Objective Rapid testing is paramount during a pandemic to prevent continued viral spread and excess morbidity and mortality. This study investigates whether testing strategies based on sample pooling can increase the speed and throughput of screening for SARS-CoV-2, especially in resource-limited settings. Methods In a mathematical modelling approach conducted in May 2020, six different testing strategies were simulated based on key input parameters such as infection rate, test characteristics, population size, and testing capacity. The situations in five countries were simulated, reflecting a broad variety of population sizes and testing capacities. The primary study outcome measurements were time and number of tests required, number of cases identified, and number of false positives. Findings The performance of all tested methods depends on the input parameters, i.e. the specific circumstances of a screening campaign. To screen one tenth of each country’s population at an infection rate of 1%, realistic optimised testing strategies enable such a campaign to be completed in ca. 29 days in the US, 71 in the UK, 25 in Singapore, 17 in Italy, and 10 in Germany. This is ca. eight times faster compared to individual testing. When infection rates are lower, or when employing an optimal, yet more complex pooling method, the gains are more pronounced. Pool-based approaches also reduce the number of false positive diagnoses by a factor of up to 100. Conclusions The results of this study provide a rationale for adoption of pool-based testing strategies to increase speed and throughput of testing for SARS-CoV-2, hence saving time and resources compared with individual testing.

Many complex model functions allow the reduction of their effective dimension through active subspaces. These are computed by an eigenvalue decomposition of the average of the outer product of the function's gradient with itself. The size of the eigenvalues indicates how much the function changes on average along the direction given by the eigenvectors. This motivates to omit directions belonging to small eigenvalues and therefore to effectively reduce the model's dimension without losing much accuracy. The remaining directions form the active subspace, a linear combination of the input parameters. For real-world applications the required gradients are usually not explicitly known and they are thus commonly approximated with finite differences or ridge functions. The average of the outer product is then calculated using Monte Carlo quadrature. This converges slowly, resulting in long runtimes if the evaluation of the model function is expensive. The differentiation and integration of B-splines is numerically fast and analytically exact. Together with adaptive sparse grid discretization, they can be employed in higher-dimensional approximation. We use this to create a surrogate for the objective function, which provides us with better approximations for the gradient and thus better approximations for the active subspace. Furthermore we present a new integration technique for functions with a one-dimensional active subspace, that is based on a geometric interpretation of B-splines.

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