Respiratory Virus Pattern Of Diffusion : Size Influence Luisetto m, Almukthar N, Tarro G. et al
1. J Huma Soci Scie, 2021
Respiratory Virus Pattern Of Diffusion : Size Influence
Short Comunication
1
Luisetto m IMA ACADEMY Marijnskaja NATURAL SCIENCE
BRANCH itlay 29121
2
Naseer Almukthar, Professor, Department of Physiology /College
of Medicine, University of Babylon, Iraq
3
Prof. Giulio Tarro Primario emerito dell’ Azienda Ospedaliera “D.
Cotugno”,Napoli Chairman della Commissione sulle Biotecnologie
della Virosfera, WABT
3
UNESCO, Parigi, Rector of the University Thomas More U.P.T.M.,
Rome Presidente della Fondazione de Beaumont Bonelli per le
ricerche sul cancro -ONLUS, Napoli
4
Behzad Nili Ahmadabadi, Innovative Pharmaceutical product
development specialist, USA
5
Ahmed Yesvi Rafa , Founder and President, Yugen Research
Organization; Undergraduate Student, Western Michigan
University, MI, USA 49008
6
Ghulam Rasool Mashori Professor and head dep. Pharmacology
,Medical & Health Sciences for Woman, Peoples University of
Medical and Health Sciences for Women,Pakistan
7
Tuweh Prince GADAMA the great, Professor, Cypress University
Malawi
8
Oleg Yurievich Latyshev IMA academy president
*
Corresponding author
Mauro Luisetto, Ima Academy Marijnskaja Natural Science Branch Itlay
29121.
Submitted:15Oct2020;Accepted:05Nov 2020;Published:07Apr 2021
Luisetto M1*
, Naseer Almukthar2
, Tarro G3
, Behzad Nili Ahmadabadi4
, Ahmed Yesvi Rafa5
, Ghulam Rasool
Mashori6
, Tuweh Prince Gadama7
, Oleg Yurievich Latyshev8
Journal of Humanities and Social Sciences
www.opastonline.com
Abstract
Aim of this work is to verify difference in spread attitudes of covid-19 and other coronavirus versus Smalpox and try to seek
rational explain of the specific pattern of diffusion.
The rapid increase of covid- 19 cases in FRANCE in second wave in fisrt day of october 2020 seem to follow not only a diffusion
related direct contact and by droplet but also by airborne trasmission.
A real fact is the diffenece in size of virus smalpox vs coronaviruses.
Virus size is an relevant factor involved in kind of spread.
ISSN: 2690 - 0688
Volume 4 | Issue 1 | 163
Keywords: Covid-19 , Coronavirus , Smalpox , Respiratory Virus, Spread, Diffusion , Airborne Wind Effetc, time of Spread
Introduction
Related covid-19 pandemia it is interesticg to notice that many
document related past SPANISH FLU was extremely similar to
nawadays allert produced by public intrnational health organiza-
tion to prevent spread of this dangerosu disease ( see fig. 1)
Citation: Luisetto M, Naseer Almukthar, Behzad Nili Ahmadabadi, Ahmed Yesvi Rafa, Ghulam Rasool Mashori, Tuweh Prince Gada-
ma, Oleg Yurievich Latyshev (2021) Respiratory Virus Pattern Of Diffusion : Size Influence. J Huma Soci Scie, 4(1): 163-171
2. J Huma Soci Scie, 2021 www.opastonline.com Volume 4 | Issue 1 | 164
Figure 1: Chicago Theaters Displayed Posters Like This one to
Slow the Spread of the Spanish Flu During The 1918 pandemic.
At the same time, it is interesting to observe the difference in size
of some respiratory virus: from the greater size of smallpox to the
small SARS virus.
This variability in size can be responsible of the different kind of
diffusion of this virus?
Smallpox more diffused by direct contact and by droplets then
other coronavirus and this instead seem involved also in airborne
transmission.
The kinetics of the diffusion of this virus seem to tell us that in the
cases of covid.19 second wave in France where numerous cases
increased but in very rapid ay (weeks) in October 2020 is a patter
different to the spread of smallpox diffusion in north America in
1781 in HUSTON BAY.
Figure 2: Virus Size and Dimension ( Variola – Smallpox)
Material and methods
Whit an observational methods some relavant maps and images
related some respiratory virus diffusion in the world are analysed.
Also some literature involved and useful to this topic is presented
in order to produce a global conclusion Fact-related.
All literature comes from Pub med or other open science journal .
It is used in this work a VISUal method to find the final conclusion.
Results
Figure 3:
Figure 4: 10 march 2020 The Locations of People Who Have Test-
ed Positive Covid-19 in the U.S.
Source The New York times
Figure 5: Covid Cases September 2020 from Jama Network
3. J Huma Soci Scie, 2021 www.opastonline.com Volume 4 | Issue 1 | 165
Figure 6: form Business Insider
Figure 7: H1N1 Swine Flu Spread June 2014 form Rachael
Rettner, LiveScience
Figure 8:
Amos Ssematimba et al:
“We calculate the distance-dependent probability of infection for
farms downwind of an infected farm by combining our model
predictions of the hourly depositions with the virus amount and
infection probability models, the inhalation model and the with-
in-flock epidemic model as described in the Materials and Meth-
ods section. We use the Dutch 2003 epidemic data to test whether
wind-borne HPAI spread was possible and if so, determine its pos-
sible contribution during the epidemic by comparing our model
predictions with the observed pattern in the epidemic. As can be
seen from equations reported, for small infection probability per
inhalation the model-predicted probabilities are to a very good ap-
proximation proportional to the deposition pattern. As a result, in
the parameter range of interest here, the distance-dependence of
the model-predicted probabilities is practically indistinguishable
from that of the deposition pattern.
The comparison in figure reported more importantly shows a qual-
itative difference in the tail. Compared to the observed pattern,
there is a faster drop in the predicted infection probability beyond
0.45 km. At all distances from the source, the predicted probabil-
ities are smaller than the observed risk. Also, beyond 1 km dis-
tance the predicted risk of solo wind-borne infection is decaying
significantly faster with distance than the observed risk. The ob-
served rapid decrease of the predicted risk with distance is only
very weakly sensitive to the precise value of pathogen decay rate,
settling velocity and the within-flock basic reproduction ratio as
shown in figure reported. Based on these results, we conclude that
the wind-borne route alone could not explain the pattern of the
2003 epidemic.”
Figure 9: Spanish flu 1918 Spread and Death
Figure 10: Spanish Flu 1918 Spread
Figure 11: HONG KONG flu 1968 Diffusion
4. J Huma Soci Scie, 2021 www.opastonline.com Volume 4 | Issue 1 | 166
Figure 12: Smalpox Spread USA Case of Smallpox During The
1775-82 Epidemic.
The strange truth about smallpox and Native Americans
Posted on June 15, 2019 Memories of the people
“Did Europeans deliberately give smallpox-infected blankets
to Native Americans? Absolutely. There is one proven case and
many other suspicious ones. But the largest smallpox outbreak, the
one that killed possibly hundreds of thousands of Natives, start-
ed during the Revolutionary War. While the war naturally brought
people – and the virus – together and then re-distributed them, the
virus was also spread when the British army, most of whom had
already been exposed to the disease, deliberately tried to infect
American colonists with smallpox.”
Figure 13: Small pox1837
https://alchetron.com/1837-Great-Plains-Smallpox-Epidemic:
“The 1837 Great Plains smallpox epidemic spanned 1836 through
1840, but reached its height after the spring of 1837 when anAmer-
ican Fur Company steamboat, the S.S. St. Peter, carried infected
people and supplies into the Missouri Valley. More than 15,000
Native Americans died along the Missouri River alone, with some
tribes becoming nearly extinct. Having witnessed the effects of the
epidemic on the Mandan tribe, fur trader Francis Chardon wrote,
"the small-pox had never been known in the civilized world, as it
had been among the poor Mandans and other Indians. Only twen-
ty-seven Mandans were left to tell the tale.
Smallpox has afflicted Native Americans since it was carried to
the western hemisphere by the Spanish conquerors, with credible
accounts of epidemics dating back to at least 1515. The Mandan
tribe, also called the People of the Pheasants, had previously ex-
perienced a major smallpox epidemic in 1780-81 which severely
reduced their numbers down to less than a few thousand. Many
other tribes along the Missouri river suffered smallpox epidemics
during 1801-02 and 1831”
From CDC
Origin of Smallpox
“The origin of smallpox is unknown. Smallpox is thought to date
back to the Egyptian Empire around the 3rd century BCE (Be-
fore Common Era), based on a smallpox-like rash found on three
mummies. The earliest written description of a disease that clear-
ly resembles smallpox appeared in China in the 4th century CE
(Common Era). Early written descriptions also appeared in India
in the 7th
century and in Asia Minor in the 10th century
• 17th
Century – European colonization imports smallpox into
North America.
Old World, the most common form of smallpox killed perhaps 30
percent of its victims while blinding and disfiguring many others.
But the effects were even worse in the Americas, which had no
exposure to the virus prior to the arrival of Spanish and Portuguese
conquistadors. Tearing through the Incas before Francisco Pizarro
even got there, it made the empire unstable and ripe for conquest.
It also devastated the Aztecs, killing, among others, the second-to-
last of their rulers. In fact, historians believe that smallpox and oth-
er European diseases reduced the indigenous population of North
and South America by up to 90 percent, a blow far greater than any
defeat in battle. “
• “Smallpox patients became contagious once the first sores
appeared in their mouth and throat (early rash stage). They
spread the virus when they coughed or sneezed and droplets
from their nose or mouth spread to other people. They re-
mained contagious until their last smallpox scab fell off.
• These scabs and the fluid found in the patient’s sores also con-
tained the variola virus. The virus can spread through these
materials or through the objects contaminated by them, such
as bedding or clothing. People who cared for smallpox pa-
tients and washed their bedding or clothing had to wear gloves
and take care to not get infected.
• Rarely, smallpox has spread through the air in enclosed set-
tings, such as a building (airborne route).
• Smallpox can be spread by humans only. Scientists have no
evidence that smallpox can be spread by insects or animals.”
• Smallpox: Emergence, Global Spread, and Eradication Frank
Fenner 1993
5. J Huma Soci Scie, 2021 www.opastonline.com Volume 4 | Issue 1 | 167
Ann M.Carlos et al :
“The route of infection is the respiratory tract
This requires direct contact with an infected person, and trans-
mission, with rare exceptions, through inhaled liquid droplets.
Unlike measles, patients with smallpox do not generally have re-
spiratory symptoms such as coughing or sneezing which generate
large clouds of infection in the air. As a result, “direct and fairly
prolonged face-to-face contact is required to spread the disease
from one person to another,” usually contact within about six to
seven feet for a period of a few hours (CDC, 2010, “Smallpox Dis-
ease Overview”). Although droplets or scabs that fall on bedding
or clothing remain infectious in principle, laboratory tests using
vaccinia virus indicate that infection is unlikely because of how
the material is handled by the respiratory tract. Also, in experi-
ments on the persistence of infectivity, it has been found that the
virus is rapidly inactivated, even on heavily contaminated objects.
There are instances of laundry workers contracting smallpox, but
the documented cases of smallpox transmission via fomites are
very rare.”
Figure 14:
Figure 15: Dengue Pattern of Spread form The New York times
June 2019
Figure 16: from AWEA
6. J Huma Soci Scie, 2021 www.opastonline.com Volume 4 | Issue 1 | 168
In this figure it is interesting to observe the distribution of wind
manufacturing facilities in USA
(an indirect indicator of wind status)
Zhili Zuo et al :
“Normalized infectious virus size distribution, total virus size dis-
tribution, SMPS particle number distribution, and SMPS particle
volume distribution for airborne MS2. Values are means ± one
standard n = 3). Similar plots for TGEV, SIV, and AIV are avail-
able online. To better understand virus transmission by aerosols, it
is important to determine the relationship between airborne virus
infectivity/survivability and particle size. Only a few studies are
available on this issue in the scientific literature. To determine the
distribution of infectious virus among polydisperse particles, an
Andersen cascade impactor was used to sample aerosols of cox-
sackie virusA-21 and simian rotavirus. The concentration of infec-
tious virus appeared to be related to particle volume distribution
for particle size >0.5 μm. Using the same instrument, Appert et
al. (2012) confirmed the above findings for MS-2 bacteriophage,
but not for adenovirus. Tyrrell (1967) found that rhinovirus sur-
vived better in coarse particles (>4 μm) than in smaller particles
(0–4 μm), while adenovirus infectivity was best preserved in the
size range of 0.56–1.9 μm compared with 1.9–10 μm indicating
that particle size may also affect virus survivability. Although the
use of size-segregated samplers, such as impactors, provides size
fractionation for virus infectivity, not much is known about virus
aerosol particles off human and animal viruses remains an issue.
The objective of this study was to examine infectivity and sur-
vivability of three airborne animal viruses as a function of their
carrier particle size in the submicron size range using a newly de-
veloped sampling method. In addition, the behavior of widely used
MS2 bacteriophage was studied for comparative purposes MATE-
RIALS AND METHODS 2.1. Propagation and Titration of MS2
Bacteriophage MS2 bacteriophage (ATCC 15597-B1) is a small
(27–34 nm), icosahedral, non-enveloped, single stranded, positive
sense RNA virus, infecting only the male Escherichia coli (those
bearing an F pilus). For the purposes of this study, we considered
MS2 as a model virus because it has been widely used in many
virus aerosol studies. The virus was propagated in E. coli famp
(ATCC 700891), as described elsewhere. Briefly, 0.1 mL of MS2
and 1 mL of a log phase culture of E. coli were added to top agar
tubes held at 48◦C. After mixing, the contents of the tubes were
poured on trypticase soy agar (TSA) plates. The top agar was al-
lowed to solidify followed by inversion and incubation of plates at
37◦C for 24 h. After plaques were confluent (within 24 h of incu-
bation), 5 mL of tryptic soy broth (TSB) was added to each plate.
After 2 h at room temperature, the solution was aspirated, centri-
fuged at 2500 × g for 15 min, and sterile-filtered. The resulting
bacteriophage stock was aliquoted into 50 mL tubes, followed by
storage at −80◦C until use. The amount of MS2 bacteriophage in
virus stock and various other samples was determined by using a
double agar layer procedure as described elsewhere. The amount
of virus was expressed as plaque forming units per unit volume of
the sample (PFU/mL)”.
Figure 17: Schematic Diagram of the Experimental Setup for the
Characterization of Virus Aerosols.
Figure 18 :
“Four viruses (MS2 bacteriophage, transmissible gastroenteritis
virus, swine influenza virus, and avian influenza virus) were aero-
solized, size classified (100–450 nm) using a differential mobility
analyzer (DMA), and collected onto gelatin filters. Uranine dye
was also nebulized with the virus, serving as a particle tracer. Virus
infectivity assay and quantitative reverse transcription-polymerase
chain reaction were then used to quantify the amount of infectious
virus and total virus present in the samples, respectively. The virus
distribution was found to be better represented by the particle vol-
ume distribution rather than the particle number distribution. The
capacity for a particle to carry virus increased with the particle
size and the relationship could be described by a power law. Virus
survivability was dependent on virus type and particle size”
Nanomedicine Volume I: Basic Capabilities Robert A. Freitas Jr
“Large Molecule Binding, Sorting and Transport Is there any size
limit for target molecules to be transported?
Natural receptors have already been found for large molecules in-
cluding low-density lipoproteins (LDLs) > 1,000,000 daltons426
7. J Huma Soci Scie, 2021 www.opastonline.com Volume 4 | Issue 1 | 169
and high-density lipoproteins (HDLs).103The methods described
in earlier Sections can be adapted for binding large molecules
(>1000 atoms; Fig. 3.15), including molecules far wider than
the binding device itself (e.g., ~200-nm diameter virus particles
and larger). Making a binding site for a large molecule should be
physically easier (albeit computationally more challenging) than
making a binding site for a small molecule because of the greatly
increased area of interaction.
For example, a binding energy of 400 zJ may be realized by cre-
ating a dispersion-force binding area covering only ~25% of the
surface of a 10,000-atom target molecule (Table 3.6) or a mere
~0.02% of a 200-nm virus particle.
Assuming a roughly spherical large molecule and laminar fluid
flow at 1 atm forcing pressure (Section 9.2.7), a 10-nm diameter
molecule moves through a 20-nm long pump (~10-20 kg, ~106
atoms) in ~10(-6) sec at ~0.02 m/sec, consuming ~0.02 pW during
transfer.
A 200-nm virus-size target molecule moves through a 400-nm
long pump (~10-17 kg, ~109 atoms) in ~10 (-2) sec at ~60 mi-
crons/sec, consuming ~10-16 watts during transfer; at ~0.0002
atm, release time is diffusion limited.
The transfer force exerted on a 10-nm molecule is ~1 pN, ~600 pN
on a 200-nm virion; a binding energy of 400 zJ at a 0.2-nm contact
distance gives a binding force of ~2300 pN, sufficient to hold a
particle of either size firmly during transport and release” (4)
“As demonstrated previously, particle size can significantly affect
survival of airborne viruses “(3)
Zhili Zuo et al :
“Although laboratory generated virus aerosols have been wide-
ly studied in terms of infectivity and survivability, how they are
related to particle size, especially in the submicron size range, is
little understood. Four viruses (MS2 bacteriophage, transmissible
gastroenteritis virus, swine influenza virus, and avian influen-
za virus) were aerosolized, size classified (100–450 nm) using a
differential mobility analyzer (DMA), and collected onto gelatin
filters. Uranine dye was also nebulized with the virus, serving as
a particle tracer. Virus infectivity assay and quantitative reverse
transcription-polymerase chain reaction were then used to quan-
tify the amount of infectious virus and total virus present in the
samples, respectively. The virus distribution was found to be bet-
ter represented by the particle volume distribution rather than the
particle number distribution. The capacity for a particle to carry
virus increased with the particle size and the relationship could be
described by a power law. Virus survivability was dependent on vi-
rus type and particle size. Survivability of the three animal viruses
at large particle size (300–450 nm) was significantly higher than
at particle size close to the size of the virion (100–200 nm), which
could be due to the shielding effect. The data suggest that particle
size plays an important role in infectivity and survivability of air-
borne viruses and may, therefore, have an impact on the airborne
transmission of viral illness and disease. The data in this study do
not support the use of MS2 bacteriophage as a general surrogate
for animal and human viruses.
Infectious/Total Virus Size Distribution
Figure reported represent the infectious virus and total virus size
distribution from 100 nm to 450 nm normalized by the maximum
values. In general, both the infectious and total virus concentrations
increased with particle size and the maximum values at 400–450
nm were around 5000 PFU/cm3, 35 TCID50/cm3, 180 TCID50/
cm3, and 60 TCID50/ cm3 for MS2, TGEV, SIV, and AIV, re-
spectively, which were several orders of magnitude lower than the
particle number concentration at the same particle size. The virus
size distributions were normalized to compare them more easily
with particle size distributions. As seen in Figures reported , the
infectious and total virus distributions had a similar trend, both
appearing to follow particle volume distribution rather than parti-
cle number distribution. Infectious and total virus concentrations
collected by the gelatin filters are available online.
Survivability of Airborne Virus
Similar to RRIV, survivability of TGEV and AIV was much lower
at 200 nm than at larger size. One could argue that the discretiza-
tion phenomenon is responsible for this finding, i.e., as the carrier
particle size gets smaller and approaches the size of virion, it be-
comes more difficult for the particle to carry virus. However, the
particle size-independent RRTV shown in figure reported sug-
gests the presence of virus in particles even at 100 nm. Therefore,
the discretization phenomenon was probably not the reason. The
main reason for the particle size associated survivability could be
the shielding effect. More specifically, compared with virus exist-
ing as a singlet or in association with fewer organics (e.g., solutes
in the nebulizer suspension), the virus at larger particles may be
surrounded by more organic material, which may form a shield.
Shielding effect has been demonstrated to better protect virus
from environmental stress such as ultraviolet irradiation. It may
also reduce sampling stress such as desiccation and sampler de-
pendent-mechanical forces, thus better maintaining the infectivity
of airborne virus. However, as particle size increased to 300 nm
and above, virus survivability seemed to reach a plateau, suggest-
ing the shielding effect was maintained once a specific particle
size was reached. The same explanation applies to MS2. Because
all collected particle sizes were more than four times the virion
size (27–34 nm), the survivability reached the plateau regime and
therefore was no longer depended on particle size. This is sup-
ported by Lee (2009), who showed that survivability of MS2 at
120–200 nm was higher than at 30 nm, despite the large experi-
mental variation.” (3)
8. J Huma Soci Scie, 2021 www.opastonline.com Volume 4 | Issue 1 | 170
Figure 19: Schematic Representation of the Shielding Effect of
the Hydration Layer Due to the Presence of Zwitterionic Moieties.
(from References)
Environ Res. 2020 Sep; 188: 109819.
Published online 2020 Jun 13. doi: 10.1016/j.envres.2020.109819
PMCID: PMC7293495
PMID: 32569870
Transmission of COVID-19 virus by droplets and aerosols: A crit-
ical review on the unresolved dichotomy
Mahesh Jayaweera,a,
* Hasini Perera,b
Buddhika Gunawardana,a
and Jagath Manatungea
Author information Article notes Copyright and License informa-
tion Disclaimer
4. Behavior of droplets and aerosols against environmental fac-
tors
“The most important environmental factors that could impact
on the viability of airborne microorganisms are temperature, hu-
midity, radiation (sunlight), and open-air (ventilation) (Marthi, 1994
).
Most viruses, including SARS-CoV-2, are less than 100 nm in size
(Kumar and Morawska, 2019
). Viruses in aerosols loss or gain the viability
and infectivity because of environmental stresses caused by tem-
perature, relative humidity, and sunlight before they reach a sus-
ceptible host. Environmental tolerance of the virus-laden aerosols
depends on the specific phenotype available, the composition of
the bioaerosols containing virus and their payload, and physical
characteristics in the surrounding environment (Schuit et al., 2020
). As the
environmental factors play a major role in transmitting payloads of
SARS-CoV-2 virus in different geographical locations of outdoor
and indoor environments, it is worthy of exploring the effects of
environmental factors on the transmission of SARS-CoV-2 virus.
Furthermore, there have been associations between air pollution
represented by air pollutants such as PM2.5
, PM10
, NO2
, and O3
and
COVID-19 infection (Zhu et al., 2020
)” (6)
J R Soc Interface. 2011 Aug 7; 8(61): 1176–1184.
Published online 2011 Feb 7. doi: 10.1098/rsif.2010.0686
PMCID: PMC3119883
PMID: 21300628
Concentrations and size distributions of airborne influenza A vi-
ruses measured indoors at a health centre, a day-care centre and
on aeroplanes
Wan Yang,1
Subbiah Elankumaran,2
and Linsey C. Marr1,*
“The concentrations and size distributions of airborne influen-
za viruses were measured in a health centre, a day-care facility
and aeroplanes by qRT–PCR. During the 2009–2010 flu season,
50 per cent of the samples collected (8/16) contained IAVs with
concentrations ranging from 5800 to 37 000 genome copies m−3.
On average, 64 per cent of virus-laden particles were found to be
associated with particles smaller than 2.5 µm, which can remain
airborne for hours. Modelling of virus concentrations indoors sug-
gests a source strength of 1.6 ± 1.2 × 105
genome copies m3
h−1
and
a deposition flux onto surfaces of 13 ± 7 genome copies m−2
h−1
.
Doses of 30 ± 18, 236 ± 140 and 708 ± 419 TCID50
were estimated
for 1, 8 and 24 h exposures, respectively. As a whole, these results
provide quantitative support for the possibility of airborne trans-
mission of influenza “(7)
A physicist view of COVID-19 airborne infection through convec-
tive airflow in indoor spaces Luis A. Anchordoqui and Eugene M.
Chudnovsky Physics Department, Herbert H. Lehman College and
Graduate School, The City University of New York 250 Bedford
Park Boulevard West, Bronx, New York 10468-1589, USA(Dated:
March 2020)
“II. MODELING THE EFFECT OF CONVECTION CURRENTS
IN THE TRANSMISSION OF SARS-COV-2 In the presence of
air resistance, compact heavy objects fall to the ground quickly,
while light objects exhibit Brownian motion and follow the pattern
of turbulent convection of the air. For aerosol particles contain-
ing the virus, the boundary between these two behaviors depends
on the size of the particle. We begin with a simple question: how
long does a virus float in the air under the influence of gravity?
To answer this query, we model the virus as a sphere of radius r ~
90 nm and mass m ~ 2.5×10−19 kg [12], and we assume that this
spherical particle is suspended in a viscous fluid (the air) feeling
the Earth’s gravitational field. Herein, gravity tends to make the
particles settle, while diffusion and convection act to homogenize
them, driving them into regions of smaller concentration. On the
one hand, the convection mechanism provides particle macro-mix-
ing within the fluid through the tendency of hotter and consequent-
ly less dense material to rise, and colder, denser material to sink
under the influence of gravity. On the other hand, the diffusion
mechanism acts on the scale of an individual particle (micro-mix-
ing) slowly and randomly moving through the media. Under the
action of gravity, the virus acquires a downward terminal speed
that follows from Stokes law.
is the virus mobility in the fluid, and where η = 1.8 × 10−5 kg/
(ms) is the dynamic viscosity of air [13]? Substituting (2) into (1)
we find that the downward terminal speed of the virus in dry air
is indeed negligible, vdown ~ 8 × 10−8 m/s. It is therefore clear
that gravity plays no role in the motion of an isolated virus through
the air. Rather it follows a convection pattern in a manner simi-
lar to how smelly substances move through the air. The survival
probability of the virus in the dry air is then given by the likeli-
hood of survival outside its natural environment. The half-life of
SARS-CoV-2 in aerosols has been found to be about 1.1 hours
[5]. For large droplets whose diameters & 1000 µm, the effect of
air resistance is negligible and so the falling time can be directly
estimated using Newton’s equations for gravitational settling. For
smaller droplets whose diameters < 100 µm, the falling times must
instead be determined using the downward terminal speed given
