Study of Nucleic Acid Detection Model Based on Optimal Mixed Detection

In this paper, we study the optimal number of mixed samples and the length of testing for a region of the new crown epidemic. In this paper, we consider a variety of factors to establish a model and give conclusions and recommendations on issues related to nucleic acid testing for the new crown epidemic. First, the mathematical model of sample pool counting is established, and the infection rate, mixed sample size, and total number of samples are set as variables, and the equation relationship between the three is established to calculate the average expected number of tests per sample, using the value for simple mathematical operations. Then the model is solved by bringing different infection rates into the equation to obtain the relationship between the infection rate and the total number of reagent tests. Finally, this paper constructs a mathematical expectation model for this, and transforms the problem into finding the minimal value of the mathematical expectation $E(X)$ to obtain the corresponding stem of the infection probability and the mixed sample size. And on this basis, the mathematical expectation model and the sample pool counting model established in this paper are combined to derive the total time of three rounds of nucleic acid testing.