Prossimi Seminari

Lunedì 17 Dic ore 14:30
presso VII piano
seminario interdisciplinare
Modelling Dengue dynamics: how to approximate an epidemic attractor and to estimate the infectivity parameters
Stefanella Boatto
Migratory fluxes of humans and of insects of various species have favoured the spreading of diseases world-wise. It is important to stress that those epidemics can have strong social and economical impacts if not seriously controlled. Only in 2010 in Brazil, one million infected individual of which 80,000 where hospitalised. I shall present the SIR-Network model, introduced in Stolerman et al (2015), and revisite the SIR model with birth and death terms and time-varying infectivity parameter β(t). In the particular case of a sinusoidal parameter, we show that the average Basic Reproduction Number Ro, already introduced in Bacaer et al. (2006) is not the only relevant parameter and we emphasise the role played by the initial phase, the amplitude and the period. For a quite general slowly varying β(t) (not necessarily periodic) infectivity parameter all the trajectories of the system are proven to be attracted into a tubular region around a suitable curve, which is then an approximation of the underlying attractor. Numerical simulations are given and comparison with real data from Dengue epidemics in Rio de Janeiro allow us to estimate the infectivity rate and make predictions about what are the periods more at risk of infection.
Mercoledì 19 Dic ore 14:00
presso - Aula Da Stabilire -
seminario di algebra e geometria
Parabolic geometries
Andrea Santi
Venerdì 21 Dic ore 11:00
presso Aula Cremona
seminario di analisi matematica
nell'ambito della serie
Colloquio di Dipartimento
The many faces of dispersive equations
Gigliola Staffilani
In recent years great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a variety of techniques from Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of problems connected with dispersive equations, such as the derivation of a certain nonlinear Schrodinger equations from a quantum many-particles system, periodic Strichartz estimates, the concept of energy transfer, the invariance of a Gibbs measure associated to an infinite dimension Hamiltonian system and, if time allows it, non-squeezing theorems for such systems when they also enjoy a symplectic structure.