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A delayed HIV-1 model with virus waning term
1. | Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, 3041#, 2 Yi-Kuang street, Harbin, 150080, China |
2. | Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada |
3. | Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street, Harbin, 150080 |
References:
[1] |
, Possible transfusion-associated acquired immune deficiency syndrome (AIDS)- California,, MMWR Morb Mortal Wkly Rep, 31 (1982), 652.
|
[2] |
, Unexplained immunodeficiency and opportunistic infections infants-New York,, New Jersey, 31 (1982), 665.
|
[3] |
, Immunodeficiency among female sexual partners males with acquired immune deficiency syndrome(AIDS)-New York,, MMWR Morb Mortal Wkly Rep, 31 (1983), 697.
|
[4] |
D. Burg, L. Rong, A. Neumann and H. Dahari, Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection, J. Theor. Biol., 259 (2009), 751-759.
doi: 10.1016/j.jtbi.2009.04.010. |
[5] |
M. Ciupe, B. Bivort, D. Bortz and P. Nelson, Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models, Math. Biosci., 200 (2006), 1-27.
doi: 10.1016/j.mbs.2005.12.006. |
[6] |
V. R. Culshaw, S. Ruan and R. J. Spiteri, Optimal HIV treatment by maximising immune response, J. Math. Biol., 48 (2004), 545-562.
doi: 10.1007/s00285-003-0245-3. |
[7] |
P. de Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327.
doi: 10.1137/S0036139902406905. |
[8] |
A. S. Fauci, HIV and AIDS: 20 years of science, Nature Medicine, 9 (2003), 839-843.
doi: 10.1038/nm0703-839. |
[9] |
R. C. Gallo, Historical essay. The early years of HIV/AIDS, Science, 298 (2002), 1728-1730.
doi: 10.1126/science.1078050. |
[10] |
J. K. Hale and S. V. Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4342-7. |
[11] |
J. M. Heffernan and L. M. Wahl, Monte carlo estimates of natural variation in HIV infection, J. Theor. Biol., 236 (2005), 137-153.
doi: 10.1016/j.jtbi.2005.03.002. |
[12] |
V. Herz, S. Bonhoeffer, R. Anderson, R. M. May and M. A. Nowak, Viral dynamics in vivo: Limitations on estimations on intracellular delay and virus delay, Proc. Natl. Acad. Sci. USA, 93 (1996), 7247-7251.
doi: 10.1073/pnas.93.14.7247. |
[13] |
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals of delay differential equations model of viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708.
doi: 10.1137/090780821. |
[14] |
A. Kent and M. D. Sepkowitz, AIDS-The First 20 Years, The New England Journal of Medicine, 344 (2001), 1764-1772. |
[15] |
B. Li and S. Liu, A delayed HIV-1 model with multiple target cells and general nonlinear incidence rate, Journal of Biological Systems, 21 (2013), 1340012, 20pp.
doi: 10.1142/S0218339013400123. |
[16] |
M. Y. Li and H. Shu, Impact of intercellular delays and target-cell dynamics on in vivo viral infections, SIAM J. Appl. Math., 70 (2010), 2434-2448.
doi: 10.1137/090779322. |
[17] |
S. Liu and L. Wang, Global stability of an HIV-1 model with distributed intercellular delays and a combination therapy, Mathematical Biosciences and Engineering, 7 (2010), 675-685.
doi: 10.3934/mbe.2010.7.675. |
[18] |
X. Lu, L. Hui, S. Liu and J. Li, A Mathematical model of HTLV-1 infection with two time delays, Mathematical Biosciences and Engineering, 12 (2015), 431-449.
doi: 10.3934/mbe.2015.12.431. |
[19] |
L. Montagnier, Historical essay. A history of HIV discovery, Science, 298 (2002), 1727-1728.
doi: 10.1126/science.1079027. |
[20] |
M. A. Nowak and C. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79.
doi: 10.1126/science.272.5258.74. |
[21] |
M. A. Nowak and R. M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, Oxford, 2000. |
[22] |
K. A. Pawelek, S. Liu, F. Pahlevani and L. Rong, A model of HIV-1 infection with two time delays: Mathematical analysis and comparison with patient data, Mathematical Biosciences, 235 (2012), 98-109.
doi: 10.1016/j.mbs.2011.11.002. |
[23] |
J. E. Pearson, P. Krapivsky and A. S. Perelson, Stochastic theory of early viral infection: Continuous versus burst productionofvirions, PLoS Comput Biol., 7 (2011), e1001058, 17 pp.
doi: 10.1371/journal.pcbi.1001058. |
[24] |
A. S. Perelson, A. U. Neumann, M. Markowitz, J. M. Leonard and D. D. Ho, HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time, Science, 271 (1996), 1582-1586.
doi: 10.1126/science.271.5255.1582. |
[25] |
R. Ribeiro, L. Qin, L. Chavez, D. Li, S. Self and A. Perelson, Estimation of the Initial Viral Growth Rate and Basic Reproductive Number during Acute HIV-1 Infection, Journal of Virology, 84 (2010), 6096-6102.
doi: 10.1128/JVI.00127-10. |
[26] |
L. Rong, Z. Feng and A. S. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bulletin of Mathematical Biology, 69 (2007), 2027-2060.
doi: 10.1007/s11538-007-9203-3. |
[27] |
H. Shu, L. Wang and J. Watmough, Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL immune responses, SIAM J. Appl. Math., 73 (2013), 1280-1302.
doi: 10.1137/120896463. |
[28] |
H. L. Smith and X. Zhao, Robust persistence for semidynamical systems, Nonlinear Anal., 47 (2001), 6169-6179.
doi: 10.1016/S0362-546X(01)00678-2. |
[29] |
H. Song, W. Jiang and S. Liu, Virus dynamics model with intracellular delays and immune response, Mathematical biosciences and engineering, 12 (2015), 185-208.
doi: 10.3934/mbe.2015.12.xx. |
[30] |
M. A. Stafford, L. Corey, Y. Cao, E. S. Daar, D. D. Ho and A. S. Perelson, Modeling plasma virus concentration during primary HIV infection, J. Theor. Biol., 203 (2000), 285-301.
doi: 10.1006/jtbi.2000.1076. |
[31] |
X. Wang and S. Liu, A class of delayed viral models with saturation infection rate and immune response, Mathematical Methods in the Applied Science, 36 (2013), 125-142.
doi: 10.1002/mma.2576. |
[32] |
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), 901-934.
doi: 10.1007/s00285-012-0580-3. |
[33] |
J. Wei and S. Ruan, Stability and bifurcation in a neural network model with two delays, Physica D, 130 (1999), 255-272.
doi: 10.1016/S0167-2789(99)00009-3. |
[34] |
X. Zhao, Dynamical Systems in Population Biology, Springer, Berlin, 2003.
doi: 10.1007/978-0-387-21761-1. |
show all references
References:
[1] |
, Possible transfusion-associated acquired immune deficiency syndrome (AIDS)- California,, MMWR Morb Mortal Wkly Rep, 31 (1982), 652.
|
[2] |
, Unexplained immunodeficiency and opportunistic infections infants-New York,, New Jersey, 31 (1982), 665.
|
[3] |
, Immunodeficiency among female sexual partners males with acquired immune deficiency syndrome(AIDS)-New York,, MMWR Morb Mortal Wkly Rep, 31 (1983), 697.
|
[4] |
D. Burg, L. Rong, A. Neumann and H. Dahari, Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection, J. Theor. Biol., 259 (2009), 751-759.
doi: 10.1016/j.jtbi.2009.04.010. |
[5] |
M. Ciupe, B. Bivort, D. Bortz and P. Nelson, Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models, Math. Biosci., 200 (2006), 1-27.
doi: 10.1016/j.mbs.2005.12.006. |
[6] |
V. R. Culshaw, S. Ruan and R. J. Spiteri, Optimal HIV treatment by maximising immune response, J. Math. Biol., 48 (2004), 545-562.
doi: 10.1007/s00285-003-0245-3. |
[7] |
P. de Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327.
doi: 10.1137/S0036139902406905. |
[8] |
A. S. Fauci, HIV and AIDS: 20 years of science, Nature Medicine, 9 (2003), 839-843.
doi: 10.1038/nm0703-839. |
[9] |
R. C. Gallo, Historical essay. The early years of HIV/AIDS, Science, 298 (2002), 1728-1730.
doi: 10.1126/science.1078050. |
[10] |
J. K. Hale and S. V. Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4342-7. |
[11] |
J. M. Heffernan and L. M. Wahl, Monte carlo estimates of natural variation in HIV infection, J. Theor. Biol., 236 (2005), 137-153.
doi: 10.1016/j.jtbi.2005.03.002. |
[12] |
V. Herz, S. Bonhoeffer, R. Anderson, R. M. May and M. A. Nowak, Viral dynamics in vivo: Limitations on estimations on intracellular delay and virus delay, Proc. Natl. Acad. Sci. USA, 93 (1996), 7247-7251.
doi: 10.1073/pnas.93.14.7247. |
[13] |
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals of delay differential equations model of viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708.
doi: 10.1137/090780821. |
[14] |
A. Kent and M. D. Sepkowitz, AIDS-The First 20 Years, The New England Journal of Medicine, 344 (2001), 1764-1772. |
[15] |
B. Li and S. Liu, A delayed HIV-1 model with multiple target cells and general nonlinear incidence rate, Journal of Biological Systems, 21 (2013), 1340012, 20pp.
doi: 10.1142/S0218339013400123. |
[16] |
M. Y. Li and H. Shu, Impact of intercellular delays and target-cell dynamics on in vivo viral infections, SIAM J. Appl. Math., 70 (2010), 2434-2448.
doi: 10.1137/090779322. |
[17] |
S. Liu and L. Wang, Global stability of an HIV-1 model with distributed intercellular delays and a combination therapy, Mathematical Biosciences and Engineering, 7 (2010), 675-685.
doi: 10.3934/mbe.2010.7.675. |
[18] |
X. Lu, L. Hui, S. Liu and J. Li, A Mathematical model of HTLV-1 infection with two time delays, Mathematical Biosciences and Engineering, 12 (2015), 431-449.
doi: 10.3934/mbe.2015.12.431. |
[19] |
L. Montagnier, Historical essay. A history of HIV discovery, Science, 298 (2002), 1727-1728.
doi: 10.1126/science.1079027. |
[20] |
M. A. Nowak and C. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79.
doi: 10.1126/science.272.5258.74. |
[21] |
M. A. Nowak and R. M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, Oxford, 2000. |
[22] |
K. A. Pawelek, S. Liu, F. Pahlevani and L. Rong, A model of HIV-1 infection with two time delays: Mathematical analysis and comparison with patient data, Mathematical Biosciences, 235 (2012), 98-109.
doi: 10.1016/j.mbs.2011.11.002. |
[23] |
J. E. Pearson, P. Krapivsky and A. S. Perelson, Stochastic theory of early viral infection: Continuous versus burst productionofvirions, PLoS Comput Biol., 7 (2011), e1001058, 17 pp.
doi: 10.1371/journal.pcbi.1001058. |
[24] |
A. S. Perelson, A. U. Neumann, M. Markowitz, J. M. Leonard and D. D. Ho, HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time, Science, 271 (1996), 1582-1586.
doi: 10.1126/science.271.5255.1582. |
[25] |
R. Ribeiro, L. Qin, L. Chavez, D. Li, S. Self and A. Perelson, Estimation of the Initial Viral Growth Rate and Basic Reproductive Number during Acute HIV-1 Infection, Journal of Virology, 84 (2010), 6096-6102.
doi: 10.1128/JVI.00127-10. |
[26] |
L. Rong, Z. Feng and A. S. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bulletin of Mathematical Biology, 69 (2007), 2027-2060.
doi: 10.1007/s11538-007-9203-3. |
[27] |
H. Shu, L. Wang and J. Watmough, Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL immune responses, SIAM J. Appl. Math., 73 (2013), 1280-1302.
doi: 10.1137/120896463. |
[28] |
H. L. Smith and X. Zhao, Robust persistence for semidynamical systems, Nonlinear Anal., 47 (2001), 6169-6179.
doi: 10.1016/S0362-546X(01)00678-2. |
[29] |
H. Song, W. Jiang and S. Liu, Virus dynamics model with intracellular delays and immune response, Mathematical biosciences and engineering, 12 (2015), 185-208.
doi: 10.3934/mbe.2015.12.xx. |
[30] |
M. A. Stafford, L. Corey, Y. Cao, E. S. Daar, D. D. Ho and A. S. Perelson, Modeling plasma virus concentration during primary HIV infection, J. Theor. Biol., 203 (2000), 285-301.
doi: 10.1006/jtbi.2000.1076. |
[31] |
X. Wang and S. Liu, A class of delayed viral models with saturation infection rate and immune response, Mathematical Methods in the Applied Science, 36 (2013), 125-142.
doi: 10.1002/mma.2576. |
[32] |
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), 901-934.
doi: 10.1007/s00285-012-0580-3. |
[33] |
J. Wei and S. Ruan, Stability and bifurcation in a neural network model with two delays, Physica D, 130 (1999), 255-272.
doi: 10.1016/S0167-2789(99)00009-3. |
[34] |
X. Zhao, Dynamical Systems in Population Biology, Springer, Berlin, 2003.
doi: 10.1007/978-0-387-21761-1. |
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