| Viruses pose a threat to human health. Understanding how viruses work helps us develop vaccines and antivirals. Experimental techniques are now advanced enough to provide quantitative data regarding viral infection. Using this data, we can develop mathematical models to describe viral infection processes. Two such modeling paradigms are deterministic and stochastic reaction systems. Useful mathematical models require accurate estimates of model parameters from data. In this dissertation, I present parameter estimation methods for deterministic and stochastic reaction models, focusing on the stochastic models. I present two new classes of parameter estimation methods for stochastic chemical kinetic models, namely, importance sampling and approximate direct methods. Using examples from systems biology, I demonstrate the use of these newly developed methods and compare them with literature methods with favorable results. Guidelines on experimental and model design and directions for further research are presented in the end. |
