Stability and Hopf bifurcation of an HIV infection model with saturation incidence and two delays
Pages: 2365  2387,
Issue 6,
August
2017
doi:10.3934/dcdsb.2017121 Abstract
References
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Hui Miao  College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China (email)
Zhidong Teng  College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China (email)
Chengjun Kang  The Basic Science Department, Xinjiang Institute of Engineering, Urumqi, Xinjiang 830091, China (email)
1 
E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent paramaters, SIAM J. Math. Anal., 33 (2002), 11441165. 

2 
A. A. Canabarro, I. M. Gleria and M. L. Lyra, Periodic solutions and chaos in a nonlinear model for the delayed cellular immune response, Physica A, 342 (2004), 234241. 

3 
S. Chen, C. Cheng and Y. Takeuchi, Stability analysis in delayed withinhost viral dynamics with both viral and cellular infections, J. Math. Anal. Appl., 442 (2016), 642672. 

4 
R. V. Culshaw and S. Ruan, A delaydifferential equation model of HIV infection of CD4+Tcell, Math. Biosci., 165 (2000), 2739. 

5 
R. Culshaw, S. Ruan and G. Webb, A mathematical model of celltocell HIV1 that include a time delay, J. Math. Biol., 46 (2003), 425444. 

6 
D. Ebert, C. D. Z. Rohringer and H. J. Carius, Dose effects and densitydependent regulation of two microparasites of Daphnia magna, Oecologia, 122 (2000), 200209. 

7 
H. W. Hethcote, M. A. Lewis and P. Driessche, An epidemiological model with a delay and a nonlinear incidence rate, J. Math. Biol., 27 (1989), 4964. 

8 
G. Huang, W. Ma and Y. Takeuchi, Global properties for virus dynamics model with BeddingtonDeAngelis functional response, Appl. Math. Lett., 22 (2009), 16901693. 

9 
G. Huang, H. Yokoi, Y. Takeuchi, T. Kajiwara and T. Sasaki, Impact of intracellular delay, immune activation delay and nonlinear incidence on viral dynamics, Japan J. Indust. Appl. Math., 28 (2011), 383411. 

10 
R. A. Koup, J. T. Safrit, Y. Cao, C. A. Andrews, G. McLeod, W. Borkowsky, C. Farthing and D. D. Ho, Temporal association of cellular immune responses with the initial control of viremia in primary human immunodeficiency virus type 1 syndrome, J. Virol., 68 (1994), 46504655. 

11 
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Mathematics in Science and Engineering, 191, Academic Press, Inc., Boston, MA, 1993. 

12 
M. Y. Li and H. Shu, Global dynamics of a mathematical model for HTLV1 infection of CD4+T cells with delayed CTL response, Nonlinear Anal.: RWA., 13 (2012), 10801092. 

13 
Z. Ma, Y. Zhou, W. Wang and Z. Jin, Mathematical Models and Dynamics of Infectious Diseases, China Science Press, Beijing, 2004. 

14 
M. A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 7479. 

15 
P. W. Nelson and A. Perelson, Mathematical analysis of a delaydifferential equation model of HIV1 infection, Math. Biosci., 179 (2002), 7394. 

16 
R. Ouifki and G. Witten, Stability analysis of a model for HIV infection with RTI and three intracellular delays, Biosys., 95 (2009), 16. 

17 
K. A. Pawelek, S. Liu, F. Pahlevani and L. Rong, A model of HIV1 infection with two time delays: Mathematical analysis and comparison with patient data, Math. Biosci., 235 (2012), 98109. 

18 
R. R. Regoes, D. Ebert and S. Bonhoeffer, Dosedependent infection rates of parasites produce the Allee effect in epidemiology, Proc. R. Soc. Lond. Ser. B., 269 (2002), 271279. 

19 
H. Shu, L. Wang and J. Watmough, Global stability of a nonlinear viral infection model with in infinitely distributed intracellular delays and CTL immune response, SIAM J. Appl. Math., 73 (2013), 12801302. 

20 
X. Song and A. U. Neumann, Global stability and periodic solution of the viral dynamics, J. Math. Anal. Appl., 329 (2007), 281297. 

21 
X. Song, X. Zhou and X. Zhao, Properties of stability and Hopf bifurcation for a HIV infection model with time delay, Appl. Math. Modelling, 34 (2010), 15111523. 

22 
M. Stafford, L. Corey, Y. Cao, E. Daar, D. Ho and A. Perelson, Modelling plasma virus concentration during primary HIV infection, J. Theor. Biol., 203 (2000), 285301. 

23 
X. Tian and Rui. Xu, Global stability ang Hopf bifurcation of an HIV1 infection model with saturation incidence and delayed CTL immune response, Appl. Math. Comput., 237 (2014), 146154. 

24 
X. Wang, A. Elaiw and X. Song, Global properties of a delayed HIV infection model with CTL immune response, Appl. Math. Comput., 218 (2012), 94059414. 

25 
K. Wang, W. Wang, H. Pang and X. Liu, Complex dynamic behavior in a viral model with delayed immune response, Physica D, 226 (2007), 197208. 

26 
Y. Wang, Y. Zhou, F. Brauer and J. M. Heffernan, Viral dynamics model with CTL immune response incorporating antiretroviral therapy, J. Math. Biol., 67 (2013), 901934. 

27 
D. Wodarz, Hepatitis C virus dynamics and pathology: The role of CTL and antibody responses, J. Gen. Virol., 84 (2003), 17431750. 

28 
R. Xu, Global stability of an HIV1 infection model with saturation infection and intracellular delay, J. Math. Anal. Appl., 375 (2011), 7581. 

29 
Y. Yang, L. Zou and S. Ruan, Global dynamics of a delayed withinhost viral infection model with both virustocell and celltocell transmissions, Math. Biosci., 270 (2015), 183191. 

30 
X. Zhou, X. Song and X. Shi, A differential equation model of HIV infection of CD4+ Tcells with cure rate, J. Math. Anal. Appl., 342 (2008), 13421355. 

31 
H. Zhu, Y. Luo and M. Chen, Stability and Hopf bifurcation of a HIV infection model with CTLresponse delay, Comput. Math. Appl., 62 (2011), 30913102. 

32 
H. Zhu and X. Zou, Impact of delays in cell infection and virus production on HIV1 dynamics, Math. Med. Biol., 25 (2008), 99112. 

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