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Mathematical Modeling and Sensitivit...

Aggarwal, Manu.

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Mathematical Modeling and Sensitivity Analysis for Biological Systems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematical Modeling and Sensitivity Analysis for Biological Systems./
Author:	Aggarwal, Manu.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	127 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-03, Section: B.
Contained By:	Dissertations Abstracts International81-03B.
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13809839
ISBN:	9781085596251

Mathematical Modeling and Sensitivity Analysis for Biological Systems.
Aggarwal, Manu.

Mathematical Modeling and Sensitivity Analysis for Biological Systems. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 127 p.

Source: Dissertations Abstracts International, Volume: 81-03, Section: B.

Thesis (Ph.D.)--The Florida State University, 2019.

This item must not be sold to any third party vendors.

In this work, we propose a framework to develop testable hypotheses for the effects of changes in the experimental conditions on the dynamics of a biological system using mathematical models. We discuss the uncertainties present in this process and show how information from different experiment regimes can be used to identify a region in the parameter space over which subsequent mathematical analysis can be conducted. To determine the significance of variation in the parameters due to varying experimental conditions, we propose using sensitivity analysis. Using our framework, we hypothesize that the experimentally observed decrease in the survivability of bacterial populations of Xylella fastidiosa (causal agent of Pierce's Disease) upon addition of zinc, might be because of starvation of the bacteria in the biofilm due to an inhibition of the diffusion of the nutrients through the extracellular matrix of the biofilm.We also show how sensitivity is related to uncertainty and identifiability; and how it can be used to drive analysis of dynamical systems, illustrating it by analyzing a model which simulates bursting oscillations in pancreatic β-cells. For sensitivity analysis, we use Sobol' indices for which we provide algorithmic improvements towards computational efficiency. We also provide insights into the interpretation of Sobol' indices, and consequently, define a notion of the importance of parameters in the context of inherently flexible biological systems.

ISBN: 9781085596251Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Bacterial growth

Mathematical Modeling and Sensitivity Analysis for Biological Systems.
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245 1 0 $a Mathematical Modeling and Sensitivity Analysis for Biological Systems.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 127 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-03, Section: B.
500 $a Advisor: Cogan, Nick;Hussaini, M. Y.
502 $a Thesis (Ph.D.)--The Florida State University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a In this work, we propose a framework to develop testable hypotheses for the effects of changes in the experimental conditions on the dynamics of a biological system using mathematical models. We discuss the uncertainties present in this process and show how information from different experiment regimes can be used to identify a region in the parameter space over which subsequent mathematical analysis can be conducted. To determine the significance of variation in the parameters due to varying experimental conditions, we propose using sensitivity analysis. Using our framework, we hypothesize that the experimentally observed decrease in the survivability of bacterial populations of Xylella fastidiosa (causal agent of Pierce's Disease) upon addition of zinc, might be because of starvation of the bacteria in the biofilm due to an inhibition of the diffusion of the nutrients through the extracellular matrix of the biofilm.We also show how sensitivity is related to uncertainty and identifiability; and how it can be used to drive analysis of dynamical systems, illustrating it by analyzing a model which simulates bursting oscillations in pancreatic β-cells. For sensitivity analysis, we use Sobol' indices for which we provide algorithmic improvements towards computational efficiency. We also provide insights into the interpretation of Sobol' indices, and consequently, define a notion of the importance of parameters in the context of inherently flexible biological systems.
590 $a School code: 0071.
650 4 $a Applied mathematics. $3 2122814
650 4 $a Mathematics. $3 515831
650 4 $a Biostatistics. $3 1002712
653 $a Bacterial growth
653 $a Dynamical systems
653 $a Mathematical modeling
653 $a Sensitivity analysis
653 $a Sobol Indices
653 $a Xylella fastidiosa
690 $a 0364
690 $a 0405
690 $a 0308
710 2 $a The Florida State University. $b Mathematics. $3 2095897
773 0 $t Dissertations Abstracts International $g 81-03B.
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792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13809839