Background The optimal treatment for patients with severe coronavirus-19 disease (COVID-19) and hyper-inflammation remains debated. Material and methods A cohort study was designed to evaluate whether a therapeutic algorithm using steroids with or without interleukin-1 antagonist (anakinra) could prevent death/invasive ventilation. Patients with a ≥5-day evolution since symptoms onset, with hyper-inflammation (CRP≥50mg/L), requiring 3–5 L/min oxygen, received methylprednisolone alone. Patients needing ≥6 L/min received methylprednisolone + subcutaneous anakinra daily either frontline or in case clinical deterioration upon corticosteroids alone. Death rate and death or intensive care unit (ICU) invasive ventilation rate at Day 15, with Odds Ratio (OR) and 95% CIs, were determined according to logistic regression and propensity scores. A Bayesian analysis estimated the treatment effects. Results Of 108 consecutive patients, 70 patients received glucocorticoids alone. The control group comprised 63 patients receiving standard of care. In the corticosteroid±stanakinra group (n = 108), death rate was 20.4%, versus 30.2% in the controls, indicating a 30% relative decrease in death risk and a number of 10 patients to treat to avoid a death (p = 0.15). Using propensity scores a per-protocol analysis showed an OR for COVID-19-related death of 0.9 (95%CI [0.80–1.01], p = 0.067). On Bayesian analysis, the posterior probability of any mortality benefit with corticosteroids+/-anakinra was 87.5%, with a 7.8% probability of treatment-related harm. Pre-existing diabetes exacerbation occurred in 29 of 108 patients (26.9%). Conclusion In COVID-19 non-ICU inpatients at the cytokine release phase, corticosteroids with or without anakinra were associated with a 30% decrease of death risk on Day 15.

Suppose ρ is a simple graph, then its eccentric harmonic index is defined as the sum of the terms 2 / e a + e b for the edges v a v b , where e a is the eccentricity of the a th vertex of the graph ρ . We symbolize the eccentric harmonic index (EHI) as H e = H e ρ . In this article, we determine H e for the Cartesian product (CP) of particularly chosen graphs. Lower bounds for H e of the CP of the two graphs are established. The formulas of EHI for the Hamming and Hypercube graphs are obtained. These obtained formulas can be used in QSAR and QSPR studies to get a better understanding of their applications in mathematical chemistry.