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Titolo/Abstract/Parole chiave

Asymptotic mean-square stability analysis and simulations of a stochastic model for the human immune response with memory

Notarangelo, Girolama (2011) Asymptotic mean-square stability analysis and simulations of a stochastic model for the human immune response with memory. Tesi di Dottorato , Università degli Studi di Ferrara.

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    Abstract

    In this thesis we extended a deterministic model for the Human Immune response, consisting of a non-linear system of differential equations with distributed time delay, which was introduced by Beretta, Kirshner and Marino in 2007, by incorporating stochastic perturbations with multiplicative noise around equilibria of the deterministic model. Our aim is to study the robustness of the equilibria of the deterministic model for the human immune response system with respect to fluctuations due to considering the human body as a noisy enviroment. We do this by analysing the asymptotic mean square stability of the equilibria of our stochastic model. Our work could be divided roughly into two parts. In the first part we analyse the stability of a general non linear system of stochastic differential equations with distributed memory terms by studying the stability properties of the linearisation in the first approximation. First of all we state, using Halanay's inequalities, comparison results useful in the investigation of exponential mean square stability of linear stochastic delay differential systems with distributed memory terms. Then we provide conditions under which asymptotic mean square stability of a nonlinear system of stochastic delay differential equations is implied by the exponential mean square stability of linearised stochastic delay system in the first approximation. In the second part we apply the theoretical results obtained in the first part to investigate the stochastic stability properties of the equilibria of our stochastic model of human immune response. The theoretical results are illustrated by numerical simulations and an uncertainty and sensivity analysis of our stochastic model, suggesting that the deterministic model is robust with respect to the stochastic perturbations.

    Tipologia del documento:Tesi di Dottorato (Tesi di Dottorato)
    Data:1 Aprile 2011
    Relatore:Zanghirati, Gaetano - Buckwar, Evelyn - Carletti, Margherita
    Coordinatore ciclo:Ruggiero, Valeria
    Istituzione:Università degli Studi di Ferrara
    Dottorato:XXIII Anno 2008 > MATEMATICA E INFORMATICA
    Struttura:Dipartimento > Matematica
    Soggetti:Area 01 - Scienze matematiche e informatiche > MAT/08 Analisi numerica
    Parole chiave:Equazioni differenziali stocastiche con ritardo, stabilità, risposta immunitaria umana, simulazioni numeriche, Stochastic delay differential equations, stability, human immune response, numerical simulations
    Depositato il:13 Apr 2012 15:00

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