Introduction: The 2D:4D digit ratio is sexually-dimorphic, probably due to testosterone action through the perinatal period. We characterize the 2D:4D ratio in newborn (NB) infants, in between the pre-and postnatal surges of testosterone, and relate it to the mother's 2D:4D and to testosterone levels in the amniotic fluid (AF). Subjects and methods: Testosterone was assayed in samples of maternal plasma and AF collected at amniocentesis. Shortly after birth, 106 NBs and their mothers were measured for 2D:4D ratio. Results: NB males had lower mean 2D:4D ratios than females but this dimorphism was significant only for the left hand (males: 0.927; females: 0.950; p =0.004). Mothers who had sons had lower 2D:4D ratios than those who had daughters and the mother's 2D:4D were higher than those of NBs regardless of sex. Both hands of NB females were negatively correlated with AF testosterone and positively correlated with the mother's 2D:4D, but males showed no significant associations. Maternal plasma testosterone also showed a negative weak correlation with NB's digit ratio in both sexes. Conclusions: Sexual dimorphism at birth was only significant for the left hand, in contrast with reports of greater right hand dimorphism, suggesting that postnatal testosterone is determinant for 2D:4D stabilization. The lower 2D:4D ratios in mothers who had sons support claims that hormone levels in parents are influential for determining their children's sex. NB female's digit ratio, but not males', was associated to the level of AF testosterone. The mother's 2D:4D ratios were positively correlated with their daughters' 2D:4D, but the same was not observed for male NBs, suggesting that prenatal testosterone levels in male fetus lead their 2D:4D ratios to stray from their mothers' with high individual variability.

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There is a consensus that mass vaccination against SARS-CoV-2 will ultimately end the COVID-19 pandemic. However, it is not clear when and which control measures can be relaxed during the rollout of vaccination programmes. We investigate relaxation scenarios using an age-structured transmission model that has been fitted to age-specific seroprevalence data, hospital admissions, and projected vaccination coverage for Portugal. Our analyses suggest that the pressing need to restart socioeconomic activities could lead to new pandemic waves, and that substantial control efforts prove necessary throughout 2021. Using knowledge on control measures introduced in 2020, we anticipate that relaxing measures completely or to the extent as in autumn 2020 could launch a wave starting in April 2021. Additional waves could be prevented altogether if measures are relaxed as in summer 2020 or in a step-wise manner throughout 2021. We discuss at which point the control of COVID-19 would be achieved for each scenario.

Population patterns of infection are determined largely by susceptibility to infection. Infection and vaccination induce an immune response that, typically, reduces susceptibility to subsequent infections. With a general epidemic model, we detect a 'reinfection threshold', above which reinfection is the principal type of transmission and, consequently, infection levels are much higher and vaccination fails. The model is further developed to address human tuberculosis (TB) and the impact of vaccination. The bacille Calmette-Guérin (BCG) is the only vaccine in current use against TB, and there is no consensus about its usefulness. Estimates of protection range from 0 to 80%, and this variability is aggravated by an association between low vaccine efficacy and high prevalence of the disease. We propose an explanation based on three postulates: (i) the potential for transmission varies between populations, owing to differences in socio-economic and environmental factors; (ii) exposure to mycobacteria induces an immune response that is partially protective against reinfection; and (iii) this protection is not significantly improved by BCG vaccination. These postulates combine to reproduce the observed trends, and this is attributed to a reinfection threshold intrinsic to the transmission dynamics. Finally, we demonstrate how reinfection thresholds can be manipulated by vaccination programmes, suggesting that they have a potentially powerful role in global control.

The effect of spatial correlations on the spread of infectious diseases was investigated using a stochastic SIR (Susceptible-Infective-Recovered) model on complex networks. It was found that in addition to the reduction of the effective transmission rate, through the screening of infectives, spatial correlations may have another major effect through the enhancement of stochastic fluctuations. As a consequence large populations will have to become even larger to 'average out' significant differences from the solution of deterministic models. Furthermore, time series of the (unforced) model provide patterns of recurrent epidemics with slightly irregular periods and realistic amplitudes, suggesting that stochastic models together with complex networks of contacts may be sufficient to describe the long term dynamics of some diseases.The spatial effects were analysed quantitatively by modelling measles and pertussis, using a SEIR (Susceptible-Exposed-Infective-Recovered) model. Both the period and the spatial coherence of the epidemic peaks of pertussis are well described by the unforced model for realistic values of the parameters.

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