope is RNA, a few enzymes and proteins, along with cell cytosol at physiological salt concentration. This matters because if one puts a cell in an environment containing lower salt concentration than in cytosol, the cell membrane acts as an osmosis membrane and eventually ruptures[
28]. Enveloped viruses will have the same issue, although the smaller diameter should give greater stability to rupture per equation 3.
Where F = membrane tensile force, P = pressure, r = radius
Infectious droplets from the lungs start out with physiological levels of salts. These salts could cause rupture of virion envelopes as droplets collect distilled water from humid air. Schaffer et al[
27] studied stability of enveloped viruses from different cell lines (viz. kidney, chick embryo) and these cell lines buffer osmotic pressures at different rates[
28]. Those results indicate that cells which are better at buffering themselves to osmotic pressure produce enveloped viruses that survive longer at higher RH. We are not aware of any direct study of osmotic destruction of enveloped virions, although it makes considerable sense.
At lower RH, enveloped viruses are quite stable and infectious; at high RH they are not. One possibility is the above-mentioned osmotic pressure issue. Another is the theory that droplet particles settle more quickly as they take on water[
17] under high RH, which fits Stokes' law[
2]. In addition, enlargement of the particle as a condensation nucleus will cause it not to penetrate as far into lungs as a result[
2]. However, none of these hypotheses explain the viability trough at 50% RH nor the secondary peak at 65% RH, although the rapid decline toward 80% RH does fit. The primary variable between
in-vitro studies and Lowen et al. appears to be differences between the synthetic droplet media of the
in-vitro studies[
25,
27] and the natural droplets from exhalation, which are likely to be glycoproteins, salts and other components of mucus[
29].
A study by Harper[
25] examined,
in-vitro, survival of 4 cultured viruses in aerosol, at temperatures ranging from 21°C to 24°C. To the degree his results differ from Lowen in the 50% + humidity range, they might be explained by his higher temperature. If so, that would change the contours of influenza transmission risk (Figure
1) somewhat, although the current transmission risk contours would remain conservative. Alternatively, this difference may be from the droplet fluid carrying virus used by Harper, as mentioned above.
There is an argument that influenza strains might vary in stability from mutations sufficiently to affect the contours of transmission as taken from Lowen. However, evolutionary argument supports virus stability in aerosol as strongly conserved, since in humans, viruses with lesser aerosol stability will not propagate as well as those with greater stability (unless aerosol stability is compensated for by some other propagation enhancement), and viruses with optimum stability will be selected for during host to host transmission[
30,
31]. Thus, literature results from human influenza virus strains would be expected to be from virus near the practical limit of aerosol stability. Further, osmotic pressure generates tensile force on the envelope, which will exhibit resistance to osmotic pressure not exceeding the weakest envelope bilayer hydrogen bonds.
Based on the considerations above, contours were generated based on linear interpolation of Lowen et al.[
16,
17] cross-validated with others[
5,
25,
27,
32]. These contours apply to RH conditions from 20% to 80%, although it is likely that contours above 80% RH have lower transmission risk than at 80%. Both the region from 0% to 20% RH and that above 80% RH are less clear and need investigation. The justification for using these risk contours in larger scale environments is based on data from studies that show long term persistence (hours) of viable aerosol virus[
25,
27].
Statistical validity of the contour graph
As presented by Lowen et al.[
16,
17] in studies of aerosol transmission of influenza over 7 days, there are three temperature groups, 5°C, 20°C and 30°C at varying RH. For the 5°C temperature there are four RH categories, 35%, 50%, 65% and 80%. At 20°C and 30°C there is an additional fifth at 20% RH. At 30°C there is no transmission. At 5°C transmission varies from 100% to 50% and at 20°C from 100% to 0%. Thus, where statistical power is in question is between 5°C and 20°C. As discussed[
17], the difference in transmissibility between 5°C and 20°C at 50% and 80% humidity is significant (
p < 0.05). This leaves the 65% relative humidity results at 20°C to be examined.
To further evaluate the Lowen data, we considered it in the context of Harper[
25] and Schaffer[
27] data on time course viability of influenza virions at differing temperature and humidity, because it is axiomatic that the longer virions can remain viable in aerosol, the more likely they are to cause infection by this route. Harper shows support for the transmission decline of Lowen, as viability declines when RH increases toward 50%. Schaffer data for one hour survival at 21°C (see figure two of Schaffer et al.) also shows a viability trough at 50% RH rising at humidity above 50% followed by a decline[
27]. These features of Harper and Schaffer further support the Lowen 20°C data for 50% RH, which was already of sufficient statistical significance. Additionally, Schaffer supports the 65% RH increase in transmission called out as statistically of insufficient power by Lowen et al. A further argument in favor of the 65% RH increase in transmission is care to present conservative contagion contours where there is a question; thus we retained the feature showing a rise in contagion at 65% RH.
Consequently, although p values for Lowen et al. alone are insufficient for acceptance of the 65% RH rise in contagion, taking alternative data sources and conservatism into account, we retained the 65% RH feature. We understand that the details of the type of contour map we present may change with larger datasets between 5°C and 30°C and we strongly encourage performance of larger experiments with multiple strains of influenza and other respiratory viruses. It would be highly desirable to have a larger dataset on the order of 30 animals or more at each temperature and RH setting and more temperature and RH values.
25%G7 transmission risk contour selection
For visual inspection purposes the 25%G7 transmission estimate contour is emphasized and became the reference using the following rationale.
Since Lloyd-Smith et al. reported the SARS epidemic was primarily propagated by superspreaders infecting 4 or more people[
33], we chose conditions that should limit spreading to infect 1 or 2 on average.
The guinea pig experiments of Lowen were performed for 7 days. In most public places such as banks and hotel lobbies with good conditions for transmission of influenza, the time people spend is on the order of 10 minutes. This corresponds by integration of equation
2 to a crude risk of 1/1959 for any one entry and exit at the 25%
G7 contour. Thus, assuming 300 patrons per day yields approximately 1 case every 6 days for a usual branch, assuming an infected individual is shedding virus continuously. Risk on a bus ride of 8 hours at the 25%
G7 contour yields a crude risk of 1/41, which roughly corresponds to 1 new infection per 8 hour bus ride assuming continuous virus shedding. Assuming an influenza case of 7 days virus shedding duration, we thought it improbable most locals would take more than two 8 hour luxury bus rides with 50 passengers per bus in that time span (vendors excluded) for a total of 2 new infections. (Table
1)
These crude risks represent the rationale of our risk cutoff in enclosed spaces. However, we do not think one contour cutoff is always appropriate.
Aircraft data interpretation
A considerable amount of data was collected for aircraft, however, transmission risk on aircraft is complex. First, the influenza contagion space relative to temperature and RH on aircraft is mostly unknown since studies have not been done below 20% RH, and large portions of flights can occur with RH in the 3% to 15% range (Figure
10). How such extremely low RH affects transmission is unknown. Second, although influenza was communicated well to aircraft passengers circa 1979 during a ground delay (38 of 54 passengers in 4.5 hours, 1 index case) given lack of air circulation[
34], HEPA filtration of recirculated cabin air on most aircraft today mitigates this hazard, together with outside air exchange in flight. Literature raises questions about efficacy of HEPA filters on aircraft[
35]; however, the careful epidemiology of SARS on an aircraft[
24] suggests HEPA filters and air exchange were fairly effective on that aircraft because of the apparent wake pattern of infection. That correlates with modeling of wake particles carried behind persons moving along the aisle[
36]. SARS, like influenza, is an enveloped RNA virus of the same size, which likely has similar filtration characteristics. Third, on some aircraft, ozone is negligible due to catalytic units[
37]. Ozone would be expected to deactivate virions significantly[
38], but the extent this occurs at ozone levels of aircraft lacking catalytic units is unknown. One must also weigh ozone causing a possible increase in host susceptibility and worse course of disease[
39], another unknown. Consequently, we believe risk, per our study criteria, to be low on aircraft outside deplaning, but worth continued attention.