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Title of Journal: J Math Biol

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Abbravation: Journal of Mathematical Biology

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Springer Berlin Heidelberg

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DOI

10.1007/bfb0028742

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1432-1416

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A glycemiastructured population model

Authors: Alessandro Borri Simona Panunzi Andrea De Gaetano
Publish Date: 2015/10/06
Volume: 73, Issue: 1, Pages: 39-62
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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 glycemiastructured population model based on a linear partial differential equation with variable coefficients The model is characterized by three rate functions a newadult population glycemic profile a glycemiadependent mortality rate and a glycemiadependent 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 reallife data and we hypothesize some plausible modifications of the rate functions to obtain a more beneficial steadystate 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 individualbased 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

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