Mathematical models are a core component in the foundation of cancer theory and have been developed as clinical tools in precision medicine. Modeling studies for clinical applications often assume an individual’s characteristics can be represented as parameters in a model and are used to explain, predict, and optimize treatment outcomes. However, this approach relies on the identifiability of the underlying mathematical models. In this study, we build on the framework of an observing-system simulation experiment to study the identifiability of several models of cancer growth, focusing on the prognostic parameters of each model. Our results demonstrate that the frequency of data collection, the types of data, such as cancer proxy, and the accuracy of measurements all play crucial roles in determining the identifiability of the model. We also found that highly accurate data can allow for reasonably accurate estimates of some parameters, which may be the key to achieving model identifiability in practice. As more complex models required more data for identification, our results support the idea of using models with a clear mechanism that tracks disease progression in clinical settings. For such a model, the subset of model parameters associated with disease progression naturally minimizes the required data for model identifiability.

Abstract. Honey mesquite (Prosopis juliflora), a representative species of the Sonoran Desert ecosystem, was studied as a possible bioindicator for industrial smelter pollution. Samples from soils, leaves and bark were collected along distance and elevation gradients from the largest operating copper smelter in Arizona and analyzed for element concentrations of Zn, Cu, Fe, Ti, Mn, A1, Mg, Cs, Sm, Ce, U, Th, Yb, As, La, Hf, Sb, Sc, V, In, W, Ba, Br, K, Na, C1 and Au. Depending on the sample type -soil, leaf or bark -between 5 and 15 elements were identified as smelter immissions. Two distinct covariate element groups formed in samples from the study site could be related to the chemistry of different smelting processes. A common atmospheric transport pattern was found to exist for the smelter emittants Cu, Sb and As over long distances. The identification and specification of smelter immissions in honey mesquite makes this tree a well-suited bioindicator for industrial smelter pollution.