A glycemia-structured population model
Authored by Alessandro Borri, Simona Panunzi, Gaetano Andrea De
Date Published: 2016
DOI: 10.1007/s00285-015-0935-7
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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.
Tags
Obesity
Overweight
growth
Epidemic
Mathematical-model
Glucose
Age-size structure
Diabetes progression