The Chain Reaction of Covid-19

Abstract

Covid-19 establishes a chain reaction that leads to explosive increases in the viral load. Asymptomatic carriers are systematically underestimated. They establish a chain reaction where they infect others, others re-infect them, they re-infect others and so on. The sequence of infection and re-infection leads to an explosion of the aggregate viral load observed in closed spaces like hospitals and apartments. The viral loads of each exposure may be small but in the aggregate the viral load is not. The key to prevent the chain reaction is rapid testing and better ventilation like open windows. Rapid testing can prevent the chain reaction that leads to explosion of the viral load.

Full text

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The Chain Reaction of Covid-19
Kim R. Sawyer*
April 12 2020
__________________________________________________________________________________
Covid-19 is more than a virus. Covid-19 establishes a chain reaction that leads to explosive
increases in the viral load. It has changed how we live. Let us consider some of the issues.
Chain Reaction of the Asymptomatic
Covid-19 is anomalous. The secret to Covid-19 is that it hides better than other viruses.
1
A high proportion of the infected show no symptoms. The virus depends on them.
The asymptomatic are driving the virus. They establish a chain reaction where they infect
others, others re-infect them, they re-infect others again and so on. The sequence of infection
and re-infection leads to an explosion of the aggregate viral load observed in closed spaces
like hospitals. When the aggregate viral load becomes extreme, severe infections result.
The explosion occurs because the virus spreads easily not just through coughing and sneezing
but through breathing and conversation.
“According to the US Centers for Disease Control and Prevention, the virus spreads from
person to person when people are within about 6 feet of each other "through respiratory
droplets produced when an infected person coughs or sneezes …but if you're outside, the
breeze will likely disperse it.”
2
The chain reaction of infection and re-infection is not observed until severe outcomes of
infection are observed when the viral load is as much as sixty times that of mild cases.
3
While each transmission of the infection may involve only a small amount of viral load, the
aggregate viral load can become extreme. The unobservable chain reaction is driven by those
without symptoms. While Apple and Google are teaming up to contact trace the virus, the
contact trace that matters is the one we are not observing.
4
To stop the chain reaction, we
must find asymptomatic spreaders and isolate them.
* Associate School of Historical and Philosophical Studies, University of Melbourne.

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The asymptomatic are the story of this virus. We gain some insight from one of the earliest
studies by Yan Bai et al (February 21, 2020).
5
An asymptomatic carrier, a 20-year-old
woman, living in Wuhan traveled to Anyang on January 10, 2020. She met with five relatives,
four of whom were women aged 42 to 57. On January 17 one relative developed fever and
sore throat. Her symptoms improved over the next few days but worsened on January 24, and
she was admitted to hospital. Between January 23 and 26, the other four relatives developed
fever and respiratory symptoms and were admitted to hospital. All five relatives tested
positive for COVID-19 on January 26-7. After the development of disease in her relatives,
the 20-year old woman was isolated. She tested negative on January 26, positive on January
28, and negative on February 5 and 8. None of the relatives had visited Wuhan or been in
contact with any others who had traveled to Wuhan. Two of the relatives developed severe
pneumonia; the other infections were moderate. The asmptomatic carrier started a chain
reaction that induced an explosion in the viral load.
Transmissions within families accounted for 75 to 80 percent of all the infections in China.
6
In the above case, one person without symptoms infected five relatives, and two severely.
The asymptomatic carrier was the central node but tested positive only once in four tests.
The central node of the cluster was not observed until the cluster had been fully observed.
To stop the chain reaction, the carrier had to be identified before she infected the others.
However, not only was the carrier without symptoms, she tested negative three times in four.
Therein lies the problem. The asymptomatic spreader was not identified through testing but
through the relatives she infected. It is the story of this virus.
The number of asymptomatic is larger than we think. Evidence of the asymptomatic effect
first emerged in an early study in Vos Italy and in a sample of 18,000 in Iceland where one-
half of the infected had no symptoms. German researchers have estimated the global number
of confirmed infections as only 6% of actual, almost certainly because of the asymptomatic.
7
On cruise ships chain reactions become explosive. On the Diamond Princess 46% of the
infected had no symptoms; on the Greg Mortimer the asymptomatic are in large numbers
8
"Nearly 60 percent of 217 people on board a cruise ship off the coast of Uruguay have tested
positive..There are currently no fevers on board, and all are asymptomatic.”
Asymptomatic carriers are systematically present and are systematically underestimated.
The asymptomatic establish chain reactions of infection and re-infection which has led to an
explosion of the aggregate viral load in clusters. The chain reactions are identified too late.

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Testing
The problem is in the testing. If we had the right test or right combination of tests which
could identify the asymptomatic, we could test and isolate them before they infect others.
Testing prevents the chain reaction that leads to the explosion of the viral load. Without a
vaccine, test and isolate is the vaccine. We have to test, isolate and re-test to keep the
aggregate viral load below a threshold. It is a strategy on which most researchers agree.
9
There are three problems however. The tests are not quite good enough. As the case above
shows, the asymptomatic carrier tested negative three times in four. False negatives
associated with the asymptomatic are a major limitation of the current tests. Secondly, the
testing pattern observed in this case of negative, positive, negative and negative has been
observed elsewhere. A recent Korean study found that 51 patients who had been regarded as
cured tested positive again.
10
What this suggests is that the virus does not leave the body.
The viral load becomes too low to be found by the test. But with renewed interaction, the
viral load increases again so that it can be detected by testing. This is consistent with a chain
reaction hypothesis. The third problem is that the chain reactions are occurring everywhere.
We cannot isolate everyone. We have to manage the process subject to this constraint.
The best reference I have sourced on testing is a report prepared for the New Zealand Office
of the Prime Minister’s Chief Science Advisor.
11
There are two general types of test
(i) PCR tests that detect whether an individual has the virus.
(ii) Antibody tests that detect whether an individual has been exposed but is not infectious.
The PCR test is considered to be the most accurate test, but may not be accurate enough. It
tests for viral RNA using nasal and throat swabs. The test has high specificity to the virus.
However, PCR test kits are in short supply which limits the possibility of use in mass testing.
There are also delays in getting results, but more rapid tests are now becoming available.
12
The main problem is the problem of false negatives. The PCR test was used in the case above.
The alternative is to test the two main types of antibodies generated by the immune system in
response to the virus. The advantage of antibody tests is they are cheap, can easily be mass
produced, and results are obtained in fifteen minutes. The most successful testing regimes
(for example in South Korea and Germany) have allowed commercial labs to volume test.
This strategy will have to be adopted everywhere as suggested by recent articles in the main
stream and other media.
13
Necessarily, antibody tests may be the basis of universal testing.

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Antibody tests are not without limitations. Antibody tests are not designed to detect an active
infection, rather the legacy of an infection. The immune system takes time to respond to the
virus, usually up to five days. Antibody tests should be regarded as a means of mapping the
virus, where it has been and where it is likely to go. They are exploratory tests. Problems with
their accuracy have meant antibody testing has been delayed in a number of countries.
14
There is another problem. Researchers in Shanghai have found low levels of Covid-19
antibodies in a sample of 175 recovered Covid-19 patients. Nearly a third had unexpectedly
low levels of antibodies and in some cases, antibodies could not be detected.
15
Low levels of
antibodies would reduce the power of antibody tests.
Antibody tests are analogous to the screening tests used for other diseases like bowel cancer.
In hypothesis testing there is always a trade-off between Type I and Type II errors. In the
context of screening, the trade-off is between a false negative result and a false positive result.
All screening tests generate false negatives and false positives. Bowel cancer tests are not
without problems.
16
In the current situation however, there is another trade-off. There is a
need to test now rather than later. We need to test now to prevent more viral clusters forming.
We have to trade-off the accuracy of tests with the need to map the virus now.
False negatives in the testing of Covid-19 are far more important than in standard testing. As
the twenty-year old who travelled from Wuhan to Anyang showed, if someone tests negative
and they are infected, they may infect five others. We do not know the proportion of false
negatives for PCR tests or antibody tests. However we can conjecture. Zou et al (2020)
17
asserted “the viral nucleic acid shedding pattern of patients infected with Covid-19 resembles
that of patients with influenza.” If that is correct then the following may be relevant
"There is a large body of evidence that some COVID-19 infected individuals remain largely
asymptomatic. Advocates for adoption of antibody-based testing will (rightly) point out that
the subclinical infection means that PCR-based tests may ‘miss’ individuals either because
they are never tested or because their viral loads are too low. This is perhaps best explained
though comparisons with influenza infections: a (meta) analysis of available literature
measured the fraction of asymptomatic infections detected by PCR assays as approximately
16%, while the fraction of asymptomatic infections detected by antibody response was
measured as approximately 75%. Put simply, in cases where the patient has formed
antibodies and cleared the virus that a legacy remains of past exposure to the virus that PCR
tests can’t detect.
18

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Universal testing is necessary, an imperative forced on us by the unobservability of the virus.
We cannot reopen the economy without testing. The virus will return with new chain
reactions and clusters. Viruses tend to be cyclical and seasonal. They transmit more
efficiently in winter. Covid-19 is expected to be the same.
19
The testing regime will be
constrained by resources. Necessarily there will have to be both random and cluster sampling.
Testing is also weakened by the problem of false negatives for PCR tests and antibody tests.
The false negatives will have to be managed through re-testing. Test, isolate and re-test is the
vaccine before we find a vaccine. It is our passport to normality.
Both PCR and antibody tests will have to be deployed in a multi-stage process defined by
(i) Pre-test using antibody test
(ii) Test using the PCR
(iii) Re-test every two weeks
(iv) Isolate if both tests positive
Schematically this can be represented as
Figure I
Negative
Positive
Negative
Positive
Re-test
Re-test
Antibody
Test
PCR Test
Isolate

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Viral Load
Data curiosities often provide insights. Inter alia five curiosities seem to define Covid-19
1. Spreading before exploding
There is evidence Covid-19 was spreading in Wuhan in November 2019. The first known
case was on November 17, but by the end of December there were at least 266 infections.
20
Why did it not explode into clusters earlier? What was the trigger? The lead time before the
explosion is consistent with a chain reaction where some critical threshold is exceeded.
2. Extreme loads
Liu et al (2020)
21
in their study of 76 Covid-19 in Nanchang found that the mean viral load
of severe cases was about 60 times that of mild cases. Viral load seems to be correlated with
the severity of the clinical outcome. It suggests the jump in the viral load from mild sto
severe is associated with an explosive process.
3. Asymptomatic viral loads
Zou et al (April 9, 2020)
22
analysed the viral loads in symptomatic and asymptomatic patients
in Zhuhai, Guandong. They found the viral loads in asymptomatic patients to be similar to
those with mild symptoms suggesting the transmission potential of asymptomatic patients.
4. Testing sequence
The asymptomatic carrier who traveled to Anyang on January 10, had a testing pattern
observed in other data. The sequence negative, positive, negative, negative indicates that the
asymptomatic individual is near the critical value of the test.
5. Closed spaces
In closed spaces, it is puzzling that not all people are infected. They breathe the same air.
Perhaps they have all been exposed, but their viral load is too low to be found by testing.
Hypothetically there may be five groups defined by symptoms, PCR test and viral load
Group 1: Severe symptoms, positive PCR test and extreme viral load.
Group 2: Mild symptoms, positive PCR test and moderate viral load.
Group 3: Asymptomatic, positive PCR test and moderate viral load.
Group 4: Asymptomatic, negative PCR test and less than moderate viral load.
Group 5: No exposure to the virus, negative PCR test and no viral load.

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The viral load seems to be important. The diagnostic tests are binary tests that determine
whether an individual is infected or not. The test we need is one that determines the viral load.
Existing tests cannot distinguish viral loads. They do not have the power to find all the
asymptomatic individuals. This becomes important when individuals congregate particularly
in confined spaces like cruise ships, planes, hospitals and apartments.
23
It becomes important
because of the aggregate viral load in a closed space.
When the aggregate load exceeds a certain threshold, it sets off a chain reaction that leads to
severe cases. Perhaps everyone is exposed in a hospital, cruise ship or apartment, but the viral
loads of each exposure are too small. In the aggregate they may not be. Once the aggregate
exceeds a critical value, the process of infection and re-infection becomes explosive.
Let me illustrate with two individuals A and B in a closed space. Suppose A is an
asymptomatic carrier and A infects B. B becomes infectious and they re-infect A. The
pattern continues. The aggregate viral load increases with each transmission.
𝐴 → 𝐵, then 𝐵 → 𝐴, then A → B, ….
The process can become explosive once the aggregate viral loads exceeds some threshold.
Even when each individual has a small initial viral load, the sequence of infection and re-
infection creates the possibility of an aggregate load exceeding a critical value.
The process will be particularly explosive for large congregations clustered together as in
churches, or congregations breathing the same air as on cruise ships or in hospitals. For an
asmptomatic carrier who infects five others, the sequence becomes
𝐴1→ 𝐴2,….,𝐴6 , 𝐴2→ 𝐴1, 𝐴3… . , 𝐴6, 𝐴3→ 𝐴1, 𝐴2… . , 𝐴6,..
With large numbers in small spaces, even when the asymptomatic carrier has a small viral
load, the sequence of infection and re-infection can generate an extreme aggregate load;
consistent with the clusters in small Italian towns, cruise ships, nursing homes and hospitals.
The aggregate viral load matters. Even when individuals have small viral loads initially, the
process of infection and re-infection can generate an explosive chain reaction.
The implications are threefold. First to develop better tests to be able to identify the viral
loads of individuals. Second to recognise that the aggregate viral load is important in closed
spaces suggesting the need for better ventilation and social distancing inside. Third to
understand that the exponential curve may re-emerge as the result of new chain reactions.

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What is to be Done?
We should be analytical but also practical. Here is one plan. There are seven billion others.
1. Expect the unexpected
In a black swan event no one can be certain. The unobservable cannot easily be hedged.
The virus has re-emerged just when countries believed they had controlled it.
2. Mass testing
Mass testing should commence employing a multi--stage process
(i) Pre-test using antibody test
(ii) Test using the PCR
(iii) Re-test every two weeks
(iv) Isolate if both tests positive
3. Social distancing
Social distancing inside is as important as social distancing outside.
4. Fresh air
Fresh air is the key.
24
Put simply for individuals
(i) Open the windows
(ii) Take a walk in the fresh air
(iii) Breathing exercises
25
5. Hospitals
(i) Testing conducted outside
(ii) Cross-ventilation systems and the infusion of fresh air
26
(iii) Separate Covid-19 patients as much as possible from others.
6. The Moral Choice
The choice between lives and livelihoods will define how we remember this pandemic.
7. Reflection
We have more silence than ever. Perhaps a time for reflection on the state of the planet, on
who we have become, and how we will change hereafter. We may never get this chance again.

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I Spent Twenty Hours on My Own Today
27
I spent twenty hours on my own today,
Twenty hours away from the fray,
Everybody thinks that we all need company,
But when you’re alone you are free to be me.
I spent twenty-one hours on my own today,
Twenty-one hours away from E-Bay,
Everybody thinks that we all need a transaction,
But when you’re alone there’s no need for retraction.
I spent twenty-two hours on my own today,
Twenty-two hours away from a good’ day,
Everybody thinks that we all need a greeting,
But when you’re alone you can choose your own meeting.
I spent twenty-three hours on my own today,
Twenty-three hours away from the play,
Everybody thinks that we all need an act,
But when you’re alone there’s no need for tact.
I spent twenty-four hours on my own today,
Twenty-four hours with the time to pray,
Everybody thinks that we all need to reflect,
But when you’re alone you can also respect.

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3
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6
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8
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9
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10
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12
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13
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https://www.wired.com/story/opinion-to-end-the-pandemic-give-universal-testing-the-
green-light/

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14
https://www.theguardian.com/society/2020/apr/08/uk-covid-19-antibody-tests-not-
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15
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16
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17
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18
Bunce, M. and M. Estcourt (March 30, 2020). Op. cit.
19
Marc Lipsitch (2020) https://ccdd.hsph.harvard.edu/will-covid-19-go-away-on-its-own-in-
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20
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21
Yang Liu, Li-Meng Yan, Lagen Wan,Tian-Xin Xiang, Aiping Le, Jia-Ming Liu, Malik Peiris,
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22
Zou, L., Ruan, F., Huang, M., Liang, L., Huang, H., Hong, Z., Yu, J., Kang, M., Song, Y., Xia, J.,
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23
https://edition.cnn.com/2020/04/02/health/aerosol-coronavirus-spread-white-house-
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24
Sawyer, K. R. (2020). The Paradox of Covid-19.
25
An example is given at https://youtu.be/HwLzAdriec0
26
An example is at https://www.iom-world.org/iom-50/fresh-air-for-the-control-of-hospital-
infection/
27
Sawyer, K. R. (2013). Poetica.