An optimal time control problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter

In this paper, we study the optimal time problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter. To begin with, we build an exact solution. The dependence of this solution as regards the scaling parameter naturally opens the way to study the existence and uniqueness of an optimal time control. If, moreover, one assumes the L∞ − null controllability, it enables to establish a bang-bang type property

Low incidence of SARS-CoV-2, risk factors of mortality and the course of illness in the French national cohort of dialysis patients

International audienceThe aim of this study was to estimate the incidence of COVID-19 disease in the French national population of dialysis patients, their course of illness and to identify the risk factors associated with mortality. Our study included all patients on dialysis recorded in the French REIN Registry in April 2020. Clinical characteristics at last follow-up and the evolution of COVID-19 illness severity over time were recorded for diagnosed cases (either suspicious clinical symptoms, characteristic signs on the chest scan or a positive reverse transcription polymerase chain reaction) for SARS-CoV-2. A total of 1,621 infected patients were reported on the REIN registry from March 16th, 2020 to May 4th, 2020. Of these, 344 died. The prevalence of COVID-19 patients varied from less than 1% to 10% between regions. The probability of being a case was higher in males, patients with diabetes, those in need of assistance for transfer or treated at a self-care unit. Dialysis at home was associated with a lower probability of being infected as was being a smoker, a former smoker, having an active malignancy, or peripheral vascular disease. Mortality in diagnosed cases (21%) was associated with the same causes as in the general population. Higher age, hypoalbuminemia and the presence of an ischemic heart disease were statistically independently associated with a higher risk of death. Being treated at a selfcare unit was associated with a lower risk. Thus, our study showed a relatively low frequency of COVID-19 among dialysis patients contrary to what might have been assumed