A comparison between random and stochastic modeling for a SIR model

Tomás Caraballo; Renato Colucci

doi:10.3934/cpaa.2017007

Article Contents

2017, Volume 16, Issue 1: 151-162. Doi: 10.3934/cpaa.2017007

This issue Previous Article Asymptotic behavior and uniqueness of traveling wave fronts in a delayed nonlocal dispersal competitive system Next Article Resonant problems for fractional Laplacian

A comparison between random and stochastic modeling for a SIR model

Tomás Caraballo^, and
Renato Colucci

Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080–Sevilla, Spain

Author Bio: E-mail address: renatocolucci@hotmail.com
E-mail address: caraball@us.es
E-mail address: caraball@us.es

Received: May 31, 2016

Revised: July 31, 2016

Published: January 2018

Partially supported by FEDER and Ministerio de Economía y Competitividad under grant MTM2015-63723-P and Junta de Andalucía under Proyecto de Excelencia P12-FQM-1492.

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Abstract

In this article, a random and a stochastic version of a SIR nonautonomous model previously introduced in ^[19] is considered. In particular, the existence of a random attractor is proved for the random model and the persistence of the disease is analyzed as well. In the stochastic case, we consider some environmental effect on the model, in fact, we assume that one of the coefficients of the system is affected by some stochastic perturbation, and analyze the asymptotic behavior of the solutions. The paper is concluded with a comparison between the two different modeling strategies.

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Mathematics Subject Classification: Primary: 34C11, 34F05; Secondary: 60H10.

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