Mathematical Modeling and Analysis of Asthma Stability and Severity

Asthma is one of the most common chronic conditions in the United States. Asthma affects about one in fifteen people. It affects children more than adults and blacks more than whites. People with asthma experience attacks of wheezing, breathlessness, chest tightness, and coughing. Asthma can be fatal and the costs for the disease (direct and indirect) are approximated to be tens of billions of dollars each year. There is no cure for asthma. However; for most people if asthma is controlled well they can lead normal, active lives. Therefore asthma controllability is a main factor in clinical practice. In order to control asthma, the disease has to be completely understood. Asthma is very heterogeneous and this makes the exact diagnosis and control procedures difficult. To better evaluate and study asthma, mathematical tools can be very beneficial. In this study we first develop a complete system for lung impedance analysis of laboratory models of asthma. Our designed system is capable of precisely diagnosing the diseased models and predicting the severity of their condition. We also evaluate the treatment progress in mouse models of asthma. We then study an asthma database of humans including measurements of four related laboratory parameters and cluster patients based on inherent properties of the study variables. This mathematical approach clustered patients with specific characteristics and segregated the unstable asthmatic patients in a single group. Our method is very promising in predicting the instability of asthma, which is highly correlated with frequent asthma attacks and increased utilization of care

Modélisation des phénomènes de diffusion thermique dans un milieu fini homogène en vue de l’analyse, de la synthèse et de la validation de commandes robustes

The work of this thesis concerns the study of the thermal diffusion phenomena to have a model (white box approach) for the analysis, the frequency synthesis and the time validation of robust commands. The Part 1 composed of chapter 1 focuses on the definitions and the interpretations of the integro-differential non-integer operator. The simulation problem in the time domain of the fractional differential systems is specified. Part 2 entitled "Analytical Study" includes two chapters whose objective is to make a detailed analysis of the fractional order behavior, first in a semi-infinite medium (chapter 2), then in a finite medium (chapter 3). Part 3, entitled "Numerical simulation of time responses" combining two chapters (4 and 5), aims the implementation of the "thermal process" plant (model validation of a finite medium) of a simulator of the thermal control loop time responses.Les travaux de cette thèse concernent l’étude des phénomènes de diffusion thermique en vue de disposer de modèles de connaissances (approche boîte blanche) pour l’analyse, la synthèse fréquentielle et la validation temporelle de commandes robustes. La Partie 1 composée du chapitre 1 se focalise sur les définitions et les interprétations de l’opérateur intégro-différentiel non entier. La problématique de la simulation, dans le domaine temporel, des SDNE est précisée. La Partie 2 intitulée "Etude analytique" regroupe deux chapitres dont l’objectif est de faire une analyse fine des comportements d’ordre non entier, d’abord dans un milieu semi-infini (chapitre 2), puis dans un milieu fini (chapitre 3). La Partie 3, intitulée "Simulation numérique des réponses temporelles" regroupant deux chapitres (4 et 5), a pour finalité la mise en oeuvre de la partie « Procédé thermique » (modèle de validation d’un milieu fini) d’un simulateur des réponses temporelles d’une boucle de régulation thermique