Constructions for Nonadaptive Tropical Group Testing (preprint)

PCR testing is an invaluable diagnostic tool that has most recently seen widespread use during the COVID-19 pandemic. A recent work by Wang, Gabrys and Vardy proposed tropical codes as a model for group PCR testing. For a known but arbitrary number of infected persons, a sufficient condition on the underlying block design of a zero-error tropical code, called double disjunction, is proposed. Despite this, the parameters for which the construction of doubly disjunct block designs is known to exist are very limited. In this paper, we define probabilistic tropical codes and consider random block designs that are doubly disjunct with high probability. We also provide a deterministic construction for a doubly disjunct block design given a disjunct block design. We show that for certain choices of parameters, our probabilistic construction has vanishing error. Our constructions, combined with existing methods, give us three different ways to construct tropical codes. We compare the number of tests required by each, and bounds on the error.

The Association Between Quarantine Duration and Psychological Outcomes, Social Distancing, and Vaccination Intention During the Second Outbreak of COVID-19 in China

Objectives: To examine the association between quarantine duration and psychological outcomes, social distancing, as well as vaccination intention during the second outbreak of COVID-19 in China. Methods: A cross-sectional online survey was conducted in January 2021. Participants were invited to complete the measurement of quarantine duration, social distancing, psychological distress, wellbeing (WHO-5), and vaccination intention. Multiple linear regression and logistic regression were performed to examine the relationship between quarantine duration and psychological distress, wellbeing, social distancing, and vaccination intention. Results: Of the 944 participants, 17.2% of the participants experienced quarantine. Quarantine for 1–7 days increased the social distancing (β = 2.61 95% confidence interval (CI) 1.90–3.33) and vaccination intention (OR = 2.16 95% CI 1.22–3.82). Quarantine for >7 days was associated with the increased social distancing (β = 3.00 95% CI 2.37–3.64) and psychological distress (β = 1.03 95% CI 0.22–1.86), and decreased wellbeing (β = 1.27 95% CI 0.29–2.26). Conclusion: Longer quarantine duration showed increased social distancing, increased psychological distress, and decreased wellbeing. Quarantine for 1–7 days was associated with increased vaccination intention.