Supplementary data are available at Bioinformatics online.

No abstract

Data-based mathematical modeling of biochemical reaction networks, e.g. by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present non-sloppy designs for a benchmark model.

Highlights d Mathematical modeling enables integration of heterogeneous data d Single-cell modeling captures a binary decision process d Multiple sources of cell-to-cell variability exist in erythroid progenitor cells d Minimal amount of active STAT5 is sufficient for erythroid progenitor cell survival

Ordinary differential equation models are frequently applied to describe the temporal evolution of epidemics. However, ordinary differential equation models are also utilized in other scientific fields. We summarize and transfer state-of-the art approaches from other fields like Systems Biology to infectious disease models. For this purpose, we use a simple SIR model with data from an influenza outbreak at an English boarding school in 1978 and a more complex model of a vector-borne disease with data from the Zika virus outbreak in Colombia in 2015-2016. Besides parameter estimation using a deterministic multistart optimization approach, a multitude of analyses based on the profile likelihood are presented comprising identifiability analysis and model reduction. The analyses were performed using the freely available modeling framework Data2Dynamics (data2dynamics.org) which has been awarded as best performing within the DREAM6 parameter estimation challenge and in the DREAM7 network reconstruction challenge.