Optimal Group Size Under Halving Algorithm

From the source to prevent and control epidemic diseases,it is necessary to accurately and efficiently detect the diseased individual to carry out targeted isolation and treatment.Therefore,group testing method has received great attention from scholars in this respect,and many scholars have conducted in-depth research on it.The use of group testing method enables rapid and accurate identification of diseased individuals in large population samples.Halving group testing improves the detection efficiency based on the Dorfman group testing method.In the existing literature,domestic and foreign scholars have conducted in-depth research on the optimal group size of group testing.However,most of the relationship between the single detection efficiency index and the group size is used to solve the optimal group size.In this paper,we first calculate the mean of the number of detections for group testing,and then expand the concept of group sensitivity and group specificity,and derive the specific formula.Combining the above three detection efficiency indicators,we construct three objective functions S1,S2,and S3,and obtain the optimal group size scheme under the group testing situation by minimizing the function value.Based on Dorfman group testing,single-halving-group detection,and multiple-halving-group testing,we derive the efficiency index and optimize the objective function to solve the optimal group size under various conditions.Then we performed statistical simulation based on R software,and under the conditions of prevalence,reagent sensitivity and specificity,we simulated in the case of Dorfman group testing,single-half-group testing,and second-half group testing.The results of the optimal group size optimized by the three objective functions S1,S2 and S3 and their corresponding related indicators are shown by the graph.The existence of the optimal group size of the three group testing is verified.The simulation results show that the optimal group size obtained under the new objective function can make the halving group testing method improve the detection efficiency under the premise of ensuring accuracy,thus saving the detection cost.