Abstract
This paper proposes a stochastic model to study the evolution of normal and excess weight population between 24 - 65 years old in the region of Valencia (Spain). An approximate solution process of the random model is obtained by taking advantage of Wiener-Hermite expansion together with a perturbation method (WHEP). The random model takes as starting point a classical deterministic SIS—type epidemiological model in order to improve it in several ways. Firstly, the stochastic model enhances the deterministic one because it considers uncertainty in its formulation, what it is considered more realistic in dealing with a complex problem as obesity is. Secondly, WHEP approach provides valuable information such as average and variance functions of the approximate solution stochastic process to random model. This fact is remarkable because other techniques only provide predictions in some a priori chosen points. As a consequence, we can compute and predict the expectation and the variance of normal and excess weight population in the region of Valencia for any time. This information is of paramount value to both doctors and health authorities to set optimal investment policies and strategies.
Highlights
In the physical, engineering, economical or epidemiological sciences, random differential equations arise in a quite natural manner in the description of models
An approximate solution process of the random model is obtained by taking advantage of Wiener-Hermite expansion together with a perturbation method (WHEP)
In this paper, based on this consideration, we propose to modify the obesity model (2.1), considering that the dynamic of normal weight subpopulation is described by the random differential equation: N t A BN t C N t 2 n t, (2.3)
Summary
In the physical, engineering, economical or epidemiological sciences, random differential equations arise in a quite natural manner in the description of models. As we will see, the random model takes as starting point useful conclusions provided by the classical deterministic approach In this way, the random model improves the deterministic one because it considers uncertainty in its formulation, what it is considered more realistic. The random model improves the deterministic one because it considers uncertainty in its formulation, what it is considered more realistic This approach provides valuable information such as average and variance functions of the approximate solution stochastic process. WHE constitutes a powerful technique to represent any stochastic process in terms of the so-called Wiener-Hermite polynomials as well as certain deterministic kernels to be calculated Interesting contributions where this technique have been used successfully to solve other class of random differential equations can be found in references [7,8,9,10] and other contained therein.
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