Detect newly the technology lets Beijing won't become next Wuhan absolutely

Author brief introduction: pa, doctor of computer of Chinese Academy of Sciences, 211 universities are taught, ever won junior high school and first prize of league matches of Olympic of maths of high school whole nation, jiangsu competion area the first, full marks of maths of the university entrance exam. Set public date Xuanbamath.

A few days of in the past, beijing discovered native land case of illness many cases continuously, have mop of 46 people pharynx child the test shows masculine gender. Via preliminary investigation, this second epidemic situation erupts with new hair ground terminal market is concerned. Detect detect in the chopping board that personnel imports 3 article fish from cut gave new coronal virus, and its supply of goods comes from market of Yu Jingshen seafood.

Seafood market, stand on where the wind and the waves are highest again.

Time pulls the Wuhan before returning 5 many months, china Nanhai fresh market is shut, detect personnel detects from inside example of spot much portion gave masculine gender. How familiar setting. Different is, last time suspicion is batty to seeming, and this, 3 article fish became target of public criticism.

Then, somebody fears Beijing can become next Wuhan. In a terrified, how should be we done? Passed the fight of 5 months and virus, actually we have rich experience and better technology to answer new coronal now, what do not have panic completely is necessary. Odd from technical angle, let the whole people detect become a possibility mix measure a law to be able to let everybody eat next sth capable of comforting sb.

On June 2, 2020 afternoon, pneumonic epidemic situation prevents Hubei province new coronal accuse headquarters to hold the 104th press conference. From May 14 0 when to on June 1 24 when, the nucleic acid in Wuhan bazaar detects 9899828 people, did not discover diagnose case of illness, 300 name, check give the person that check goes out to be affected without the symptom rate for 0.303/ 10 thousand. On June 8 afternoon, city of Heilongjiang peony river also reported the result that goes 7 days to undertake nucleic acid of the whole people detects greatly, in all the person that check gives 19 to be affected without the symptom. And city of Hubei another name for Hubei province also will come to undertook centralized checking to whole town personnel on June 17 on June 11.

Once we think impossible the whole people detects, turning into step by step reality. But this is not an imagination is so simple, want to know, the United States that Telangpu takes great pride all the time, detect up to now gross also has 21 million only, and our Wuhan one city detected 10 million.

I notice, the ten million that this Wuhan city finishs detects, those who use is " mixture example nucleic acid detects method " (later development abbreviation mixes check law) . What is the law that confuse be careful in one's conduct? Simple for, it is a N nose pharynx mop child undertake mixture after sampling, undertake detecting to mixing the example after, if detect eventuate is electronegative, show N individual is electronegative, and if detect eventuate is electropositive, need to be opposite again the example of N individual undertakes detecting respectively.

So, when infection rate is lower, use this kind to mix measure a law to be able to reduce detected number greatly; And should affect when rate is higher, criterion the efficiency of this method will be reduced considerably.

For example, hypothesis N=2, if do not mix, need to detect 2 times. And if mix two the individual's example,be together, if infection is led for 10% , criterion the probability that two people did not affect is 90%*90%=81% , the probability that has one individual infection at least is 1-81%=19% , former should measure 1 times only, and latter need is measured 3 times. Accordingly, use those who mix the expectation that measure a way to detect the frequency is × of 1 × 81%+3 19%=1.38 second, under do not use mix 2 times when measure a way.

And if infection is led for 90% , criterion the probability that two people did not affect is 10% × 10%=1% , the probability that is put in one individual infection at least is 99% , use those who mix the expectation that measure a way to detect the frequency is × of 1 × 1%+3 99%=2.98 second, want prep above to be not used mix 2 times when measure a way. In fact, if infection is led for 30% , two people are 0.7 × without the probability of infection 0.7=0.49, the probability that has one individual infection at least is 0.51, use those who mix the expectation that measure a way to detect the frequency is × 0.51=2.02 of 1 × 0.49+3, already prep above is not used be mixed 2 times when measure a way.

Accordingly, infection rate is lower, mix the effectiveness that measures a way taller.

Besides infection rate, the example that another influencing factor is mix up counts N. N is bigger, the number that can detect 1 times is more. But at the same time, n is bigger, the probability of nonexistent infection also jumps over N individual low. If we take no account of what more or less bring as a result of example amount,detect sensitivity problem, only consideration N is right detect the influence of the frequency, so, if assume infection rate is P, expect detect the frequency analyses as follows:

N individual is electronegative probability: (1-p)^N

N individual has the probability of one factitious positive at least: 1-(1-p)^N

Then, of expectation detect the frequency is:

1 × (1-p)^N+(N+1) × [1-(1-p)^N]

=(1-p)^N+N-N(1-p)^N+1- (1-p)^N

=N+1-N(1-p)^N

Should mix the expectation that measures a way to detect when number does not have an advantage, contented:

N+1-N(1-p)^N ≥ N

N(1-p)^N ≤ 1

Namely:

Next watches gave out the value of N and

take a cost, visible, when N=10, if affect rate P=20% , so mix the expectation that measures a way to check a frequency to still be less than do not use mix measure a way, but when N=11, mix measure a law to have an advantage no longer.

2 0.707

3 0.693

4 0.707

5 0.725

6 0.742

7 0.757

8 0.775

9 0.783

10 0.794

11 0.804

When next graphs gave out to affect rate P=10% and P=20% , use mix measure law and do not use mix when measuring a way, detect on average the metabolic condition that the frequency figures N as mixture portion, can see infection rate is inferior (when P=10%) , use mix measure a law to have an advantage.

Of course, if infection rate is very low, for example P=1% , if right now N=10, use mix the expectation that measures a way to examine the frequency is merely: × of 1 × 0.99^10+11 (1-0.99^10) ≈ 1.96, far be less than do not use mix 10 times when measure a way.

If infection rate is very low, so in susceptibility acceptability circumstance falls, can 15 example mix a test, accordingly, to the city of a 23 million level, test the volume level that the frequency is in 1.5 million times about, belong to acceptable range.

When discussing this issue with the son yesterday, he still offerred a kind of think of a way, think to detect in below the case that presents masculine gender, can continue to use dichotomy to undertake detecting, for example first time N=12 is measured come out to be masculine gender, criterion to 6 people the 2nd times a group example has a test. Nevertheless he realizes this kind of method immediately and can not achieve the result of dichotomy, because be not,only a person is positive.