Year: 2010
Type: article
Abstract: 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.
Author: Saishuai Tang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1969723645