Many attempts to build epidemic models of the current Covid-19 epidemic have been made in the recent past. However, only models postulating permanent immunity have been proposed. In this paper, we propose a SI(R) model in order to forecast the evolution of the epidemic under the hypothesis of not permanent immunity. This model offers an analytical solution to the problem of finding possible steady states, providing the following equilibrium values: Susceptible about 17%, Recovered (including deceased and healed) ranging from 79 to 81%, and Infected ranging from 2 to 4%. However, it is crucial to consider that the results concerning the recovered, which at first glance are particularly impressive, include the huge proportion of asymptomatic subjects. On the basis of these considerations, we analyse the situation in the province of Pesaro-Urbino, one of the main outbreaks of the epidemic in Italy.

Since the beginning of the COVID-19 pandemic, a large number of epidemiological models have been developed. The principal objective of the present study is to provide a new six-compartment model for the COVID-19 pandemic, which takes into account both the possibility of re-infection and the differentiation between asymptomatic and symptomatic infected subjects. The model, denoted as θ-SI(R)D, is a six-compartment model, described by as many ordinary differential equations. The six compartments are denoted as Susceptible (S), Symptomatic Infected (Is), Asymptomatic Infected (Ia), Recovered from Asymptomatic fraction (Ra), Recovered from Symptomatic fraction (Rs), and Deceased (D). Such a model has no analytical solutions, so we performed both a simulation and a model validation (R2=0.829). Based on the results of our simulations (and, on the other hand, on the results of most of the models in the scientific literature), it is possible to draw the reasonable conclusion that the epidemic tends, even without vaccination, to a steady state.

The humoral response after vaccination was evaluated in 1248 individuals who received different COVID-19 vaccine schedules. The study compared subjects primed with adenoviral ChAdOx1-S (ChAd) and boosted with BNT162b2 (BNT) mRNA vaccines (ChAd/BNT) to homologous dosing with BNT/BNT or ChAd/ChAd vaccines. Serum samples were collected at two, four and six months after vaccination, and anti-Spike IgG responses were determined. The heterologous vaccination induced a more robust immune response than the two homologous vaccinations. ChAd/BNT induced a stronger immune response than ChAd/ChAd at all time points, whereas the differences between ChAd/BNT and BNT/BNT decreased over time and were not significant at six months. Furthermore, the kinetic parameters associated with IgG decay were estimated by applying a first-order kinetics equation. ChAd/BNT vaccination was associated with the longest time of anti-S IgG negativization and with a slow decay of the titer over time. Finally, analyzing factors influencing the immune response by ANCOVA analysis, it was found that the vaccine schedule had a significant impact on both the IgG titer and kinetic parameters, and having a Body Mass Index (BMI) above the overweight threshold was associated with an impaired immune response. Overall, the heterologous ChAd/BNT vaccination may offer longer-lasting protection against SARS-CoV-2 than homologous vaccination strategies.

The endeavor to evaluate the linearity of myofibrillar structures and their potential deviation from a straight line is a fascinating problem in muscle tissue image analysis. In this Letter, we suggest two different strategies for solving the same challenge. The first strategy is based on an alignment index, which could be derived by comparing the sum of the lengths of the individual sarcomeres with the distance between the "head" of the first and the "tail" of the last sarcomere. The second strategy relies on circular statistics, which takes a cue from an already suggested method. Our proposed methods are alternatives: the former has the advantage of simplicity; the latter is certainly more elegant and gives greater substance to statistical analysis, but in contrast, it also has greater computational complexity.

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