
Previous Article
Effect of residual stress on peak cap stress in arteries
 MBE Home
 This Issue

Next Article
Disease dynamics for the hometown of migrant workers
Impact of delay on HIV1 dynamics of fighting a virus with another virus
1.  Department of Applied Mathematics, Western University, London, Ontario N6A 5B7, Canada, Canada, Canada 
References:
[1] 
E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33 (2002), 11441165. doi: 10.1137/S0036141000376086. 
[2] 
S. Busenberg and K. Cooke, Vertically Transmitted Diseases: Models and Dynamics, Springer, New York, 1993. doi: 10.1007/9783642753015. 
[3]  
[4] 
J. Hale and S. Verduyn Lunel, Introduction to Functional Differential Equations, SpringerVerlag, New York, 1993. doi: 10.1007/9781461243427. 
[5] 
B. D. Hassard, N. D. Kazarinoff and Y.H. Wan, Theory and Applications of Hopf Bifurcation, Cambridge University Press, Cambridge, 1981. 
[6] 
X. Jiang, P. Yu, Z. Yuan and X. Zou, Dynamics of an HIV1 therapy model of fighting a virus with another virus, Journal of Biological Dynamics, 3 (2009), 387409. doi: 10.1080/17513750802485007. 
[7] 
T. Kajiwara, T. Saraki and Y. Takeuchi, Construction of lyapunov functionals for delay differential equations in virology and epidemiology, Nonlinear Analysis: Real World Applications, 13 (2012), 18021826. doi: 10.1016/j.nonrwa.2011.12.011. 
[8] 
J. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, 1976. 
[9] 
C. Michie, A. McLean, C. Alcock and P. Beverly, Lifespan of human lymphocyte subsets defined by cd45 isoforms, Nature, 360 (1992), 264265. doi: 10.1038/360264a0. 
[10] 
J. Mittler, B. Sulzer, A. Neumann and A. Perelson, Influence of delayed virus production on viral dynamics in HIV1 infected patients, Math. Biosci., 152 (1998), 143163. 
[11] 
P. W. Nelson, J. D. Murray and A. S. Perelson, A model of HIV1 pathogenesis that includes an intracellular delay, Mathematical Biosciences, 163 (2000), 201215. doi: 10.1016/S00255564(99)000553. 
[12] 
G. Nolan, Harnessing viral devices as pharmaceuticals: Fighting HIV1s fire with fire, Cell, 90 (1997), 821824. 
[13] 
T. Revilla and G. GarcíaRamos, Fighting a virus with a virus: A dynamic model for HIV1 therapy, Math. Biosci., 185 (2003), 191203. doi: 10.1016/S00255564(03)000919. 
[14] 
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, Vol. 41, American Mathematical Socienty, Providence, RI, 1995. 
[15] 
E. Wagner and M. Hewlett, Basic Virology, Blackwell, New York, 1999. 
[16] 
P. Yu, Y. Ding and W. Jiang, Equivalence of MTS method and CMR method for delay differential equations associated with semisimple singularity, Int. J. Bifurcation and Chaos, 24 (2014), 1450003, 49 pp. doi: 10.1142/S0218127414500035. 
[17] 
P. Yu and X. Zou, Bifurcation analysis on an HIV1 Model with constant injection of recombinant, Int. J. Bifurcation and Chaos, 22 (2012), 1250062, 21 pp. doi: 10.1142/S0218127412500629. 
[18] 
H. Zhu and X. Zou, Impact of delays in cell infection and virus production on HIV1 dynamics, Math. Medic. Bio., 25 (2008), 99112. doi: 10.1093/imammb/dqm010. 
[19] 
H. Zhu and X. Zou, Dynamics of a HIV1 infection model with cellmediated immune response and intracellular delay, Disc. Cont. Dyan. Syst. B., 12 (2009), 511524. doi: 10.3934/dcdsb.2009.12.511. 
show all references
References:
[1] 
E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33 (2002), 11441165. doi: 10.1137/S0036141000376086. 
[2] 
S. Busenberg and K. Cooke, Vertically Transmitted Diseases: Models and Dynamics, Springer, New York, 1993. doi: 10.1007/9783642753015. 
[3]  
[4] 
J. Hale and S. Verduyn Lunel, Introduction to Functional Differential Equations, SpringerVerlag, New York, 1993. doi: 10.1007/9781461243427. 
[5] 
B. D. Hassard, N. D. Kazarinoff and Y.H. Wan, Theory and Applications of Hopf Bifurcation, Cambridge University Press, Cambridge, 1981. 
[6] 
X. Jiang, P. Yu, Z. Yuan and X. Zou, Dynamics of an HIV1 therapy model of fighting a virus with another virus, Journal of Biological Dynamics, 3 (2009), 387409. doi: 10.1080/17513750802485007. 
[7] 
T. Kajiwara, T. Saraki and Y. Takeuchi, Construction of lyapunov functionals for delay differential equations in virology and epidemiology, Nonlinear Analysis: Real World Applications, 13 (2012), 18021826. doi: 10.1016/j.nonrwa.2011.12.011. 
[8] 
J. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, 1976. 
[9] 
C. Michie, A. McLean, C. Alcock and P. Beverly, Lifespan of human lymphocyte subsets defined by cd45 isoforms, Nature, 360 (1992), 264265. doi: 10.1038/360264a0. 
[10] 
J. Mittler, B. Sulzer, A. Neumann and A. Perelson, Influence of delayed virus production on viral dynamics in HIV1 infected patients, Math. Biosci., 152 (1998), 143163. 
[11] 
P. W. Nelson, J. D. Murray and A. S. Perelson, A model of HIV1 pathogenesis that includes an intracellular delay, Mathematical Biosciences, 163 (2000), 201215. doi: 10.1016/S00255564(99)000553. 
[12] 
G. Nolan, Harnessing viral devices as pharmaceuticals: Fighting HIV1s fire with fire, Cell, 90 (1997), 821824. 
[13] 
T. Revilla and G. GarcíaRamos, Fighting a virus with a virus: A dynamic model for HIV1 therapy, Math. Biosci., 185 (2003), 191203. doi: 10.1016/S00255564(03)000919. 
[14] 
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, Vol. 41, American Mathematical Socienty, Providence, RI, 1995. 
[15] 
E. Wagner and M. Hewlett, Basic Virology, Blackwell, New York, 1999. 
[16] 
P. Yu, Y. Ding and W. Jiang, Equivalence of MTS method and CMR method for delay differential equations associated with semisimple singularity, Int. J. Bifurcation and Chaos, 24 (2014), 1450003, 49 pp. doi: 10.1142/S0218127414500035. 
[17] 
P. Yu and X. Zou, Bifurcation analysis on an HIV1 Model with constant injection of recombinant, Int. J. Bifurcation and Chaos, 22 (2012), 1250062, 21 pp. doi: 10.1142/S0218127412500629. 
[18] 
H. Zhu and X. Zou, Impact of delays in cell infection and virus production on HIV1 dynamics, Math. Medic. Bio., 25 (2008), 99112. doi: 10.1093/imammb/dqm010. 
[19] 
H. Zhu and X. Zou, Dynamics of a HIV1 infection model with cellmediated immune response and intracellular delay, Disc. Cont. Dyan. Syst. B., 12 (2009), 511524. doi: 10.3934/dcdsb.2009.12.511. 
[1] 
Jinliang Wang, Lijuan Guan. Global stability for a HIV1 infection model with cellmediated immune response and intracellular delay. Discrete and Continuous Dynamical Systems  B, 2012, 17 (1) : 297302. doi: 10.3934/dcdsb.2012.17.297 
[2] 
Bing Li, Yuming Chen, Xuejuan Lu, Shengqiang Liu. A delayed HIV1 model with virus waning term. Mathematical Biosciences & Engineering, 2016, 13 (1) : 135157. doi: 10.3934/mbe.2016.13.135 
[3] 
Jinhu Xu, Yicang Zhou. Bifurcation analysis of HIV1 infection model with celltocell transmission and immune response delay. Mathematical Biosciences & Engineering, 2016, 13 (2) : 343367. doi: 10.3934/mbe.2015006 
[4] 
Shengqiang Liu, Lin Wang. Global stability of an HIV1 model with distributed intracellular delays and a combination therapy. Mathematical Biosciences & Engineering, 2010, 7 (3) : 675685. doi: 10.3934/mbe.2010.7.675 
[5] 
Hui Miao, Zhidong Teng, Chengjun Kang. Stability and Hopf bifurcation of an HIV infection model with saturation incidence and two delays. Discrete and Continuous Dynamical Systems  B, 2017, 22 (6) : 23652387. doi: 10.3934/dcdsb.2017121 
[6] 
Huiyan Zhu, Xingfu Zou. Dynamics of a HIV1 Infection model with cellmediated immune response and intracellular delay. Discrete and Continuous Dynamical Systems  B, 2009, 12 (2) : 511524. doi: 10.3934/dcdsb.2009.12.511 
[7] 
Fabien Crauste. Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model. Mathematical Biosciences & Engineering, 2006, 3 (2) : 325346. doi: 10.3934/mbe.2006.3.325 
[8] 
Rachid Ouifki, Gareth Witten. A model of HIV1 infection with HAART therapy and intracellular delays. Discrete and Continuous Dynamical Systems  B, 2007, 8 (1) : 229240. doi: 10.3934/dcdsb.2007.8.229 
[9] 
Hossein Mohebbi, Azim Aminataei, Cameron J. Browne, Mohammad Reza Razvan. Hopf bifurcation of an agestructured virus infection model. Discrete and Continuous Dynamical Systems  B, 2018, 23 (2) : 861885. doi: 10.3934/dcdsb.2018046 
[10] 
Yu Yang, Shigui Ruan, Dongmei Xiao. Global stability of an agestructured virus dynamics model with BeddingtonDeAngelis infection function. Mathematical Biosciences & Engineering, 2015, 12 (4) : 859877. doi: 10.3934/mbe.2015.12.859 
[11] 
Hongying Shu, Lin Wang. Global stability and backward bifurcation of a general viral infection model with virusdriven proliferation of target cells. Discrete and Continuous Dynamical Systems  B, 2014, 19 (6) : 17491768. doi: 10.3934/dcdsb.2014.19.1749 
[12] 
Stephen Pankavich, Nathan Neri, Deborah Shutt. Bistable dynamics and Hopf bifurcation in a refined model of early stage HIV infection. Discrete and Continuous Dynamical Systems  B, 2020, 25 (8) : 28672893. doi: 10.3934/dcdsb.2020044 
[13] 
Tinevimbo Shiri, Winston Garira, Senelani D. Musekwa. A twostrain HIV1 mathematical model to assess the effects of chemotherapy on disease parameters. Mathematical Biosciences & Engineering, 2005, 2 (4) : 811832. doi: 10.3934/mbe.2005.2.811 
[14] 
Xia Wang, Shengqiang Liu, Libin Rong. Permanence and extinction of a nonautonomous HIV1 model with time delays. Discrete and Continuous Dynamical Systems  B, 2014, 19 (6) : 17831800. doi: 10.3934/dcdsb.2014.19.1783 
[15] 
Nikolay Pertsev, Konstantin Loginov, Gennady Bocharov. Nonlinear effects in the dynamics of HIV1 infection predicted by mathematical model with multiple delays. Discrete and Continuous Dynamical Systems  S, 2020, 13 (9) : 23652384. doi: 10.3934/dcdss.2020141 
[16] 
Zhijun Liu, Lianwen Wang, Ronghua Tan. Spatiotemporal dynamics for a diffusive HIV1 infection model with distributed delays and CTL immune response. Discrete and Continuous Dynamical Systems  B, 2022, 27 (5) : 27672790. doi: 10.3934/dcdsb.2021159 
[17] 
BaoZhu Guo, LiMing Cai. A note for the global stability of a delay differential equation of hepatitis B virus infection. Mathematical Biosciences & Engineering, 2011, 8 (3) : 689694. doi: 10.3934/mbe.2011.8.689 
[18] 
Runxia Wang, Haihong Liu, Fang Yan, Xiaohui Wang. Hopfpitchfork bifurcation analysis in a coupled FHN neurons model with delay. Discrete and Continuous Dynamical Systems  S, 2017, 10 (3) : 523542. doi: 10.3934/dcdss.2017026 
[19] 
Cuicui Jiang, Kaifa Wang, Lijuan Song. Global dynamics of a delay virus model with recruitment and saturation effects of immune responses. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 12331246. doi: 10.3934/mbe.2017063 
[20] 
Aiping Wang, Michael Y. Li. Viral dynamics of HIV1 with CTL immune response. Discrete and Continuous Dynamical Systems  B, 2021, 26 (4) : 22572272. doi: 10.3934/dcdsb.2020212 
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]