The last decade has seen an explosion in models that describe phenomena in
systems medicine. Such models are especially useful for studying signaling
pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to
showcase current mathematical and statistical techniques that enable modelers
to gain insight into (models of) gene regulation, and generate testable
predictions. We introduce a range of modeling frameworks, but focus on ordinary
differential equation (ODE) models since they remain the most widely used
approach in systems biology and medicine and continue to offer great potential.
We present methods for the analysis of a single model, comprising applications
of standard dynamical systems approaches such as nondimensionalization, steady
state, asymptotic and sensitivity analysis, and more recent statistical and
algebraic approaches to compare models with data. We present parameter
estimation and model comparison techniques, focusing on Bayesian analysis and
coplanarity via algebraic geometry. Our intention is that this (non exhaustive)
review may serve as a useful starting point for the analysis of models in
systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte