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Chin. Phys. B, 2015, Vol. 24(5): 050204    DOI: 10.1088/1674-1056/24/5/050204
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Effects of two types of noise and switching on the asymptotic dynamics of an epidemic model

Xu Wei (徐伟)a, Wang Xi-Ying (王喜英)a, Liu Xin-Zhi (刘新芝)b
a Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
b Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Abstract  This paper mainly investigates dynamics behavior of HIV (human immunodeficiency virus) infectious disease model with switching parameters, and combined bounded noise and Gaussian white noise. This model is different from existing HIV models. Based on stochastic Itô lemma and Razumikhin-type approach, some threshold conditions are established to guarantee the disease eradication or persistence. Results show that the smaller amplitude of bounded noise and R0<1 can cause the disease to die out; the disease becomes persistent if R0>1. Moreover, it is found that larger noise intensity suppresses the prevalence of the disease even if R0>1. Some numerical examples are given to verify the obtained results.
Keywords:  stochastic switched HIV model      Razumikhin-type approach      extinction      permanence  
Received:  27 November 2014      Revised:  05 February 2015      Accepted manuscript online: 
PACS:  02.50.Fz (Stochastic analysis)  
  05.10.Gg (Stochastic analysis methods)  
  64.10.+h (General theory of equations of state and phase equilibria)  
  87.16.A- (Theory, modeling, and simulations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11172233, 11472212, 11272258, and 11302170) and the Natural Science and Engineering Research Council of Canada (NSERC).
Corresponding Authors:  Wang Xi-Ying     E-mail:  wangxiying1768@mail.nwpu.edu.cn, wangxiying668@163.com
About author:  02.50.Fz; 05.10.Gg; 64.10.+h; 87.16.A-

Cite this article: 

Xu Wei (徐伟), Wang Xi-Ying (王喜英), Liu Xin-Zhi (刘新芝) Effects of two types of noise and switching on the asymptotic dynamics of an epidemic model 2015 Chin. Phys. B 24 050204

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