# Solutions for Covid-19 related problems and no one to tell?

• COVID
MUZE
In the search to submit my solution to save Covid-19 tests to the right people, I was not able to find out if sharing a Covid-19 spit test is even possible? I have tried to give the solution to different agencies including the CDC at various points of contact. I am hoping someone here can understand the value of this solution and explain why this may or may not work? I have attached a simple diagram on how the tests would be
implemented to save tests.

MUZE
Can anyone tell me if this solution will save Covid-19 tests?

MUZE
Can a group of people like family or a department share a spit test?

Homework Helper
Gold Member
Can a group of people like family or a department share a spit test?View attachment 261960
I like the way you think, here: Theoretically, if $N$ people needed to be tested, the number of required tests could be reduced idealy from $N$ tests to $\log_2 N$ tests.

There are several practical problems with this approach.

• Samples would have to be combined for a given test, effectively diluting each individual sample. This alone could render the test ineffective.
• This method would cause a huge increase in error rate. Every individual test has nonzero probability of producing a false positive or false negative result. In this method these errors would propagate from one level to the next, even between different people. The propagation could render the results pretty useless (and arguably dangerously ineffective).
• At this time, the sample collection is not as simple as just providing saliva. The antigen test (the test to determine if you are presently infected) involves sticking a swab way up into sinuses, and the antibody test (the one that determines if you have already had the virus) involves drawing blood. The proposed method would seem to me like it might require more samples per person.

So no, I don't think that this approach would work. It does make for a fun math problem though.

Mentor
Would it be really practical? Assuming it works it will save tests, but in case of a positive takes longer to determine who is positive and who is not, which is not necessarily a good idea.

russ_watters
jartsa
30 test results can not contain the information of 50 individual's corona status.

30 bits can not contain the information that 50 bits can contain.

Homework Helper
Gold Member
30 test results can not contain the information of 50 individual's corona status.

30 bits can not contain the information that 50 bits can contain.
Agreed. If you had $N$ people and you know a priory that $0$ to $N$ of those people might have the virus with uniform probability, and you want results specific for each and every person, then it will take $N$ tests. There's no getting around this.

On the other hand, It might be possible (again, theoretically) to statistically reduce the average number of tests if you knew a priory that the probability of any person testing positive was non-uniform (i.e., not 50%). (It's not practical though for reasons already discussed.)

Or, if you knew somehow a priori that exactly 1 out of the $N$ people had the virus and you wanted to figure out precisely who, you could reduce the number of tests. (Still not practical though.)

But again, none of this is really practical for several reasons. So no,this is not going to help us in our real-world situation. It does make a fun math problem though.

Gold Member
2022 Award
30 test results can not contain the information of 50 individual's corona status.

30 bits can not contain the information that 50 bits can contain.
Yes, but I don't think that's quite the right analogy for the OPs question. As Collinsmark just pointed out, things in the real world may not exactly fit your assumption. That is, you may not have the equivalent of 50 bits of info. Suppose, to take an extreme example, you have 50 "bits" but you know for sure that no more than 1 of them will be a 1. How many tests does it take to isolate that one? Not 50 and not even 30, more like 6 or 7

MUZE
I like the way you think, here: Theoretically, if $N$ people needed to be tested, the number of required tests could be reduced ideally from $N$ tests to $\log_2 N$ tests.

There are several practical problems with this approach.

• Samples would have to be combined for a given test, effectively diluting each individual sample. This alone could render the test ineffective.
• This method would cause a huge increase in the error rate. Every individual test has a nonzero probability of producing a false positive or false-negative result. In this method, these errors would propagate from one level to the next, even between different people. The propagation could render the results pretty useless (and arguably dangerously ineffective).
• At this time, the sample collection is not as simple as just providing saliva. The antigen test (the test to determine if you are presently infected) involves sticking a swab way up into sinuses, and the antibody test (the one that determines if you have already had the virus) involves drawing blood. The proposed method would seem to me like it might require more samples per person.

So no, I don't think that this approach would work. It does make for a fun math problem though.
The new spit test does not require a swab. https://www.the-scientist.com/news-...id-19-approved-for-emergency-use-by-fda-67416 How would divide the spit test change accuracy? Again could this test be made more sensitive to accommodate? A person or sample is either positive or not?

MUZE
Yes, more spit/blood samples would be needed. Is it more likely to get a false negative from combining 2 samples?

Gold Member
From a mathematical point of view, it's certainly a valid approach.

But, possible mitigating factors would also be mathematical :

dilution : say you mix 16 samples together. Now the test has to be 16x as sensitive.

sample size : in the aforementioned batch, either you you go back to test some people 4x, or require 4x as much sample fluid from each to start.

Last edited:
MUZE
Mentor
30 test results can not contain the information of 50 individual's corona status.

You are missing the point. If you make a shared test that confirms 16 people are not infected you have proven 4 bits are zero with just one test. When you get a positive result, then you need to dig into details and it may happen that the total number of tests will be even larger than the number of people tested. But as long as we are talking about a group of people that can have their results correlated for some reason this approach (assuming it is feasible technically) doesn't sound completely off.

I doubt it would be practical - first, takes longer to detect those infected, second, requires following not so simple protocol of juggling samples, which makes it error prone.

russ_watters
MUZE
@Borek A positive group would be split using spit (or blood of the same blood type) sample into 2 sub-groups to using 2 more tests. The size of the group and the number of sub-groups will be determined by the positive whether false or not. The amount of spit needed will be determined by the number of people in the base group and the ratio of positive tests. Not much is needed per test 1:1 ratio. I'm sure one could spit as many times as needed. The group sample can be mixed and cultured in the lab without having to make another appointment. This would be good for testing a family or department staff. With each positive per group, the individual spite samples can be broken into smaller groups, and redundancy is created in theory. I'm sure this will work to save tests and is better than not getting one at all?

Last edited:
russ_watters
jartsa
You are missing the point. If you make a shared test that confirms 16 people are not infected you have proven 4 bits are zero with just one test. When you get a positive result, then you need to dig into details and it may happen that the total number of tests will be even larger than the number of people tested. But as long as we are talking about a group of people that can have their results correlated for some reason this approach (assuming it is feasible technically) doesn't sound completely off.

I doubt it would be practical - first, takes longer to detect those infected, second, requires following not so simple protocol of juggling samples, which makes it error prone.

Well, I did not say that it does not work.

https://www.news-medical.net/news/2...19-could-solve-test-kit-shortage-problem.aspx

MUZE
MUZE
Thank You. I've had this idea for months. Finally, someone of enough importance had the same idea and took the initiative.

Mentor
A positive group would be split or blood of the same blood type into half to use 2 more tests.

Confirming 4 positives out of 4 patients requires 7 tests.

MUZE
What about 50 out of 50?

Mentor
In general around 2n-1, feel free to prove it, reasonably easy math problem.

MUZE
@Borek 1 test could test a group of 64 more or fewer people.https://www.news-medical.net/news/2...19-could-solve-test-kit-shortage-problem.aspx Each sub-group would be an added factor to each person. A false-negative is far rarer than a false-positive. With this simple algorithm and the findings on this website should be a dependable means of saving tests even if all are positive with more redundancy than 2 tests to 1 person. You have been motivating. Thanks

MUZE
@Borek 1 test could test a group of 64 more or fewer people.https://www.news-medical.net/news/2...19-could-solve-test-kit-shortage-problem.aspx Each sub-group would be an added factor to each person. A false-negative is far rarer than a false-positive. With this simple algorithm and the findings on this website should be a dependable means of saving tests even if all are positive with more redundancy than 2 tests to 1 person. You have been motivating. Thanks
Also, I had this idea months before this publishment. I tried to share it and fell on deaf ears as implausable when in fact it is sound.

Gold Member
2022 Award
Also, I had this idea months before this publishment. I tried to share it and fell on deaf ears as implausable when in fact it is sound.
It should be about the idea.

MUZE
@BillTre I know, I was just so upset I had a real solution and nobody took me seriously.

Gold Member
I know : I had the same idea. I dropped it after figuring out the 'dilution' thing. Which, according to that article, isn't an issue.

Also, I had this idea months before this publishment. I tried to share it and fell on deaf ears as implausable when in fact it is sound.

Well, take it as encouragement that you did in fact have a good idea. And take the time to read carefully all the additional checks and steps they had to take to implement it.

MUZE and BillTre
Homework Helper
There has been quite a bit written about group testing since it was first proposed in 1943 to test for syphilis is army recruits. Group testing definitely saves tests. The question is how to minimize the number of tests and time to conduct them. If the idea is to test in two stages, then the optimal group size is ##G = 1\sqrt{p}## - see my initial post in this thread: https://www.physicsforums.com/threa...avirus-minimizing-the-number-of-tests.987053/

With RT-PCR testing there should not be a problem with dilution. The RT-PCR test is very sensitive to begin with. PCR amplifies the complementary DNA to the mRNA of the virus. But the one thing about the SARS-CoV-2 virus is its replication rate in infected people. It is extraordinarily fast in getting into cells and cranking out gazillions of copies of itself. So an infected person is likely to have more than one or two viruses in their saliva.

In a staged set of tests > 2, which is what is proposed, with a limit on the number of tests that can be conducted on a single saliva sample, the goal is to minimize the number of tests without exceeding that limit on the number of stages. That is achieved by choosing the right sized initial group eliminating all the individuals in the negative groups and then going to the next stage. The solution that my mathematician brother has found is that it is not achieved by dividing by 2.

Confirming 4 positives out of 4 patients requires 7 tests.
If you want to test just 4 people, why would you not just test the 4 individually? The idea of group testing is to test millions.

AM

MUZE and atyy
Mentor
If you want to test just 4 people, why would you not just test the 4 individually? The idea of group testing is to test millions.

My understanding is that in the current situation it is important to quickly detect those infected to isolate them, and the scheme that allows saving on tests in group testing slows down the process and - as we are interested in the individuals - is not guaranteed to save on tests. That's what I was trying to point out.

Could be it would work as a part of a more elaborate methodology, it is just not a miracle solving problem at hand.