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David Ellis
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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When testing for a disease such as COVID-19, the standard method is individual testing: we take a sample from each individual and test these samples separately. An alternative is pooled testing (or group testing), where samples are mixed together in different pools, and those pooled samples are tested. When the prevalence of the disease is low and the accuracy of the test is fairly high, pooled testing strategies can be more efficient than individual testing. In this chapter, we discuss the mathematics of pooled testing and its uses during pandemics, in particular the COVID-19 pandemic. We analyse some one- and two-stage pooling strategies under perfect and imperfect tests, and consider the practical issues in the application of such protocols.
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Pooled testing offers an efficient solution to the unprecedented testing demands of the COVID-19 pandemic, although with potentially lower sensitivity and increased costs to implementation in some settings. Assessments of this trade-off typically assume pooled specimens are independent and identically distributed. Yet, in the context of COVID-19, these assumptions are often violated: testing done on networks (housemates, spouses, co-workers) captures correlated individuals, while infection risk varies substantially across time, place and individuals. Neglecting dependencies and heterogeneity may bias established optimality grids and induce a sub-optimal implementation of the procedure. As a lesson learned from this pandemic, this paper highlights the necessity of integrating field sampling information with statistical modeling to efficiently optimize pooled testing. Using real data, we show that (a) greater gains can be achieved at low logistical cost by exploiting natural correlations (non-independence) between samples -- allowing improvements in sensitivity and efficiency of up to 30% and 90% respectively; and (b) these gains are robust despite substantial heterogeneity across pools (non-identical). Our modeling results complement and extend the observations of Barak et al (2021) who report an empirical sensitivity well beyond expectations. Finally, we provide an interactive tool for selecting an optimal pool size using contextual information
A mathematical model for the COVID-19 pandemic spread, which integrates age-structured Susceptible-Exposed-Infected-Recovered-Deceased dynamics with real mobile phone data accounting for the population mobility, is presented. The dynamical model adjustment is performed via Approximate Bayesian Computation. Optimal lockdown and exit strategies are determined based on nonlinear model predictive control, constrained to public-health and socio-economic factors. Through an extensive computational validation of the methodology, it is shown that it is possible to compute robust exit strategies with realistic reduced mobility values to inform public policy making, and we exemplify the applicability of the methodology using datasets from England and France. Code implementing the described experiments is available at https://github.com/OptimalLockdown.
The unprecedented coronavirus disease 2019 (COVID-19) pandemic is still a worldwide threat to human life since its invasion into the daily lives of the public in the first several months of 2020. Predicting the size of confirmed cases is important for countries and communities to make proper prevention and control policies so as to effectively curb the spread of COVID-19. Different from the 2003 SARS epidemic and the worldwide 2009 H1N1 influenza pandemic, COVID-19 has unique epidemiological characteristics in its infectious and recovered compartments. This drives us to formulate a new infectious dynamic model for forecasting the COVID-19 pandemic within the human mobility network, named the SaucIR-model in the sense that the new compartmental model extends the benchmark SIR model by dividing the flow of people in the infected state into asymptomatic, pathologically infected but unconfirmed, and confirmed. Furthermore, we employ dynamic modeling of population flow in the model in order that spatial effects can be incorporated effectively. We forecast the spread of accumulated confirmed cases in some provinces of mainland China and other countries that experienced severe infection during the time period from late February to early May 2020. The novelty of incorporating the geographic spread of the pandemic leads to a surprisingly good agreement with published confirmed case reports. The numerical analysis validates the high degree of predictability of our proposed SaucIR model compared to existing resemblance. The proposed forecasting SaucIR model is implemented in Python. A web-based application is also developed by Dash (under construction).
We propose `Tapestry, a novel approach to pooled testing with application to COVID-19 testing with quantitative Reverse Transcription Polymerase Chain Reaction (RT-PCR) that can result in shorter testing time and conservation of reagents and testing kits. Tapestry combines ideas from compressed sensing and combinatorial group testing with a novel noise model for RT-PCR used for generation of synthetic data. Unlike Boolean group testing algorithms, the input is a quantitative readout from each test and the output is a list of viral loads for each sample relative to the pool with the highest viral load. While other pooling techniques require a second confirmatory assay, Tapestry obtains individual sample-level results in a single round of testing, at clinically acceptable false positive or false negative rates. We also propose designs for pooling matrices that facilitate good prediction of the infected samples while remaining practically viable. When testing $n$ samples out of which $k ll n$ are infected, our method needs only $O(k log n)$ tests when using random binary pooling matrices, with high probability. However, we also use deterministic binary pooling matrices based on combinatorial design ideas of Kirkman Triple Systems to balance between good reconstruction properties and matrix sparsity for ease of pooling. In practice, we have observed the need for fewer tests with such matrices than with random pooling matrices. This makes Tapestry capable of very large savings at low prevalence rates, while simultaneously remaining viable even at prevalence rates as high as 9.5%. Empirically we find that single-round Tapestry pooling improves over two-round Dorfman pooling by almost a factor of 2 in the number of tests required. We validate Tapestry in simulations and wet lab experiments with oligomers in quantitative RT-PCR assays. Lastly, we describe use-case scenarios for deployment.
Large-scale testing is considered key to assess the state of the current COVID-19 pandemic. Yet, the link between the reported case numbers and the true state of the pandemic remains elusive. We develop mathematical models based on competing hypotheses regarding this link, thereby providing different prevalence estimates based on case numbers, and validate them by predicting SARS-CoV-2-attributed death rate trajectories. Assuming that individuals were tested based solely on a predefined risk of being infectious implies the absolute case numbers reflect the prevalence, but turned out to be a poor predictor, consistently overestimating growth rates at the beginning of two COVID-19 epidemic waves. In contrast, assuming that testing capacity is fully exploited performs better. This leads to using the percent-positive rate as a more robust indicator of epidemic dynamics, however we find it is subject to a saturation phenomenon that needs to be accounted for as the number of tests becomes larger.
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