Long-term outcomes of the global tuberculosis and COVID-19 co-infection cohort

Background: Longitudinal cohort data of patients with tuberculosis (TB) and coronavirus disease 2019 (COVID-19) are lacking. In our global study, we describe long-term outcomes of patients affected by TB and COVID-19. Methods: We collected data from 174 centres in 31 countries on all patients affected by COVID-19 and TB between 1 March 2020 and 30 September 2022. Patients were followed-up until cure, death or end of cohort time. All patients had TB and COVID-19; for analysis purposes, deaths were attributed to TB, COVID-19 or both. Survival analysis was performed using Cox proportional risk-regression models, and the log-rank test was used to compare survival and mortality attributed to TB, COVID-19 or both. Results: Overall, 788 patients with COVID-19 and TB (active or sequelae) were recruited from 31 countries, and 10.8% (n=85) died during the observation period. Survival was significantly lower among patients whose death was attributed to TB and COVID-19 versus those dying because of either TB or COVID-19 alone (p<0.001). Significant adjusted risk factors for TB mortality were higher age (hazard ratio (HR) 1.05, 95% CI 1.03-1.07), HIV infection (HR 2.29, 95% CI 1.02-5.16) and invasive ventilation (HR 4.28, 95% CI 2.34-7.83). For COVID-19 mortality, the adjusted risks were higher age (HR 1.03, 95% CI 1.02-1.04), male sex (HR 2.21, 95% CI 1.24-3.91), oxygen requirement (HR 7.93, 95% CI 3.44-18.26) and invasive ventilation (HR 2.19, 95% CI 1.36-3.53). Conclusions: In our global cohort, death was the outcome in >10% of patients with TB and COVID-19. A range of demographic and clinical predictors are associated with adverse outcomes

Convergence in relative error for the porous medium equation in a tube

Given a bounded domain D ⊂ RN and m > 1, we study the long-time behaviour of solutions to the porous medium equation (PME) posed in a tube ∂tu = um in D × R, t > 0, with homogeneous Dirichlet boundary conditions on the boundary ∂ D×R and suitable initial datum at t = 0. In two previous works, Vázquez and Gilding & Goncerzewicz proved that a wide class of solutions exhibit a traveling wave behaviour, when computed at a logarithmic time-scale and suitably renormalized. In this paper, we show that, for large times, solutions converge in relative error to the Friendly Giant, i.e., the unique nonnegative solution to the PME posed in the section D of the tube (with homogeneous Dirichlet boundary conditions) having a special self-similar form. In addition,sharp rates of convergence and uniform bounds for the location of the free boundary of solutions are given