Models of the tumour spheroid response to radiation: identifiability analysis

Two spatially uniform models of tumour growth after a single instantaneous radiative treatment are presented in this paper. The two ordinary differential equations models presented may be obtained from two equivalent partial derivative equations models, by integration respect to the radial distance. The main purpose of the paper is to study their identifiability properties. In fact, a preliminary condition, that is necessary to verify before performing the parameters' identification, is the global identifiability of a model. A detailed study of the identifiability properties of the two models is done, pointing out that the first one, the basic model, is only locally identifiable, whereas the second one, the model with subcompartments, is globally identifiable, provided that the responses to two different radiation doses are considered.