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Low viral persistence of an immunological model
1. | Department of Mathematics, China Agricultural University, Beijing 100083 |
References:
[1] |
P. M. Argium, P. E. Kozarsky and C. Reed, "CDC Health Information for International Travel 2008,", Elsevier, (2007). Google Scholar |
[2] |
S. A. Gourley, Y. Kuang and J. D. Nagy, Dynamics of a delay differential equation model of hepatitis B virus infection,, J. Biological Dynamic, 2 (2008), 140.
doi: 10.1080/17513750701769873. |
[3] |
R. M. Zinkernagel, What is missing in immunology to understand immunity?,, Nat. Immunol., 1 (2000), 181.
doi: 10.1038/79712. |
[4] |
B. Rehermann, C. Ferrari, C. Pasquinelli and F. V. Chisari, The hepatitis B virus persists for decades after patient's recovery from acute viral hepatitis despite active maintenance of a cytotoxic T-lymphocyte response,, Nat. Med., 2 (1996), 1104.
doi: 10.1038/nm1096-1104. |
[5] |
L. Tatyana, R. Dirk and B. Gennady, Numerical bifurcation analysis of immunological models with time delays,, Journal of Computational and Applied Mathematics, 184 (2005), 165.
doi: 10.1016/j.cam.2004.08.019. |
[6] |
L. Tatyana and E. Koen, Low level viral persistence after infection with LCMV: A quantitative insight through numerical bifurcation analysis,, Mathematical Biosciences, 173 (2001), 1.
doi: 10.1016/S0025-5564(01)00072-4. |
[7] |
G. Bocharov and B. Ludewig, etc., Underwhelming the immune response: Effect of slow virus growth rates on $CD8^+ T$ lymphocyte responses,, J. Virol., 78 (2004), 2247.
doi: 10.1128/JVI.78.5.2247-2254.2004. |
[8] |
C. T. H. Baker, Retarded differential equations,, J. Comput. Appl. Math., 125 (2000), 309.
doi: 10.1016/S0377-0427(00)00476-3. |
[9] |
G. A. Bocharov and F. A. Rihan, Numerical modelling in biosciences using delay differential equations,, J. Comput. Appl. Math., 125 (2000), 183.
doi: 10.1016/S0377-0427(00)00468-4. |
[10] |
Z. H. Wang and H. Y. Hu, Stability switches of time-delayed dynamic systems with unknown parameters,, Journal of Sound and Vibration, 233 (2000), 215.
doi: 10.1006/jsvi.1999.2817. |
[11] |
Z. H. Wang and H. Y. Hu, Delay independent stability of retarded dynamic system of multiple degrees of freedom,, Journal of Sound and Vibration, 226 (1999), 57.
doi: 10.1006/jsvi.1999.2282. |
[12] |
S. Q. Ma, Z. S. Feng and Q. S. Lu, The double Hopf bifurcation of a neuron model with time delay,, Int. J. Bifurcation and Chaos, 19 (2009), 3733.
doi: 10.1142/S0218127409025080. |
[13] |
S. Q. Ma and Z. S. Feng, Fold-Hopf Bifurcation of the Rose-Hindmarsh model with time delay,, Int. J. Bifurcation and Chaos, 19 (2011), 437.
doi: 10.1142/S0218127411028490. |
[14] |
K. Engelborghs, T. Luzyanina and D. Roose, Numerical bifurcation analysis of delay differential equations,, J. Comput. Appl. Math., 125 (2000), 265.
doi: 10.1016/S0377-0427(00)00472-6. |
[15] |
K. Engelborghs, T. Luzyanina and D. Roose, Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL,, ACM Trans. Math. Software, 28 (2002), 1.
doi: 10.1145/513001.513002. |
show all references
References:
[1] |
P. M. Argium, P. E. Kozarsky and C. Reed, "CDC Health Information for International Travel 2008,", Elsevier, (2007). Google Scholar |
[2] |
S. A. Gourley, Y. Kuang and J. D. Nagy, Dynamics of a delay differential equation model of hepatitis B virus infection,, J. Biological Dynamic, 2 (2008), 140.
doi: 10.1080/17513750701769873. |
[3] |
R. M. Zinkernagel, What is missing in immunology to understand immunity?,, Nat. Immunol., 1 (2000), 181.
doi: 10.1038/79712. |
[4] |
B. Rehermann, C. Ferrari, C. Pasquinelli and F. V. Chisari, The hepatitis B virus persists for decades after patient's recovery from acute viral hepatitis despite active maintenance of a cytotoxic T-lymphocyte response,, Nat. Med., 2 (1996), 1104.
doi: 10.1038/nm1096-1104. |
[5] |
L. Tatyana, R. Dirk and B. Gennady, Numerical bifurcation analysis of immunological models with time delays,, Journal of Computational and Applied Mathematics, 184 (2005), 165.
doi: 10.1016/j.cam.2004.08.019. |
[6] |
L. Tatyana and E. Koen, Low level viral persistence after infection with LCMV: A quantitative insight through numerical bifurcation analysis,, Mathematical Biosciences, 173 (2001), 1.
doi: 10.1016/S0025-5564(01)00072-4. |
[7] |
G. Bocharov and B. Ludewig, etc., Underwhelming the immune response: Effect of slow virus growth rates on $CD8^+ T$ lymphocyte responses,, J. Virol., 78 (2004), 2247.
doi: 10.1128/JVI.78.5.2247-2254.2004. |
[8] |
C. T. H. Baker, Retarded differential equations,, J. Comput. Appl. Math., 125 (2000), 309.
doi: 10.1016/S0377-0427(00)00476-3. |
[9] |
G. A. Bocharov and F. A. Rihan, Numerical modelling in biosciences using delay differential equations,, J. Comput. Appl. Math., 125 (2000), 183.
doi: 10.1016/S0377-0427(00)00468-4. |
[10] |
Z. H. Wang and H. Y. Hu, Stability switches of time-delayed dynamic systems with unknown parameters,, Journal of Sound and Vibration, 233 (2000), 215.
doi: 10.1006/jsvi.1999.2817. |
[11] |
Z. H. Wang and H. Y. Hu, Delay independent stability of retarded dynamic system of multiple degrees of freedom,, Journal of Sound and Vibration, 226 (1999), 57.
doi: 10.1006/jsvi.1999.2282. |
[12] |
S. Q. Ma, Z. S. Feng and Q. S. Lu, The double Hopf bifurcation of a neuron model with time delay,, Int. J. Bifurcation and Chaos, 19 (2009), 3733.
doi: 10.1142/S0218127409025080. |
[13] |
S. Q. Ma and Z. S. Feng, Fold-Hopf Bifurcation of the Rose-Hindmarsh model with time delay,, Int. J. Bifurcation and Chaos, 19 (2011), 437.
doi: 10.1142/S0218127411028490. |
[14] |
K. Engelborghs, T. Luzyanina and D. Roose, Numerical bifurcation analysis of delay differential equations,, J. Comput. Appl. Math., 125 (2000), 265.
doi: 10.1016/S0377-0427(00)00472-6. |
[15] |
K. Engelborghs, T. Luzyanina and D. Roose, Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL,, ACM Trans. Math. Software, 28 (2002), 1.
doi: 10.1145/513001.513002. |
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