Statistical description of human addiction phenomena

TL;DR

This paper introduces a kinetic model using Fokker-Planck equations to describe the statistical evolution of human addiction phenomena, showing a stable relaxation towards a generalized Gamma distribution.

Contribution

It presents a novel class of Fokker-Planck equations modeling addiction dynamics and analyzes their stability and parameter independence.

Findings

Relaxation towards generalized Gamma density

Stable process independent of microscopic parameters

New kinetic approach to addiction phenomena

Abstract

We study the evolution in time of the statistical distribution of some addiction phenomena in a system of individuals. The kinetic approach leads to build up a novel class of Fokker--Planck equations describing relaxation of the probability density solution towards a generalized Gamma density. A qualitative analysis reveals that the relaxation process is very stable, and does not depend on the parameters that measure the main microscopic features of the addiction phenomenon.