Characterisation of the sewage microbiome in four European cities throughout the COVID-19 pandemic by means of ecological and network modelling

The purpose of this work was to investigate possible patterns occurring in the sewage bacterial content of four cities (Bologna, Budapest, Rome, Rotterdam) over time (March 2020 - November 2021), also considering the possible effects of the lockdown periods due to the COVID-19 pandemic. The sewage metagenomics data were provided within VEO (Versatile Emerging infectious disease Observatory) project. The first analysis was the evaluation of the between samples diversity, looking for (dis)similarities among the cities, as well as among different time periods (seasonality). To this aim, we computed both similarity networks and Principal Coordinate Analysis (PCoA) plots based on the Bray-Curtis metric. Then, the alpha-biodiversity of the samples was estimated by means of different diversity indices. By looking at the temporal behaviour of the biodiversity in the four cities, we noticed an abrupt decrease in both Rome and Budapest in the Summer of 2020, that is related to: the prevalence of some species when the minimum occurred, and the change in correlations among species (studied via correlation networks), which is enriched in the period of minimum biodiversity. Rotterdam samples seem to be very different with respect to those from the other cities, as confirmed by PCoA. Moreover, the Rotterdam time series is proved to be stable and stationary also in terms of biodiversity. The low variability in the Rotterdam samples seems to be related to the species of Pseudomonas genus, which are highly variable and plentiful in the other cities, but are not among the most abundant in Rotterdam. Also, we observed that no seasonality effect emerged from the time series of the four cities. Regarding the impact of lockdown periods due to the COVID-19 pandemic, from the limited data available no effect on the time series considered emerges. More samples will be soon available and these analyses will be performed also on them, so that the possible effects of lockdowns may be studied.

Local and nonlocal integro-differential reaction-diffusion models for protein dynamics in Alzheimer's disease

In this work, integro-differential reaction-diffusion models are presented for the description of the temporal and spatial evolution of the concentrations of Abeta and tau proteins involved in Alzheimer's disease. Initially, a local model is analysed: this is obtained by coupling with an interaction term two heterodimer models, modified by adding diffusion and Holling functional terms of the second type. We then move on to the presentation of three nonlocal models, which differ according to the type of the growth (exponential, logistic or Gompertzian) considered for healthy proteins. In these models integral terms are introduced to consider the interaction between proteins that are located at different spatial points possibly far apart. For each of the models introduced, the determination of equilibrium points with their stability and a study of the clearance inequalities are carried out. In addition, since the integrals introduced imply a spatial nonlocality in the models exhibited, some general features of nonlocal models are presented. Afterwards, with the aim of developing simulations, it is decided to transfer the nonlocal models to a brain graph called connectome. Therefore, after setting out the construction of such a graph, we move on to the description of Laplacian and convolution operations on a graph. Taking advantage of all these elements, we finally move on to the translation of the continuous models described above into discrete models on the connectome. To conclude, the results of some simulations concerning the discrete models just derived are presented.