关键词: 时间价值, 概率群试, 多目标优化, 成本效用函数, 帕累托最优

Abstract: Since the twentieth century, regional public health events have occurred frequently around the globe, directly threatening the safety of human life and hindering socio-economic development. In 2020, COVID-19 broke out and ravaged the globe, resulting in severe impacts on many regions. The nucleic acid detection is an important means for the normalization of epidemic prevention and control. By expanding the scope of detection, we have targeted sporadic cases and concentrated on epidemics in areas where important entry ports such as Beijing, Tianjin, Heilongjiang, and Liaoning are located. Relevant departments organized multiple rounds of large-scale nucleic acid detection in relevant areas. Multiple rounds of large-scale nucleic acid detection in various regions cost a lot of money, and the group test can greatly improve efficiency and reduce cost. Therefore, it is of great significance for epidemic prevention and control and government public health management to study how to determine the reasonable mixed number of nucleic acid detection samples to improve the detection efficiency and reduce the cost of regional virus nucleic acid detection.
First, the conditional probability model is used to calculate the expected value of the newly infected numbers every day by using the mutual calculation relationship between the newly diagnosed numbers and the newly infected numbers. The bootstrap method is introduced to give the corresponding confidence interval to further calculate the number of existing infections (undiagnosed) and predict the changing trend of the number of newly diagnosed infections. The number of positive samples and the probability of positive samples are estimated, and the optimal mixing number of probability group trials is calculated.
Secondly, we should complete the nucleic acid detection of all personnel in relevant areas in the shortest possible time, which is conducive to preventing the spread of the epidemic and restoring regional development and residents’ daily life as soon as possible;we should complete the nucleic acid detection of all personnel in relevant areas at the lowest possible cost, which is conducive to saving government expenditure and reducing the financial burden. Therefore, a probability group trial bi-objective optimization model based on group test cost and time value is established to minimize the detection completion time and group test cost under the specification of nucleic acid detection, and the optimal number of mixed samples under the bi-objective optimization can be obtained.
Finally, in order to verify the applicability of the model, the detection of COVID-19 nucleic acid is analyzed, calculating Pareto optimal solution by priority method and the Pareto optimal curve under the minimum cost, and the shortest detection completion time is obtained. The results show that the reasonable mixed number of nucleic acid detection samples is about 10. In order to facilitate organization, arrangement, and statistics, 10 is often taken, except for special requirements for detection cost and detection completion time. For example, nucleic acid testing is carried out in medium and high-risk areas in underdeveloped areas and standardized nucleic acid testing is carried out regularly in areas at risk of epidemic introduction.
To sum up, the probabilistic group test model based on the consideration of group test cost and time value can improve the detection efficiency and reduce the cost of virus nucleic acid detection, which is conducive to the cost reduction and efficiency increase in public health management under the normal epidemic situation. It is of great significance for relevant departments to do a good job in epidemic prevention and control and promote the resumption of work and production.

Key words: time value, probabilistic group test, multi-objective optimization, cost-utility function, Pareto optimal