Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 904383, 7 pages
doi:10.1155/2009/904383
Research Article

The Complete Parameters Analysis of the Asymptotic Behaviour of a Logistic Epidemic Model with Two Stochastic Perturbations

Dejun Fan,1,2 Ke Wang,2 and Ling Hong1

1MOE Key Lab. for Strength and Vibration, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
2Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, Shandong 264209, China

Received 3 January 2009; Revised 28 July 2009; Accepted 22 August 2009

Academic Editor: Bin Liu

Copyright © 2009 Dejun Fan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A simple model of the dynamics of an infectious disease, taking into account environmental variability in the form of Gaussian white noise in the disease transmission rate and the increase in mortality rate due to disease, has been investigated. The probability distribution for the proportion of infected animals, plus its mean, mode, and variance, is found explicitly.