传染病高效多步批检验的建模与计算
Modeling and Computation of High Efficiency and Efficacy Multi-Step Batch Testing for Infectious Diseases
摘要：
我们提出了一个基于概率论的数学模型，通过可变批量的多步批量测试方法优化COVID-19测试。该模型和模拟工具以低成本显著提高了大量人群中测试的效率和功效，特别是在感染率较低时。所提出的方法结合了统计建模与数值方法来求解非线性方程，并在测试的每一步获得最佳批量，具有灵活性，将地理和人口统计信息。从理论上讲，这种方法大大提高了假阳性率和阳性预测值。我们还进行了蒙特卡罗模拟来验证这一理论。我们的仿真结果表明，我们的方法显着降低了假阴性率。如果考虑到稀释效应或其他实际因素，可以做出更准确的评估。所提出的方法对于传染病的早期检测和预防未来的大流行特别有用。拟议的工作将对一般传染病的医学检测产生更广泛的影响。
英文摘要：
We propose a mathematical model based on probability theory to optimize COVID-19 testing by a multi-step batch testing approach with variable batch sizes. This model and simulation tool dramatically increase the efficiency and efficacy of the tests in a large population at a low cost, particularly when the infection rate is low. The proposed method combines statistical modeling with numerical methods to solve nonlinear equations and obtain optimal batch sizes at each step of tests, with the flexibility to incorporate geographic and demographic information. In theory, this method substantially improves the false positive rate and positive predictive value as well. We also conducted a Monte Carlo simulation to verify this theory. Our simulation results show that our method significantly reduces the false negative rate. More accurate assessment can be made if the dilution effect or other practical factors are taken into consideration. The proposed method will be particularly useful for the early detection of infectious diseases and prevention of future pandemics. The proposed work will have broader impacts on medical testing for contagious diseases in general.
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