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Remarks on pattern formation in a model for hair follicle spacing
Global behaviour of a delayed viral kinetic model with general incidence rate
1. | Department of Mathematics, Heilongjiang Bayi Agricultural University, Daqing, Heilongjiang, 163319, China |
2. | Department of Mathematics, Harbin Institute of Technology(Weihai), Weihai, Shandong, 264209, China |
References:
[1] |
E. Beretta and Y. Kuang, Geometric stability switches criteria in delay differential systems with delay dependent parameters, Siam. J. Math. Anal., 33 (2002), 1144-1165.
doi: 10.1137/S0036141000376086. |
[2] |
K. Hattaf, N. Yousfi and A. Tridane, A delay virus dynamics model with general incidence rate, Differ. Equ. Dyn. Syst., 22 (2014), 181-190.
doi: 10.1007/s12591-013-0167-5. |
[3] |
S. Hews, S. Eikenberry, J. D. Nagy and Y. Kuang, Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth, Mathematical Biology, 60 (2010), 573-590.
doi: 10.1007/s00285-009-0278-3. |
[4] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[5] |
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, 1993. |
[6] |
J. P. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM Philadelphia, PA, 1976. |
[7] |
D. Li and W. Ma, Asymptotic properties of a HIV-1 infection model with time delay, Journal of Mathematical Analysis and Applications, 335 (2007), 683-691.
doi: 10.1016/j.jmaa.2007.02.006. |
[8] |
M. Y. Li and H. Shu, Global dynamics of an in-host viral model with intracellular delay, Bulletin of Mathematical Biology, 72 (2010), 1492-1505.
doi: 10.1007/s11538-010-9503-x. |
[9] |
Y. Nakata, Global dynamics of a viral infection model with a latent period and Beddington-DeAngelis response, Nonlinear Analysis, 74 (2011), 2929-2940.
doi: 10.1016/j.na.2010.12.030. |
[10] |
M. A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79. |
[11] |
A. S. Perelson, D. E. Kirschner and R. D. Boer, Dynamics of HIV infection of CD$4^+$ T-cells, Math. Biosci., 114 (1993), 81-125.
doi: 10.1016/0025-5564(93)90043-A. |
[12] |
Y. Qu and J. Wei, Bifurcation analysis in a predator-prey system with stage-structure and harvesting, Journal of Franklin Institute, 347 (2010), 1097-1113.
doi: 10.1016/j.jfranklin.2010.03.017. |
[13] |
S. Ruan and J. Wei, On the zeros of transcendental functions with applications to stability of delay differential equations with two delays, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 10 (2003), 863-874. |
[14] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, 41. American Mathematical Society, Providence, RI, 1995. |
[15] |
Y. Song, Y. Peng and J. Wei, Bifurcations for a predator-prey system with two delays, J. Math. Anal. Appl., 337 (2008), 466-479.
doi: 10.1016/j.jmaa.2007.04.001. |
[16] |
J. P. Tian, S. Liao and J. Wang, Analyzing the infection dynamics and control strategies of cholera, Discrete and Continuous Systems, (2013), 747-757. |
[17] |
J. P. Tian and J. Wang, Global stability for cholera epidemic models, Mathematical Bio-sciences, 232 (2011), 31-41.
doi: 10.1016/j.mbs.2011.04.001. |
[18] |
J. Wei and S. Ruan, Stability and bifurcation in a neural network model with two delays, Physica D: Nonlinear Phenomena, 130 (1999), 255-272.
doi: 10.1016/S0167-2789(99)00009-3. |
[19] |
J. Wei and M. Y. Li, Global existence of periodic solutions in a tri-neuron network model with delays, Physica D, 198 (2004), 106-119.
doi: 10.1016/j.physd.2004.08.023. |
show all references
References:
[1] |
E. Beretta and Y. Kuang, Geometric stability switches criteria in delay differential systems with delay dependent parameters, Siam. J. Math. Anal., 33 (2002), 1144-1165.
doi: 10.1137/S0036141000376086. |
[2] |
K. Hattaf, N. Yousfi and A. Tridane, A delay virus dynamics model with general incidence rate, Differ. Equ. Dyn. Syst., 22 (2014), 181-190.
doi: 10.1007/s12591-013-0167-5. |
[3] |
S. Hews, S. Eikenberry, J. D. Nagy and Y. Kuang, Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth, Mathematical Biology, 60 (2010), 573-590.
doi: 10.1007/s00285-009-0278-3. |
[4] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[5] |
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, 1993. |
[6] |
J. P. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM Philadelphia, PA, 1976. |
[7] |
D. Li and W. Ma, Asymptotic properties of a HIV-1 infection model with time delay, Journal of Mathematical Analysis and Applications, 335 (2007), 683-691.
doi: 10.1016/j.jmaa.2007.02.006. |
[8] |
M. Y. Li and H. Shu, Global dynamics of an in-host viral model with intracellular delay, Bulletin of Mathematical Biology, 72 (2010), 1492-1505.
doi: 10.1007/s11538-010-9503-x. |
[9] |
Y. Nakata, Global dynamics of a viral infection model with a latent period and Beddington-DeAngelis response, Nonlinear Analysis, 74 (2011), 2929-2940.
doi: 10.1016/j.na.2010.12.030. |
[10] |
M. A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79. |
[11] |
A. S. Perelson, D. E. Kirschner and R. D. Boer, Dynamics of HIV infection of CD$4^+$ T-cells, Math. Biosci., 114 (1993), 81-125.
doi: 10.1016/0025-5564(93)90043-A. |
[12] |
Y. Qu and J. Wei, Bifurcation analysis in a predator-prey system with stage-structure and harvesting, Journal of Franklin Institute, 347 (2010), 1097-1113.
doi: 10.1016/j.jfranklin.2010.03.017. |
[13] |
S. Ruan and J. Wei, On the zeros of transcendental functions with applications to stability of delay differential equations with two delays, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 10 (2003), 863-874. |
[14] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, 41. American Mathematical Society, Providence, RI, 1995. |
[15] |
Y. Song, Y. Peng and J. Wei, Bifurcations for a predator-prey system with two delays, J. Math. Anal. Appl., 337 (2008), 466-479.
doi: 10.1016/j.jmaa.2007.04.001. |
[16] |
J. P. Tian, S. Liao and J. Wang, Analyzing the infection dynamics and control strategies of cholera, Discrete and Continuous Systems, (2013), 747-757. |
[17] |
J. P. Tian and J. Wang, Global stability for cholera epidemic models, Mathematical Bio-sciences, 232 (2011), 31-41.
doi: 10.1016/j.mbs.2011.04.001. |
[18] |
J. Wei and S. Ruan, Stability and bifurcation in a neural network model with two delays, Physica D: Nonlinear Phenomena, 130 (1999), 255-272.
doi: 10.1016/S0167-2789(99)00009-3. |
[19] |
J. Wei and M. Y. Li, Global existence of periodic solutions in a tri-neuron network model with delays, Physica D, 198 (2004), 106-119.
doi: 10.1016/j.physd.2004.08.023. |
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