The social cost of contacts: Theory and evidence for the first wave of the COVID-19 pandemic in Germany.

Building on the epidemiological SIR model, we present an economic model with heterogeneous individuals deriving utility from social contacts creating infection risks. Focusing on social distancing of individuals susceptible to an infection we theoretically characterize the gap between private and social cost of contacts. Our main contribution is to quantify this gap by calibrating the model with unique survey data from Germany on social distancing and impure altruism from the beginning of the COVID-19 pandemic. The optimal policy is to drastically reduce contacts at the beginning to almost eradicate the epidemic and keep them at levels that contain the pandemic at a low prevalence level. We find that also in laissez faire, private protection efforts by forward-looking, risk averse individuals would have stabilized the epidemic, but at a much higher prevalence of infection than optimal. Altruistic motives increase individual protection efforts, but a substantial gap to the social optimum remains.

Regions at Risk in the Knee Joint of Young Professional Soccer Players: Longitudinal Evaluation of Early Cartilage Degeneration by Quantitative T2 Mapping in 3 T MRI.

PURPOSE: The study aims to detect regions at risk for (pre-)osteoarthritis in the tibiofemoral joint of young professional soccer players by evaluating cartilage composition by T2 mapping in a 3 T magnetic resonance imaging setting. METHODS: In this longitudinal study, 20 professional adolescent soccer players were included. Tibiofemoral cartilage was assessed by quantitative T2 mapping and T2 values were evaluated by regions of interest analysis. Statistical evaluation, using Wilcoxon signed-rank tests, was performed to compare global T2 values and subregional T2 values between a baseline and a follow-up investigation 4.3 years later. Based on the average of playing time (15 years) we divided the cohort in 2 groups and differences were evaluated. RESULTS: When comparing baseline and follow-up, our findings showed statistically significant increases of the global medial tibial and femoral T2 values. The most noticeable results of the subregional T2 analysis were statistically significant increases in the medial posterior zones (deep femoral 36.1 vs. 39.5, P = 0.001; superficial femoral 57.0 vs. 62.4, P = 0.034; deep tibial 28.3 vs. 34.1, P = 0.009; superficial tibial 43.2 vs. 55.3, P = 0.002). CONCLUSION: The elevation of T2 values in the medial, especially medial posterior, compartment of the knee joint indicates that these regions are at risk for early cartilage degeneration already at the time of adolescence. The findings can help individualize and optimize training concepts and to be aware of the chronic stress on these vulnerable areas. Prevention programs should be established in young players to avoid further cartilage damage.

How long do Red Queen dynamics survive under genetic drift? A comparative analysis of evolutionary and eco-evolutionary models.

BACKGROUND: Red Queen dynamics are defined as long term co-evolutionary dynamics, often with oscillations of genotype abundances driven by fluctuating selection in host-parasite systems. Much of our current understanding of these dynamics is based on theoretical concepts explored in mathematical models that are mostly (i) deterministic, inferring an infinite population size and (ii) evolutionary, thus ecological interactions that change population sizes are excluded. Here, we recall the different mathematical approaches used in the current literature on Red Queen dynamics. We then compare models from game theory (evo) and classical theoretical ecology models (eco-evo), that are all derived from individual interactions and are thus intrinsically stochastic. We assess the influence of this stochasticity through the time to the first loss of a genotype within a host or parasite population. RESULTS: The time until the first genotype is lost ("extinction time"), is shorter when ecological dynamics, in the form of a changing population size, is considered. Furthermore, when individuals compete only locally with other individuals extinction is even faster. On the other hand, evolutionary models with a fixed population size and competition on the scale of the whole population prolong extinction and therefore stabilise the oscillations. The stabilising properties of intra-specific competitions become stronger when population size is increased and the deterministic part of the dynamics gain influence. In general, the loss of genotype diversity can be counteracted with mutations (or recombination), which then allow the populations to recurrently undergo negative frequency-dependent selection dynamics and selective sweeps. CONCLUSION: Although the models we investigated are equal in their biological motivation and interpretation, they have diverging mathematical properties both in the derived deterministic dynamics and the derived stochastic dynamics. We find that models that do not consider intraspecific competition and that include ecological dynamics by letting the population size vary, lose genotypes - and thus Red Queen oscillations - faster than models with competition and a fixed population size.

The Crohn's disease-associated Escherichia coli strain LF82 relies on SOS and stringent responses to survive, multiply and tolerate antibiotics within macrophages.

Adherent Invasive Escherichia coli (AIEC) strains recovered from Crohn's disease lesions survive and multiply within macrophages. A reference strain for this pathovar, AIEC LF82, forms microcolonies within phagolysosomes, an environment that prevents commensal E. coli multiplication. Little is known about the LF82 intracellular growth status, and signals leading to macrophage intra-vacuolar multiplication. We used single-cell analysis, genetic dissection and mathematical models to monitor the growth status and cell cycle regulation of intracellular LF82. We found that within macrophages, bacteria may replicate or undergo non-growing phenotypic switches. This switch results from stringent response firing immediately after uptake by macrophages or at later stages, following genotoxic damage and SOS induction during intracellular replication. Importantly, non-growers resist treatment with various antibiotics. Thus, intracellular challenges induce AIEC LF82 phenotypic heterogeneity and non-growing bacteria that could provide a reservoir for antibiotic-tolerant bacteria responsible for relapsing infections.

Immediate action is the best strategy when facing uncertain climate change.

Mitigating the detrimental effects of climate change is a collective problem that requires global cooperation. However, achieving cooperation is difficult since benefits are obtained in the future. The so-called collective-risk game, devised to capture dangerous climate change, showed that catastrophic economic losses promote cooperation when individuals know the timing of a single climatic event. In reality, the impact and timing of climate change is not certain; moreover, recurrent events are possible. Thus, we devise a game where the risk of a collective loss can recur across multiple rounds. We find that wait and see behavior is successful only if players know when they need to contribute to avoid danger and if contributions can eliminate the risks. In all other cases, act quickly is more successful, especially under uncertainty and the possibility of repeated losses. Furthermore, we incorporate influential factors such as wealth inequality and heterogeneity in risks. Even under inequality individuals should contribute early, as long as contributions have the potential to decrease risk. Most importantly, we find that catastrophic scenarios are not necessary to induce such immediate collective action.

Chaotic provinces in the kingdom of the Red Queen.

The interplay between parasites and their hosts is found in all kinds of species and plays an important role in understanding the principles of evolution and coevolution. Usually, the different genotypes of hosts and parasites oscillate in their abundances. The well-established theory of oscillatory Red Queen dynamics proposes an ongoing change in frequencies of the different types within each species. So far, it is unclear under what conditions Red Queen dynamics persists, especially when the number of types per species increases. Some models show that with many types of hosts and parasites or more species chaotic dynamics occur. In our analysis, an arbitrary number of types within two species are examined in a deterministic framework with constant or changing population size and very simple interactions. This general framework allows for analytical solutions for internal fixed points and their stability. The numerical analysis shows that for two species, once more than two types are considered per species, irregular dynamics in their frequencies can be observed in the long run. The nature of the dynamics depends strongly on the initial configuration of the system; the usual regular Red Queen oscillations are only observed when all types initially have similar abundance.