Safe distancing in the time of COVID-19.

The spread of viruses such as SARS-CoV-2 brought new challenges to our society, including a stronger focus on safety across all businesses. Many countries have imposed a minimum social distance among people in order to ensure their safety. This brings new challenges to many customer-related businesses, such as restaurants, offices, theaters, etc., on how to locate their facilities (tables, seats etc.) under distancing constraints. We propose a parallel between this problem and that of locating wind turbines in an offshore area. The discovery of this parallel allows us to apply Mathematical Optimization algorithms originally designed for wind farms, to produce optimized facility layouts that minimize the overall risk of infection among customers. In this way we can investigate the structure of the safest layouts, with some surprising outcomes. A lesson learned is that, in the safest layouts, the facilities are not equally distanced (as it is typically believed) but tend to concentrate on the border of the available area-a policy that significantly reduces the overall risk of contagion.

Mathematical modelling of SARS-CoV-2 variant outbreaks reveals their probability of extinction.

When a virus spreads, it may mutate into, e.g., vaccine resistant or fast spreading lineages, as was the case for the Danish Cluster-5 mink variant (belonging to the B.1.1.298 lineage), the British B.1.1.7 lineage, and the South African B.1.351 lineage of the SARS-CoV-2 virus. A way to handle such spreads is through a containment strategy, where the population in the affected area is isolated until the spread has been stopped. Under such circumstances, it is important to monitor whether the mutated virus is extinct via massive testing for the virus sub-type. If successful, the strategy will lead to lower and lower numbers of the sub-type, and it will eventually die out. An important question is, for how long time one should wait to be sure the sub-type is extinct? We use a hidden Markov model for infection spread and an approximation of a two stage sampling scheme to infer the probability of extinction. The potential of the method is illustrated via a simulation study. Finally, the model is used to assess the Danish containment strategy when SARS-CoV-2 spread from mink to man during the summer of 2020, including the Cluster-5 sub-type. In order to avoid further spread and mink being a large animal virus reservoir, this situation led to the isolation of seven municipalities in the Northern part of the country, the culling of the entire Danish 17 million large mink population, and a bill to interim ban Danish mink production until the end of 2021.

Dynamic modeling of renal blood flow in Dahl hypertensive and normotensive rats.

A method is proposed in this paper which allows characterization of renal autoregulatory dynamics and efficiency using quantitative mathematical methods. Based on data from rat experiments, where arterial blood pressure and renal blood flow are measured, a quantitative model for renal blood flow dynamics is constructed. The mathematical structure for the dynamics is chosen as a "grey-box model," i.e. the model structure is inspired from physiology, but the actual parameters is found by numerical methods. Based on a number of experiments, features are extracted from the estimated parameters, which describe myogenic responses and tubuloglomerular feedback responses separately. The method is applied to data from normo- and hypertensive Dahl rats, and a discriminator that separates data from normotensive Dahl R rats and hypertensive Dahl S rats is constructed.