Miguel Angel Moreles

Parameter Estimation of Some Epidemic Models. The Case of Recurrent Epidemics Caused by Respiratory Syncytial Virus

The research presented in this paper addresses the problem of fitting a mathematical model to epidemic data. We propose an implementation of the Landweber iteration to solve locally the arising parameter estimation problem. The epidemic models considered consist of suitable systems of ordinary differential equations. The results presented suggest that the inverse problem approach is a reliable method to solve the fitting problem. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters against real data sets for the case of recurrent epidemics caused by the respiratory syncytial virus in children.

On Modeling Flow in Fractal Media form Fractional Continuum Mechanics and Fractal Geometry

In this work we present a model for radial flow in highly heterogenous porous media. Heterogeneity is modeled by means of fractal geometry, a heterogeneous medium is regarded as fractal if its Hausdorff dimension is non-integral. Our purpose is to present a derivation of the model consistent with continuum mechanics, capable to describe anomalous diffusion as observed in some naturally fractured reservoirs. Consequently, we introduce fractional mass and a generalized Gauss theorem to obtain a continuity equation in fractal media. A generalized Darcy law for flux completes the model. Then we develop the basic equation for Well test analysis as is applied in petroleum engineering. Finally, the equation is solved by Laplace transform and inverted numerically to illustrate anomalous diffusion. In this case by showing that the flow rate from fractal systems is smaller than that from the Euclidean system.

A classical approach to uniform null controllability for elastic beams

The Rayleigh beam equation is the formal limit of the Timoshenko beam equation as the shear modulus K/spl rarr/+/spl infin/. Null controllability is possible, that is, the evolution systems associated with the Rayleigh and Timoshenko equations can be driven to rest by applying appropriate controls at both ends of the beam. In this work we show that controllability of the Rayleigh system can be achieved by letting K/spl rarr/+/spl infin/ in the solution of the Timoshenko controllability problem.