Epidemiological investigations and mathematical models have revealed that the rapid diffusion of Covid-19 can mostly be attributed to undetected infective individuals who continue to circulate and spread the disease: finding their number would be of great importance in the control of the epidemic. The dynamics of an infection can be described by the SIR model, which divides the population into susceptible (S), infective I, and removed R subjects. In particular, we exploited the Kermack-McKendrick epidemic model, which can be applied when the population is much larger than the fraction of infected subjects. We proved that the fraction of undetected infectives, compared to the total number of infected subjects, is given by 1-1R0, where R0 is the basic reproduction number. The mean value R0=2.102.09-2.11 for the Covid-19 epidemic in three Italian regions yielded a percentage of undetected infectives of 52.4% (52.2%-52.6%) compared to the total number of infectives. Our results, straightforwardly obtained from the SIR model, highlight the role of undetected carriers in the transmission and spread of the SARS-CoV-2 infection. Such evidence strongly recommends careful monitoring of the infective population and ongoing adjustment of preventive measures for disease control until a vaccine becomes available for most of the population.

Entropy is a thermodynamic variable statistically correlated with the disorder of a system. The hypothesis that entropy can be used to identify potentially unhealthy conditions was first suggested by Schrödinger, one of the founding fathers of quantum mechanics. Shannon later defined entropy as the quantity of information stored in a system. Shannon’s entropy has the advantage of being adaptable across a variety of disciplines, including genetic studies on complex immunogenetic systems such as the human leukocyte antigen (HLA) and killer-cell immunoglobulin-like receptor (KIR) systems. In our study, entropy associated to the HLA and KIR systems was compared between a cohort of 619 Sardinian healthy controls and a group of 270 patients affected by multiple sclerosis (MS), the latter stratified into 81 patients with primary progressive multiple sclerosis (PPMS) and 189 patients with relapsing remitting multiple sclerosis (RRMS). The entropy associated to HLA four-loci haplotypes (A, B, C, DR) and combinations of two inhibitory KIR genes was significantly higher in patients affected by RRMS than in healthy controls. No significant differences were observed for patients with PPMS. By calculating the total HLA and KIR entropy ratio in each subject, it was possible to determine the individual risk of developing MS, particularly RRMS. In addition to the standard statistical methods used to evaluate immunogenetic parameters associated to immune-mediated disease, the analysis of entropy measures the global disorder status deriving from these parameters. This innovative approach may represent a useful complementary tool to the risk assessment of immune-mediated disorders. Improved risk assessment is particularly important for family members of patients with MS. However, further investigation is warranted to confirm our findings and to evaluate the validity of the entropy-based method in other types of immune-mediated disorders.

We propose a simple approach to the calculation of the entanglement entropy of a spherically symmetric quantum system composed of two separate regions. We consider bound states of the system described by a wave function that is scale invariant and vanishes exponentially at infinity. Our result is in accordance with the holographic bound on entropy and shows that entanglement entropy scales with the area of the boundary.

Idiopathic pulmonary fibrosis (IPF) is a chronic, progressive lung disease characterized by the disruption of the alveolar and interstitial architecture due to extracellular matrix deposition. Emerging evidence suggests that genetic susceptibility plays a crucial role in IPF development. This study explores the role of human leukocyte antigen (HLA) alleles and haplotypes in IPF susceptibility and progression within the genetically distinct Sardinian population. Genotypic data were analyzed for associations with disease onset and progression, focusing on allele and haplotype frequencies in patients exhibiting slow (S) or rapid (R) progression. While no significant differences in HLA allele frequencies were observed between IPF patients and controls, the HLA-DRB1*04:05 allele and the extended haplotype (HLA-A*30:02, B*18:01, C*05:01, DQA1*05:01, DQB1*02:01, DRB1*03:01) were associated with a slower disease progression and improved survival (log-rank = 0.032 and 0.01, respectively). At 36 months, carriers of these variants demonstrated significantly better pulmonary function, measured with single-breath carbon monoxide diffusing capacity (DLCO%p) (p = 0.005 and 0.02, respectively). Multivariate analysis confirmed these findings as being independent of confounding factors. These results highlight the impact of HLA alleles and haplotypes on IPF outcomes and underscore the potential of the Sardinian genetic landscape to illuminate immunological mechanisms, paving the way for predictive biomarkers and personalized therapies.

Objectives The emergence of new SARS-CoV-2 variants is a major challenge in the management of Covid-19 pandemic. A crucial issue is to quantify the number of variants which may represent a potential risk for public health in the future. Methods We fitted the data on the most relevant SARS-CoV-2 variants recorded by the World Health Organization (WHO). The function exploited for the fit is related to the total number of infected subjects in the world since the start of the epidemic. Results We found that the number of relevant SARS-CoV-2 variants up to November 2021 was about 44. Moreover, the number of new relevant variants per ten million cases turned out to be 1.64 in November 2021, slightly decreased in comparison to the value of 2.29 in March 2020. Conclusions Our simple mathematical model can evaluate the number of relevant SARS-CoV-2 variants as the cumulative number of cases increase worldwide and may represent a useful tool in planning strategies to effectively contrast the pandemic.

Background: A crucial role in epidemics is played by the number of undetected infective individuals who continue to circulate and spread the disease. Epidemiological investigations and mathematical models have revealed that the rapid diffusion of Covid-19 can mostly be attributed to the large percentage of undocumented infective individuals who escape testing. Methods: The dynamics of an infection can be described by the SIR model, which divides the population into susceptible ( S ), infective ( I ) and removed ( R ) subjects. In particular, we exploited the Kermack and McKendrick epidemic model which can be applied when the population is much larger than the fraction of infected subjects. Results: We proved that the fraction of undocumented infectives, in comparison to the total number of infected subjects, is given by , where R ₀ is the basic reproduction number. The mean value R ₀ = 2.10 (2.09 − 2.11) for the Covid-19 epidemic in three Italian regions yielded a percentage of undetected infectives of 52.4% (52.2% - 52.6%) compared to the total number of infectives. Conclusions: Our results, straightforwardly obtained from the SIR model, highlight the role played by undetected carriers in the transmission and spread of the SARS-CoV-2 infection. Such evidence strongly recommends careful monitoring of the infective population and ongoing adjustment of preventive measures for disease control until a vaccine becomes available.