A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event.

In 2020 the world faced with a pandemic spread that affected almost everything of humans' social and health life. Regulations to decrease the epidemiological spread and studies to produce the vaccine of SARS-CoV-2 were on one side a hope to return back to the regular life, but on the other side there were also notable criticism about the vaccines itself. In this study, we established a fractional order differential equations system incorporating the vaccinated and re-infected compartments to a S I R frame to consider the expanded and detailed form as an S V I I v R model. We considered in the model some essential parameters, such as the protection rate of the vaccines, the vaccination rate, and the vaccine's lost efficacy after a certain period. We obtained the local stability of the disease-free and co-existing equilibrium points under specific conditions using the Routh-Hurwitz Criterion and the global stability in using a suitable Lyapunov function. For the numerical solutions we applied the Euler's method. The data for the simulations were taken from the World Health Organization (WHO) to illustrate numerically some scenarios that happened.

Free carnitine levels in respiratory distress syndrome during the first week of life.

Antenatal carnitine administration has been shown to induce fetal lung maturity by increasing pulmonary surfactant in animal and human studies. The aim of this study was to investigate serum free carnitine (FC) levels in preterm infants with respiratory distress syndrome (RDS) and controls during the first week of postnatal life. The study groups consisted of 76 preterm infants with gestational ages ranging from 28 to 36 weeks, and birthweights ranging from 1046 to 2352 g. Serum FC levels were measured in preterm infants (group A, 37 with RDS; group B, 39 controls without RDS) within the first 6 hours after birth, on days 3 and 7. For specific analyses, serum FC levels were determined for gestational ages 28 to 31 weeks and 32 to 36 weeks in both groups. Initial FC levels were decreased insignificantly in group A (22.5 +/- 7.3 micromol/L) compared with group B (23.5 +/- 6.8 micromol/L; P > 0.05). On days 3 and 7 of life, serum FC levels were significantly lower in group A (18.3 +/- 6.1 and 10.2 +/- 3.3 micromol/L, respectively) than in group B (23.4 +/- 7.1 and 22.8 +/- 3.7 micromol/L, respectively; P < 0.05 and P < 0.05, respectively) on days 3 and 7 of life, respectively. Serum FC level remained stable in the non-RDS group ( P > 0.05), but it decreased significantly in the RDS group during the first week of postnatal life ( P < 0.05). No differences were seen between the corresponding gestational age groups. Serum FC levels in RDS infants decreased from days 1 to 7. Decreased neonatal serum carnitine levels in preterm infants with RDS during the first week of life might be caused by increasing consumption of carnitine in lung tissue for surfactant synthesis.