[Below is an
excerpt of the ProMED Post,
#4]
Published Date: 2013-05-27 04:56:45
A ProMED-mail post
http://www.promedmail.orgProMED-mail is a program of the
International Society for Infectious Diseases
In this update:
[1] Saudi Arabia: new fatality, Ministry of Public Health
[2] Saudi Arabia: new fatality, newswire
[3] Saudi Arabia: surveillance, Ministry of Public Health
[4] Transmissibility and cluster sizes
[4] Transmissibility and cluster sizes
Date: Sun 26 May 2013
From: David N Fisman <david.fisman@utoronto.ca> [edited]
I have watched the emergence of the MERS coronavirus with a concern
that is shared by many colleagues in the communicable disease control
world. However, given recent concerns expressed regarding the
communicability of this virus, I wished to share some thoughts on the
relationship between disease clusters, sustained chains of transmission,
and reproductive numbers of pathogens.
The basic reproductive
number (R0), the number of secondary cases of infection produced by a
primary case in a completely susceptible population, is an important
index of epidemic potential. When R0 is greater than 1 (even slightly)
self-sustaining exponential growth of case numbers becomes likely (that
is, an epidemic is expected to occur). However, it is often forgotten
that transmission can (and is expected to) occur when R0 less than 1,
with the result being (generally short) chains of transmission (observed
as disease clusters) rather than exponential increases in case numbers.
For R0 less than 1, expected cluster size (including the index case)
can be expressed as the sum of a geometric series such that:
N = 1/(1-R0)
For
instance, if R0 = 0.5, each primary case infects, on average, 0.5
secondary cases before recovering and an average cluster size would be
expected to be 2 cases (that is, one primary case, and on average, one
secondary case). If R0 is 0, the average cluster size is zero (the index
case only, with no onward transmission) and if R0 is 1, the expected
cluster size is infinite as the disease is endemic (each infectious case
"replaces itself" before recovering). I present these relationships
graphically in MERS figures 1A and 1B (available at
http://davidfisman.tumblr.com/)
We can manipulate the expression above in order to estimate R0 based on average cluster size using the relation:
R0 = -[(1/N) - 1]
Thus
we can empirically estimate the current R0 for MERS-CoV based on
average cluster sizes, as presented in the table below. These have been
largely derived from the European Centres for Disease Control Rapid Risk
Assessment on MERS-CoV (1), with the addition of 3 additional
hospital-associated cases to the large Saudi cluster as of [21 May 2013]
(2), and the addition of a 3-person cluster recently identified in
Tunisia described on ProMED on [20 May 2013 (3). Note that I assume that
5 cases in Riyadh, Saudi Arabia are un-clustered, based on the
information available to me. Furthermore, although only 2 confirmed
cases have been identified retrospectively from Jordan, these cases were
part of an 11-person cluster of respiratory illness in a hospital in
that country and I have assumed that the total cluster size was thus 11.
Cluster size / Linked countries / Notes
11 / Jordan / only 2 confirmed retrospectively
22 / Saudi Arabia / true cluster size only 20 (2 unlinked cases?)
3 / Saudi Arabia, Tunisia ex Qatar / -
1 / Germany ex UAE / -
2 / France ex UAE / secondary transmission in French hospital
3 / Pakistan, UK ex Saudi Arabia / two 2ndary transmissions in the UK
1 / UK ex Qatar / -
3 / Saudi Arabia / family cluster
1 / Saudi Arabia / isolated case in Jeddah
1 / Saudi Arabia / Riyadh
1 / Saudi Arabia / Riyadh
1 / Saudi Arabia / Riyadh
1 / Saudi Arabia / Riyadh
1 / Saudi Arabia / Riyadh
1 / Germany ex Qatar / -
The
average cluster size under these assumptions is 4.17 cases; if we make
more conservative assumptions (such as only count 2 confirmed cases from
Jordan, exclude 2 cases from the large Saudi cluster with no clear
epidemiological linkage), cluster size may be as low as 2.59;
conversely, if we assume that the 5 cases from Riyadh represent a
cluster, mean cluster size may be as high as 4.81 cases. Using the
formula above, this would give us an estimated R0 of around 0.76 (range
0.61 to 0.79).
It is possible to model an average chain of
transmission as a "Markov process", with sequential individuals classed
as "transmitters" (who create an additional case with probability equal
to R0) or "non-transmitters" who result in termination of the chain of
transmission (MERS figure 2, available at
http://davidfisman.tumblr.com/).
The probability of non-transmission for a given case is (1-R0). If we
run such a model the average cumulative cluster size is identical to
that calculated using the geometric series approach. What is perhaps
more interesting is to run this model as a 1st-order Monte Carlo
simulation, where at each generation transmission may occur (with
probability = R0) or not (with probability 1-R0). The resulting model
outputs can be interpreted as the probability of seeing clusters of a
given size, for a given R0. What we see is that, for a disease
transmission process with an R0 of 0.76, the occurrence of chains of
transmission resulting in 22 cases is incredibly unlikely (approximately
0.08 per cent) (MERS figure 3, available at
http://davidfisman.tumblr.com/).
Indeed, as far as I am aware, no cluster of 5 cases has been observed,
but we would expect to have seen approximately 140 such clusters before
seeing a single cluster of 22 cases. If the Jordan cluster was indeed 11
cases in size, we would have expected to have seen 20 such clusters
before seeing a single 22 case cluster (MERS figure 4, available at
http://davidfisman.tumblr.com/).
While
it is possible that a 22 case cluster could occur by chance
(parenthetically, somewhere between the probability of getting 10 and 11
heads in a row when tossing a fair coin), the low likelihood of such an
event (and indeed of the 11 case cluster) with a disease with R0 of
0.76 leads me to suggest that the ability of this pathogen to cause
large clusters or sustained chains of transmission in the context of the
Eastern Saudi healthcare outbreak is quite different from that seen
elsewhere, and especially outside the healthcare environment. I can
think of 3 possible mechanisms for this difference:
1. The pathogen has mutated and is now more transmissible (I know of no evidence to suggest that this is the case).
2.
The healthcare environment provides a rich environment for recognized
transmission of this pathogen, due to the frequency of contacts and
vulnerability of individuals to the development of symptomatic
recognized infection.
3. As with SARS, there may have been point
source exposures of large numbers of individuals, which resulted acutely
in infection of a large cluster of individuals with subsequent decay in
the risk of infection of secondary cases (as R0 less than 1). With
SARS, such events were certainly seen in Toronto (in the context of
emergency endotracheal intubation of an individual with SARS and
respiratory failure, with infection of 11 secondary cases, 6 of whom
were present at the emergency procedure (4)), and in Hong Kong (such as
in the Amoy Gardens episode (5)).
My suspicion (as an interested
observer without directly involvement in this situation) is that Saudi
colleagues are dealing with some combination of no 2 and no 3. Why is
this important? First, notwithstanding alarm related to person to person
transmission of this apparently highly virulent pathogen, it can be
noted that:
1. Person-to-person transmission may occur with R0
less than 1, and indeed clusters are expected. This does not imply that
epidemic transmission (that is, self-sustaining, exponentially
increasing case counts) will occur, as such chains, while concerning
(and potentially fairly large with R0 greater than 0.75), are expected
to be self-limited.
2. The processes observed in the current
Saudi healthcare outbreak (and one presumes, in the context of the
retrospectively identified Jordanian healthcare cluster) are
epidemiologically distinct, with respect to communicability, from
transmission processes occurring outside the healthcare environment.
Indeed, there may be a distinct "within-healthcare R0" for this pathogen
that is close to 1, or even exceeds 1.
a) This may have been the
case with SARS: here in Toronto, we did see spill-over cases in the
community, but these did not result in community-based outbreaks of
SARS. The occurrence of community cases did, however, result in a WHO
travel advisory (6), which caused substantial economic losses to the
city. I would suggest that the relevant health authorities recognize the
distinct epidemiology of disease transmission inside and outside
healthcare, and exercise caution prior to the issuance of any travel
advisories, which can cause tremendous economic damage to communities.
b)
If indeed MERS-CoV echo those of SARS-CoV, it is important to recognize
that a syndromic approach to excellent infection control, not targeted
at those with suspected MERS-CoV, but applied to all individuals with
as-yet-undiagnosed febrile respiratory illness, is likely to be
effective at preventing transmission of this pathogen in the healthcare
environment.
References
----------
1. European Centre for
Disease Prevention and Control. Rapid risk assessment: Severe
respiratory disease associated with Middle East respiratory syndrome
coronavirus (MERS-CoV). 17 May 2013. Available at
http://www.ecdc.europa.eu/en/publications/Publications/Forms/ECDC_DispForm.aspx?ID=1121. Last accessed 25 May 2013.
2.
ProMED-mail. MERS-CoV - Eastern Mediterranean (06): Saudi Arabia, new
fatality, meeting; archive no 20130521.1726656. 21 May 2013. Available
at
http://www.promedmail.org/direct.php?id=20130521.1726656. Last accessed 25 May 2013.
3.
ProMED-mail. MERS-CoV - Eastern Mediterranean (05): Tunisia ex Saudi
Arabia/Qatar, fatal, RFI. archive no 20130520.1725864. 20 May 2013.
Available at
http://www.promedmail.org/direct.php?id=20130520.1725864. Last accessed 20 May 2013.
4.
US Centers for Disease Control and Prevention. Cluster of severe acute
respiratory syndrome cases among protected health-care workers --
Toronto, Canada, April 2003. MMWR Morb Mortal Wkly Rep 2003; 52(19):
433-6. Available at
http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5219a1.htm.
5.
McKinney KR, Gong YY, Lewis TG. Environmental transmission of SARS at
Amoy Gardens. J Environ Health 2006; 68(9): 26-30; quiz 51-2. Available
at
http://www.thefreelibrary.com/Environmental+transmission+of+SARS+at+Amoy+Gardens.-a0145934763.
6.
Rodier GR. Why was Toronto included in the World Health Organization's
SARS-related travel advisory? CMAJ. 2003; 168(11): 1434-5. Available at
http://www.cmaj.ca/content/168/11/1434.full.pdf+html.
--
David N Fisman, MD MPH FRCPC
Associate Professor of Epidemiology, Medicine, and Health Policy
Dalla Lana School of Public Health and Institute of Health Policy, Management and Evaluation
University of Toronto
Canada
<david.fisman@utoronto.ca>
[ProMED-mail
would like to thank Dr Fisman for sharing his analyses with the
ProMED-mail readership. This moderator is in agreement with Dr Fisman's
conclusion of the need to implement strict infection control procedures
when confronted with severe acute respiratory infections (SARI) that are
as yet undiagnosed, in order to prevent potential additional
transmission of respiratory agents in the healthcare setting (see
moderator comment in ProMED-mail MERS-CoV - Eastern Mediterranean (09):
Saudi Arabia, WHO, Jordan 20130523.1733317). - Mod.MPP]
http://www.promedmail.org/
News Editor