Simple Strategy:
The strategy is the following:
N1 people will be tested together
If the test is negative, they are all negative. Only one kit will be used.
If the test is positive, we know that at least one of the samples is positive.
In this case, new tests will be run, grouping by N2 samples from N1 which can still be positive. And so on and so forth.
We assume the there can be a maximum of 30 samples being tested at the same time.
The Search for the Optimal Number of Tests
The numbers N1, N2, N3, ... are chosen through the probability of testing positive, given by the risk of infection, as to limit the number of testing kits needed. The last number of that sequence Will always be 1, which Will allow for individual testing of the positive cases.
To generate the optimal number of tests, every combination of N1, N2, N3 , etc is attempted, calculating the amount of testing kits (TK) needed to distinguish positive and negative indivuals in each tested group.
The “number of kits used multiplier” is N1 / TK, that is, the average of people tested with just one kit .
To calculate the optimal number of tests, a dynamic program was used, which calculated exact probabilities.
Simple results were favored over the possibility of more complex testing recipes, which generated little benefit in efficiency .
Example Using the Manual (risk of 5% of infection):
Estimated probability of 5% of being infected (Ni = [ 9, 3, 1 ] )
Test 9 samples as a group
If the test is negative, they are all negative.
If the test is positive, test 3 different groups of 3 samples each.
For each group
If the test is negative, they are all negative.
If the test is positive, test each one of the cases individually.
On average, 3,39 kits are used for 9 people, which translates to 2,65 people being tested by each kit