Modeling the optimization of COVID-19 pooled testing: How many samples can be included in a single test?

This study tries to answer the crucial question of how many biological samples can be optimally included in a single test for COVID-19 pooled testing.

It builds a novel theoretical model which links the local population to be tested in a region, the number of biological samples included in a single test, the "attitude" toward resource cost saving and time taken in a single test, as well as the corresponding resource cost function and time function, together. The numerical simulation results are then used to formulate the resource cost function as well as the time function. Finally, a loss function to be minimized is constructed and the optimal number of samples included is calculated.

In a numerical example, we consider a region of 1 million population which needs to be tested for the infection of COVID-19. The solution calculates the optimal number of biological samples included in a single test as 4.254 when the time taken is given the weight of 50% under the infection probability of 10%. Other combinations of numerical results are also presented.

As we can see in our simulation results, given the infection probability at 10%, setting the number of biological samples included in a single test (in the integer level) at [4,6] is reasonable for a wide range of the subjective attitude between time and resource costs. Therefore, in the current practice, 5-mixed samples would sound better than the commonly used 10-mixed samples.