Effects of two types of noise and switching on the asymptotic dynamics of an epidemic model

doi:10.1088/1674-1056/24/5/050204

中国物理B ›› 2015, Vol. 24 ›› Issue (5): 50204-050204.doi: 10.1088/1674-1056/24/5/050204

Effects of two types of noise and switching on the asymptotic dynamics of an epidemic model

徐伟^a, 王喜英^a, 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

收稿日期:2014-11-27 修回日期:2015-02-05 出版日期:2015-05-05 发布日期:2015-05-05
基金资助:
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).

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

Received:2014-11-27 Revised:2015-02-05 Online:2015-05-05 Published:2015-05-05
Contact: 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-
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: stochastic switched HIV model, Razumikhin-type approach, extinction, permanence

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.

Key words: stochastic switched HIV model, Razumikhin-type approach, extinction, permanence

中图分类号: (Stochastic analysis)

02.50.Fz

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)

徐伟, 王喜英, 刘新芝. Effects of two types of noise and switching on the asymptotic dynamics of an epidemic model[J]. 中国物理B, 2015, 24(5): 50204-050204.

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[J]. Chin. Phys. B, 2015, 24(5): 50204-050204.

参考文献 43

[1]	De Boer R J and Perelson A S 1998 J. Theor. Biol. 190 201
[2]	Perelson A S and Nelson P W 1999 SIAM Rev. 41 3
[3]	Hao P, Fan D, Wei J and Liu Q 2012 Commun. Nonlinear Sci. 17 4753
[4]	Arafa A A M, Rida S Z and Khalil M 2013 Appl. Math. Model. 37 2189
[5]	Yang Y P and Xiao Y N 2010 J. Math. Appl. 361 59
[6]	Li K Z, Xu Z P, Zhu G H and Ding Y 2014 Chin. Phys. B 23 118904
[7]	Wu Q C, Fu X C and Yang M 2011 Chin. Phys. B 20 046401
[8]	Nowak M A and Bangham C R 1996 Science 272 74
[9]	Patrick W N and Alan S N 2002 Math. Biosci. 179 73
[10]	Renshaw E 1995 Modelling Biological Population in Space and Time (Cambridge: Cambridge University Press)
[11]	Wodarz D and Nowak M A 2000 Bioessays 24 1178
[12]	Leenheer P D and Smith H L 2003 SIAM J. Appl. Math. 63 1313
[13]	D'Onofrio A 2002 Math. Comput. Model. 36 473
[14]	Wang Z G, Gao R M, Fan X M and Han Q X 2014 Chin. Phys. B 23 090201
[15]	Rong L, Feng Z and Perelson A S 2007 Bull. Math. Biol. 69 2027
[16]	Browne C J and Pilyugin S S 2012 B. Math. Biol. 73 562
[17]	Liu X Z and Stechlinski P 2012 Appl. Math. Model. 36 1974
[18]	Wang X Y, Xu Y, Cui Y J and Wang X M 2014 Abst. Appl. Anal. 2014 853960
[19]	Li D and Ma W B 2007 J. Math. Anal. Appl. 335 683
[20]	Pinto C and Carvalho A 2014 Commun. Nonlinear Sci. 19 693
[21]	Liu J, Liu X Z and Xie W C 2011 Automatica 47 899
[22]	Wang Q and Liu X Z 2011 J. Franklin I 349 1030
[23]	Zhang Y P, Liu X Z, Zhu H and Zeng Y 2014 Int. J. Bifurcat. Chaos 24 1450033
[24]	Beretta E, Kolmanovskii V and Shaikhet L 1998 Math. Comput. Simul. 45 269
[25]	Li M Y and Wang L 2014 Nonlinear Anal. RWA 17 147
[26]	Tuckwell H and Le Corfec E 1998 J. Theor. Biol. 195 451
[27]	Tan W Y and Xiang Z 1996 Math. Comput. Model. 24 67
[28]	Dalal N, Greenhalgh D and Mao X 2008 J. Math. Anal. Appl. 341 1084
[29]	Huang Z, Yang Q and Cao J 2011 Chaos Soliton. Fract. 44 954
[30]	Li D X, Xu W, Sun C Y and Wang L 2012 Phys. Lett. A 376 1771
[31]	Lei Y M and Xu W 2007 Acta Phys. Sin. 56 5103 (in Chinese)
[32]	Hao M L, Xu W, Gu X D and Qi L Y 2014 Chin. Phys. B 23 090501
[33]	Xu X, Wang X Y, Zhang H Q and Xu W 2012 Nonlinear Dyn. 68 7
[34]	Wang X Y, Xu X, Xu X and Zhang H Q 2011 J. Dyn. Contr. 9 135
[35]	Jiang L L, Luo X Q, Wu D and Zhu S Q 2012 Chin. Phys. B 21 090503
[36]	Sebastiano D F, Giulio C and Alberto D 2014 Nat. Comput. 13 297
[37]	Perelson A S, Neumann A, Markowitz M, Leonard J and Ho D 1996 Science 271 1582
[38]	van den Driessche P and Watmough J 2002 Math. Biosci. 180 29
[39]	Wang W and Zhao X Q 2008 J. Dyn. Differ. Eq. 20 699
[40]	Liu M and Wang K 2012 Appl. Math. Model. 36 5344
[41]	Guan Z H, Hill D and Shen X 2005 IEEE Trans. Automat. Contr. 50 1058
[42]	Luo Q and Mao X 2007 J. Math. Anal. Appl. 334 69
[43]	Adams B M, Banks H T, Davidian M, Kwon Hee-Dae, Tran H T, Wynne S N and Rosenberg E S 2005 J. Comput. Apppl. Math. 184 10

Effects of two types of noise and switching on the asymptotic dynamics of an epidemic model

Effects of two types of noise and switching on the asymptotic dynamics of an epidemic model

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