- 145 views
- 190 downloads
Stochastic Model for Toxicity Assessment
-
- Author / Creator
- Zong, Fei
-
In this thesis, we study a mathematical model for the survival of a cellsâ population exposed to various chemical compounds with different concentrations. For experimental planning, it is important to find the threshold value for the initial concentrations at which the cells become extinct. First, we use a deterministic model to perform parameter estimations and model validations with the experimental data sets. We estimate the parameter sets for eight chemical compounds from different clusters. To account for parameter uncertainty, we derive a stochastic version of the model and perform the numerical analysis. The global Lipschitz condition is essential for strong convergence in most explicit methods; we relax this condition and prove convergence of the implicit Euler scheme with the one-sided Lipschitz conditions solely. Then we compare the Euler scheme, the tamed Euler scheme and the implicit Euler scheme by case studies in both stability and convergence analysis. Finally, the Monte Carlo simulations for three chemical compounds are presented to explore the distribution of thresholds.
-
- Subjects / Keywords
-
- Graduation date
- Spring 2018
-
- Type of Item
- Thesis
-
- Degree
- Master of Science
-
- License
- Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.