-
Previous Article
Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes
- MBE Home
- This Issue
-
Next Article
The impact of migrant workers on the tuberculosis transmission: General models and a case study for China
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, Philadelphia, 2007. |
[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), 140-153.
doi: 10.1080/17513750701769873. |
[3] |
R. M. Zinkernagel, What is missing in immunology to understand immunity?, Nat. Immunol., 1 (2000), 181-185.
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), 1104-1108.
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), 165-176.
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), 1-23.
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), 2247-2254.
doi: 10.1128/JVI.78.5.2247-2254.2004. |
[8] |
C. T. H. Baker, Retarded differential equations, J. Comput. Appl. Math., 125 (2000), 309-335.
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), 183-199.
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), 215-233.
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), 57-81.
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), 3733-3751.
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), 437-452.
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), 265-275.
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), 1-21.
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, Philadelphia, 2007. |
[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), 140-153.
doi: 10.1080/17513750701769873. |
[3] |
R. M. Zinkernagel, What is missing in immunology to understand immunity?, Nat. Immunol., 1 (2000), 181-185.
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), 1104-1108.
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), 165-176.
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), 1-23.
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), 2247-2254.
doi: 10.1128/JVI.78.5.2247-2254.2004. |
[8] |
C. T. H. Baker, Retarded differential equations, J. Comput. Appl. Math., 125 (2000), 309-335.
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), 183-199.
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), 215-233.
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), 57-81.
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), 3733-3751.
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), 437-452.
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), 265-275.
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), 1-21.
doi: 10.1145/513001.513002. |
[1] |
Hongying Shu, Lin Wang. Global stability and backward bifurcation of a general viral infection model with virus-driven proliferation of target cells. Discrete and Continuous Dynamical Systems - B, 2014, 19 (6) : 1749-1768. doi: 10.3934/dcdsb.2014.19.1749 |
[2] |
Ting Guo, Haihong Liu, Chenglin Xu, Fang Yan. Global stability of a diffusive and delayed HBV infection model with HBV DNA-containing capsids and general incidence rate. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4223-4242. doi: 10.3934/dcdsb.2018134 |
[3] |
Alexander Rezounenko. Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1547-1563. doi: 10.3934/dcdsb.2017074 |
[4] |
Alexander Rezounenko. Viral infection model with diffusion and state-dependent delay: Stability of classical solutions. Discrete and Continuous Dynamical Systems - B, 2018, 23 (3) : 1091-1105. doi: 10.3934/dcdsb.2018143 |
[5] |
Jaouad Danane. Optimal control of viral infection model with saturated infection rate. Numerical Algebra, Control and Optimization, 2021, 11 (3) : 363-375. doi: 10.3934/naco.2020031 |
[6] |
Jinhu Xu, Yicang Zhou. Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay. Mathematical Biosciences & Engineering, 2016, 13 (2) : 343-367. doi: 10.3934/mbe.2015006 |
[7] |
Hong Yang, Junjie Wei. Dynamics of spatially heterogeneous viral model with time delay. Communications on Pure and Applied Analysis, 2020, 19 (1) : 85-102. doi: 10.3934/cpaa.2020005 |
[8] |
Stephen Pankavich, Deborah Shutt. An in-host model of HIV incorporating latent infection and viral mutation. Conference Publications, 2015, 2015 (special) : 913-922. doi: 10.3934/proc.2015.0913 |
[9] |
Wei Wang, Wanbiao Ma, Xiulan Lai. Sufficient conditions for global dynamics of a viral infection model with nonlinear diffusion. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3989-4011. doi: 10.3934/dcdsb.2020271 |
[10] |
Yu Ji. Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Mathematical Biosciences & Engineering, 2015, 12 (3) : 525-536. doi: 10.3934/mbe.2015.12.525 |
[11] |
Zhixing Hu, Weijuan Pang, Fucheng Liao, Wanbiao Ma. Analysis of a CD4$^+$ T cell viral infection model with a class of saturated infection rate. Discrete and Continuous Dynamical Systems - B, 2014, 19 (3) : 735-745. doi: 10.3934/dcdsb.2014.19.735 |
[12] |
Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq, Taza Gul, Fawad Hussain. A fractional order HBV model with hospitalization. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 957-974. doi: 10.3934/dcdss.2020056 |
[13] |
Don A. Jones, Hal L. Smith, Horst R. Thieme. Spread of viral infection of immobilized bacteria. Networks and Heterogeneous Media, 2013, 8 (1) : 327-342. doi: 10.3934/nhm.2013.8.327 |
[14] |
Jinliang Wang, Jiying Lang, Xianning Liu. Global dynamics for viral infection model with Beddington-DeAngelis functional response and an eclipse stage of infected cells. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3215-3233. doi: 10.3934/dcdsb.2015.20.3215 |
[15] |
Zhikun She, Xin Jiang. Threshold dynamics of a general delayed within-host viral infection model with humoral immunity and two modes of virus transmission. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3835-3861. doi: 10.3934/dcdsb.2020259 |
[16] |
Yu Ji, Lan Liu. Global stability of a delayed viral infection model with nonlinear immune response and general incidence rate. Discrete and Continuous Dynamical Systems - B, 2016, 21 (1) : 133-149. doi: 10.3934/dcdsb.2016.21.133 |
[17] |
Simona Viale, Elisa Caudera, Sandro Bertolino, Ezio Venturino. A viral transmission model for foxes-cottontails-hares interaction: Infection through predation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5965-5997. doi: 10.3934/dcdsb.2021158 |
[18] |
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) : 2365-2387. doi: 10.3934/dcdsb.2017121 |
[19] |
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) : 2867-2893. doi: 10.3934/dcdsb.2020044 |
[20] |
Hui Cao, Yicang Zhou, Zhien Ma. Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1399-1417. doi: 10.3934/mbe.2013.10.1399 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]