A simple planning problem for COVID-19 lockdown: a dynamic programming approach.

A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach.

Polycythemia as rare secondary direct manifestation of acromegaly: management and single-centre epidemiological data.

Polycythemia associated with acromegaly is usually caused by the systemic manifestations of the disease, such as sleep-apnea or concomitant erythropoietin-secreting kidney tumors. The recognition of underlying pathologies requires a thorough diagnostic process. We report a unique case of acromegaly with polycythemia, not caused by commonly described manifestations of the disease, and receding with octreotide therapy. The medical history of 141 acromegalic patients followed by the Endocrinology Unit of the San Martino University Hospital in Genoa has been also reviewed, together with the literature evidence for similar cases. The diagnostic workflow and 2-years follow-up of a 43-years old acromegalic, polycythemic man with a history of past smoking, moderate hypertension, and mental retardation are described. The hematological parameters of our cohort was retrospectively compared with those of a healthy, age/gender-related control group as well. Therapy with octreotide LAR, 20 mg i.m. q28d was begun soon after diagnosis of acromegaly in the polycythemic patient. Haematocrit level, hormonal setting, as well as pituitary tumor size and visual perimetry during treatment were recorded. Octreotide LAR treatment normalized hormonal alterations, as well as hematological parameters. Polycythemia has not recurred after 2 years of therapy. The median hemoglobin and hematocrit levels of the retrospectively analyzed cohort of acromegalic were significantly lower than normal ranges of a healthy, age/sex- related control population. In conclusions, polycythemia can be a direct, albeit rare, secondary manifestation of acromegaly, that must be considered during the diagnostic work-up of acromegalic patients presenting with such disorder.