Polynomial Profits in Renewable Resources Management

A system of renewal equations on a graph provides a framework to describe the exploitation of a biological resource. In this context, we formulate an optimal control problem, prove the existence of an optimal control and ensure that the target cost function is polynomial in the control. In specific situations, further information about the form of this dependence is obtained. As a consequence, in some cases the optimal control is proved to be necessarily bang--bang, in other cases the computations necessary to find the optimal control are significantly reduced

Stability and Optimization in Structured Population Models on Graphs

We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular choice of the boundary condition allows to comprehend models with very different structures. In particular, we consider a juvenile-adult model, the problem of the optimal mating ratio and a model for the optimal management of biological resources. The stability result obtained allows to tackle various optimal management/control problems, providing sufficient conditions for the existence of optimal choices/controls.Comment: 22 pages, 7 figure

The Conservation of Marcus Aurelius' Monument. Technical studies

The equestrian bronze monument of Marcus Aurelius in Rome has been further investigated, after restoration, mainly to foresee possible damages caused by outdoor exposure. At the same time a copy of it has been cast by following a new original method to obtain the intermediate model. New non-destructive tests have heen carried out to execute the above researches and in the end old and new methodologies can be consldered as a complex experimental tool to study and control outdoor bronze monument

Differential Equations Modeling Crowd Interactions

Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an "ad hoc" well posedness theorem for systems of nonlocal conservation laws in several space dimensions interacting non locally with a system of ODEs. Numerical integrations show possible applications to the interaction of different groups of pedestrians, and also with other "agents".Comment: 26 pages, 5 figure

An economic evaluation of aripiprazole vs olanzapine adapted to the Italian setting using outcomes of metabolic syndrome and risk for diabetes in patients with schizophrenia

Giorgio L Colombo1, Mauro Caruggi2, Sergio Di Matteo1, Alessandro Rossi31S.A.V.E. Studi Analisi Valutazioni Economiche, Milano, Italy; 2Università degli Studi dell’Insubria, Varese, Italy; 3Università de L’Aquila, ItalyObjective: To evaluate the cost-effectiveness of aripiprazole and olanzapine in patients with schizophrenia.Methods: Data from a double-blind, randomized study demonstrating the efficacy of aripiprazole and olanzapine were used to observe new incidence of metabolic syndrome (26-week therapy) and to model the risk of developing diabetes over 5 years of therapy. Cumulative incidence of metabolic syndrome was compared using Kaplan–Meier estimates; diabetes risk was estimated using a validated, general population risk-prediction model. Economic assessment was conducted from the third-party payer perspective by evaluating pharmacotherapy costs of treating schizophrenia and medical costs associated with treating adverse metabolic effects in a hypothetical cohort of 1000 patients. Resource utilization and costs were derived from the underlying study and published data, using a 3% rate to discount costs and benefits.Results: For the patients switched from olanzapine to aripiprazole, treatment with aripiprazole was a dominant cost-saving strategy. Use of aripiprazole avoided 184 events of metabolic syndrome over 26 weeks of treatment, contributing to a real-world (RW) cost savings of €2.53 per patient and a total savings of approximately €465.52 over a 5-year period. For the same cohort, the risk-prediction model indicated that 34 occurrences of diabetes could be avoided over 5 years, corresponding to a RW cost savings of €56.86 per patient and a total saving of approximately €1,933.24. These savings reflect avoided costs in treating adverse metabolic events and comparable costs in the acquisition of aripiprazole.Conclusions: Maintenance aripiprazole therapy offers medical and economic benefits over olanzapine, reflected by reduced incidence of metabolic syndrome and diabetes and associated lower costs.Keywords: schizophrenia, cost-consequences, apripiprazole, olanzapine, metabolic syndrome, diabete