Writer/Wisdom and Love

Darwin's herd immunity, new corona screening of authoritative elimination.

Scientific evolution is genius, and if old doesn't go away, new won't come.

Wuhan was closed on January 23rd and Wuhan was opened on April 8th. Within a 76-day period, if nucleic acid test was positive in Wuhan, what is chance of being infected with new corona? After 24 hours, two nucleic acid tests are positive, by how much does chance of a new crown infection increase? What is probability of a confirmed diagnosis if nucleic acid test is positive twice within 24 hours?

When Wuhan was closed, tens of millions of people were isolated in besieged city. Over 50,000 people have finally been diagnosed with new crown and diagnosis rate was around 0.5%. That is out of 1000 people. , 5 people were infected with new corona and 995 people were not infected with new corona. If sensitivity of nucleic acid detection kit is 99%, that is, for 100 people infected with new corona, nucleic acid can detect 99 people with a positive result; if specificity of nucleic acid detection kit is also 99%, that is, 100 nucleic acid test results are positive, 99 people were infected with new corona, 1 person was not infected with new corona, and test was false positive.

It is known that probability of a positive diagnosis in a single test = nucleic acid detection sensitivity 99% * infection rate 0.5% / (nucleic acid detection sensitivity 99% * infection rate 0.5% + false positive rate 1% * non- infection rate 99.5%) = 33%, that is, nucleic acid test is positive once, and probability of diagnosis is only about one third. You should be unhappy. Wait 24 hours and then add another test, which means, that nucleic acid test infection rate will still be diagnosed at 33% = nucleic acid test is sensitive Grade 99% * infection rate 33% / (nucleic acid detection sensitivity 99% * infection rate 33% + false positive rate 1% * non-infection rate 67%) = 98%, diagnosis can now be confirmed.

The above is an example of applying Bayes' famous conditional probability theorem in probability theory, and general Bayesian formula is: P(AB)=P(A|B)*P(B)=P(B|A) *P(A )=P(BA), push P(A|B)=P(B|A)*P(A)/P(B)

Where:

P(B)=P(B|A)*P(A)+P(B|-A)*P(-A)

Replace and Disassemble:

P(A|B)=1/[1+P(B|-A)*P(-A)/(P(B|A)*P(A))]……………( 1 )

As in example above:

Ah... new corona infection

-A... not infected

B...nucleic acid positive

P(A|B)… Nucleic Acid Detection Specificity

P(B|A)…Nucleic acid detection sensitivity

P(B|-A)...False positive ratedetection

In case of recovery and discharge: positive to negative, infected to uninfected

P(-A|-B)=1/[1+P(-B|A)*P(A)/(P(-B|-A)*P(-A))]…… . .. (2)

Where:

Ah... new corona infection

-A... not infected

-B...nucleic acid negative

P(-A|-B)…Nucleic acid detection sensitivity

P(-B|-A)… Nucleic Acid Detection Specificity

P(-B|A)... False-Negative Detection Rate

It is known that probability of a negative test result for nucleic acids P(-A|-B)=1/[1+false negative rate P(-B|A)1%*infection rate P(A)98%/( specificity of nucleic acid detection P(-B|-A)99%*frequency of uninfected P(-A)2%)]=67%,

That is, nucleic acid test is negative once, and probability of outcome is only about two-thirds. You must be dissatisfied, so wait 24 hours and then add an additional test, that is, in nucleic acid test, recovery rate is 67%, continue with nucleic acid test Probability of negative detection P(-A|-B)=1/[ 1+false negative P(-B|A)1%*Infection rate P(A)33%/(Nucleic acid detection specificity P(-B|-A)99%*Uninfected rate P(-A)67%)] =99%, now we leave hospital with relief.

As for another extensive study and application of Bayes' theorem, I'll leave it up to you to draw conclusions from one example and understand by analogy.

The water in vase is calm, and grass is calm, and meadow is dusty.

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**Note**: With permission of Zhiqing Zhenzhen, author of Zhiqingzhenxue, Editor of Brotherly Fortitude is released exclusively in today's headlines!

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