A glycemia-structured population model

Abstract

Structured models are population models in which the individuals are characterized with respect to the value of some variable of interest, called the structure variable. In the present paper, we propose a glycemia-structured population model, based on a linear partial differential equation with variable coefficients. The model is characterized by three rate functions: a new-adult population glycemic profile, a glycemia-dependent mortality rate and a glycemia-dependent average worsening rate. First, we formally analyze some properties of the solution, the transient behavior and the equilibrium distribution. Then, we identify the key parameters and functions of the model from real-life data and we hypothesize some plausible modifications of the rate functions to obtain a more beneficial steady-state behavior. The interest of the model is that, while it summarizes the evolution of diabetes in the population in a completely different way with respect to previously published Monte Carlo aggregations of individual-based models, it does appear to offer a good approximation of observed reality and of the features expected in the clinical setting. The model can offer insights in pharmaceutical research and be used to assess possible public health intervention strategies.

Keywords: Dynamical systems; Glycemia; PDEs; Qualitative behavior; Structured models.