Modeling and computation of multistep batch testing for infectious diseases.

Area of Science:

• Epidemiology
• Biostatistics
• Mathematical Modeling

Background:

• Efficient mass testing is crucial for controlling infectious diseases like COVID-19.
• Traditional testing methods can be costly and less effective, particularly at low prevalence rates.
• Optimizing testing strategies is essential for early detection and pandemic prevention.

Purpose of the Study:

• To develop and validate a mathematical model for optimizing COVID-19 testing using a multistep batch testing approach.
• To enhance the efficiency, efficacy, and cost-effectiveness of large-scale diagnostic testing.
• To improve key performance indicators such as false positive rate, positive predictive value, and false negative rate.

Main Methods:

• Development of a probability-theory-based mathematical model for multistep batch testing with variable batch sizes.
• Integration of statistical modeling and numerical methods to solve nonlinear equations for optimal batch sizing.
• Utilization of Monte Carlo simulations to verify the theoretical model and assess performance.

Main Results:

• The proposed model significantly increases testing efficiency and efficacy in large populations, especially at low infection rates.
• The method demonstrates theoretical improvements in false positive rate and positive predictive value.
• Monte Carlo simulations confirmed a significant reduction in the false negative rate.

Conclusions:

• The optimized batch testing strategy offers a cost-effective and accurate approach for COVID-19 testing.
• This method has broad applicability for early detection of infectious diseases and future pandemic preparedness.
• Further refinement can incorporate practical factors like dilution effects for even greater accuracy.