Guaranteed computation methods for compartmental in-series models under uncertainty

Abstract

The pattern of some real phenomenon can be described by compartmental in-series models. Nevertheless, most of these processes are characterized by their variability, which produces that the exact values of the model parameters are uncertain, although they can be bounded by intervals. The aim of this paper is to compute tight solution envelopes that guarantee the inclusion of all possible behaviors of such processes. Current methods, such as monotonicity analysis, enable us to obtain guaranteed solution envelopes. However, if the model includes nonmonotone compartments or parameters, the computation of solution envelopes may produce a significant overestimation. Our proposal consists of performing a change of variables in which the output is unaltered, and the model obtained is monotone with respect to the uncertain parameters. The monotonicity of the new system allows us to compute the output bounds for the original system without overestimation. These model transformations have been developed for linear and non-linear systems. Furthermore, if the conditions are not completely satisfied, a novel method to compute tight solution envelopes is proposed. The methods exposed in this paper have been applied to compute tight solution envelopes for two different models: a linear system for glucose modeling and a non-linear system for an epidemiological model.