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Tang, Saishuai (2010) STOCHASTIC METHODS IN MODELING THEIMMUNE RESPONSE. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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We discuss the application of deterministic and stochastic modeling techniques to problemsin immunology. First, we employ the example of a host response to influenza virusinfection to illustrate differences in the dynamical behavior of the deterministic and thestochastic models, and employ both versions in the analysis of the role of immune responsein controlling and suppressing the infection. Second, we develop a dynamical model of vocalfold inflammation and use random sampling techniques to calibrate the model againstavailable data.In the stochastic model, we analyze three solution techniques - Gillespie's stochastic simulationalgorithm, numerical solution of mean extinction time through the Laplace transformof the master equation, and approximate solution of a limiting case. Gillespie algorithm iscapable of dealing with large systems as the required memory depends linearly on number ofspecies, but is limited by computational time. Laplace's method is efficient and accurate butis limited by system size. We construct a novel combination of the two that takes advantageof both. We also derive an approximate Markov chain of the system and analytically computethe extinction times and probabilities in the limiting case when an infected cell generateslarge number of viruses. In the analysis of the human immune response, we find that innateresponse substantially reduces cell extinction probability, cellular response increases the virusextinction probability in limiting case, and adaptive response, combined with the other two,almost eliminates cell extinction and significantly increases virus extinction probability.In the model of vocal fold inflammation, a four-variable ordinary differential equation (ODE) model is presented. The ODE model characterizes cytokine interactions in phonotraumaand is calibrated with empirical data. Parameter values are estimated and theirprobability densities are sampled using Metropolis and parallel tempering algorithms. Sensitivityanalysis showed that 6 of 17 parameters suffice to retain the sensitivity of the modeltrajectories. The reduced parameter set is applied to individual data to be calibrated andpredict the individual outcome. The model is a part of larger study intended to find optimaltreatment strategy for phonotrauma through a personalized vocal exercise or rest program.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairSwigon, Davidswigon@pitt.eduSWIGON
Committee MemberDoiron, Brentbdoiron@pitt.eduBDOIRON
Committee MemberClermont,
Committee MemberRubin, Jonathan
Date: 1 October 2010
Date Type: Completion
Defense Date: 18 July 2010
Approval Date: 1 October 2010
Submission Date: 11 August 2010
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Extinction Probability; Gillespie’s Direct Method; Markov Chain Analysis; Metropolis Sampling; Parallel Tempering; Parameter Estimation and Reduction; Personalized Treatment Development; Roles of Immune Components; Vocal Fold Inflammation; Mean Extinction Time; Sensitivity Analysis; Stochastic Simulation Algorithm; Influenza Virus Infection; Numerical and Analytical Solution of Master Eqn
Other ID:, etd-08112010-164716
Date Deposited: 10 Nov 2011 19:59
Last Modified: 15 Nov 2016 13:48


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