Modeling Nonlinear Dynamics in Biological Systems: Effects of Uncertainty

Engineering analysis and design problems frequently involve uncertain parameters and inputs, and propagating these uncertainties through a complex dynamic model can be a challenging problem. In this work, we demonstrate the use of Taylor model methods for propagating interval uncertainties through nonlinear ODE models. Intervals provide upper and lower bounds on uncertainties, but often more information is available, and this information may include measures of central tendency, measures of variation, or even a specific probability distribution. In such a case, we may use Taylor model methods combined with probability boxes (p-boxes) to propagate all provided information through the dynamic model. This allows us to obtain p-box representations of the uncertainties in the state variables and outputs of a nonlinear ODE model based on interval and p-box representations of initial states and parameters. Examples are used to demonstrate the potential of this approach for studying the effect of uncertainties with imprecise probability distributions.