Citation: Jiazhe Lin, Rui Xu, Xiaohong Tian. Threshold dynamics of an HIV-1 model with both viral and cellular infections, cell-mediated and humoral immune responses[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 292-319. doi: 10.3934/mbe.2019015
[1] | R. A. Cangelosi, E. J. Schwartz and D. J. Wollkind, A quasi-steady-state approximation to the basic target-cell-limited viral dynamics model with a non-cytopathic effect, Front. Microbiol., 9 (2018), 54. |
[2] | J. Charles, T. Paul and W. Mark, Immunobiology, 5nd edition, Garland Science, New York, 2001. |
[3] | P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48. |
[4] | A. M. Elaiw and N. H. AlShamrani, Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal, Nonlinear Anal. RWA, 26 (2015), 161–190. |
[5] | A. M. Elaiw, A. A. Raezah and K. Hattaf, Stability of HIV-1 infection with saturated virus-target and infected-target incidences and CTL immune response, Int. J. Biomath., 10 (2017), 1750070. |
[6] | T. R. Fouts, K. Bagley, I. J. Prado, et. al., Balance of cellular and humoral immunity determines the level of protection by HIV vaccines in rhesus macaque models of HIV infection, Proc. Natl. Acad. Sci., 13 (2015), 992–999. |
[7] | J. K. Hale and S. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, New York, 1993. |
[8] | K. Hattaf and N. Yousfi, A class of delayed viral infection models with general incidence rate and adaptive immune response, Int. J. Dynam. Control, 4 (2016), 254. |
[9] | A. Hoare, D. G. Regan and D. P. Wilson, Sampling and sensitivity analyses tools (SaSAT) for computational modelling, Theor. Biol. Med. Model., 5 (2008), 4. |
[10] | G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model of viral infections, SIAM J. Appl. Math., 70 (2010), 2693–2708. |
[11] | X. Lai and X. Zou, Modeling cell-to-cell spread of HIV-1 with logistic target cell growth, J. Math. Anal. Appl., 426 (2015), 563–584. |
[12] | X. Lai and X. Zou, Modeling HIV-1 virus dynamics with both virus-to-cell infection and cell-tocell transmission, SIAM J. Appl. Math., 74 (2014), 898–917. |
[13] | F. Li and J. Wang, Analysis of an HIV infection model with logistic target-cell growth and cellto- cell transmission, Chaos Soliton Fract., 81 (2015), 136–145. |
[14] | J. Lin, R. Xu and X. Tian, Threshold dynamics of an HIV-1 virus model with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity, Appl. Math. Comput., 315 (2017), 516–530. |
[15] | C. Lv, L. Huang and Z. Yuan, Global stability for an HIV-1 infection model with Beddington- DeAngelis incidence rate and CTL immune response, Commun. Nonlinear Sci. Numer. Simulat., 19 (2014), 121–127. |
[16] | S. Marino, I. B. Hogue and C. J. Ray, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254 (2008), 178–196. |
[17] | N. Martin and Q. Sattentau, Cell-to-cell HIV-1 spread and its implications for immune evasion, Curr. Opin. HIV AIDS, 4 (2009), 143–149. |
[18] | A. Murase, T. Sasaki and T. Kajiwara, Stability analysis of pathogen-immune interaction dynamics, J. Math. Biol., 51 (2005), 247–267. |
[19] | Y. Nakata, Global dynamics of a cell mediated immunity in viral infection models with distributed delays, J. Math. Anal. Appl., 375 (2011), 14–27. |
[20] | M. Nowak, S. Bonhoeffer, G. Shaw and R. May, Anti-viral drug treatment: Dynamics of resistance in free virus and infected cell populations, J. Theor. Biol., 184 (1997), 203–217. |
[21] | A. S. Perelson and P. W. Nelson, Mathematical Analysis of HIV-1: Dynamics in Vivo, SIAM Review, 41 (1999), 3–44. |
[22] | R. R. Regoes, D. Ebert and S. Bonhoeffer, Dose-dependent infection rates of parasites produce the Allee effect in epidemiology, Proc. R. Soc. Lond. Ser. B, 269 (2002), 271–279. |
[23] | E. J. Schwartz, N. K. Vaidya, K. S. Dorman, S. Carpenter and R. H. Mealey, Dynamics of lentiviral infection in vivo in the absence of adaptive immune responses, Virology, 513 (2018), 108–113. |
[24] | 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. |
[25] | A. Sigal, J. T. Kim, A. B. Balazs, E. Dekel, A. Mayo, R. Milo and D. Baltimore, Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy, Nature, 477 (2011), 95–98. |
[26] | J. Wang, M. Guo, X. Liu and Z. Zhao, Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay, Appl. Math. Comput., 291 (2016), 149–161. |
[27] | J. Wang, J. Pang, T.Kuniya and Y. Enatsu, Global threshold dynamics in a five-dimensional virus model with cell-mediated, humoral immune responses and distributed delays, Appl. Math. Comput., 241 (2014), 298–316. |
[28] | S. Wang and D. Zou, Global stability of in-host viral models with humoral immunity and intracellular delays, Appl. Math. Model., 36 (2012), 1313–1322. |
[29] | T. Wang, Z. Hu, F. Liao and W. Ma, Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity, Math. Comput. Simulat., 89 (2013), 13–22. |
[30] | T.Wang, Z. Hu and F. Liao, Stability and Hopf bifurcation for a virus infection model with delayed humoral immunity response, J. Math. Anal. Appl., 411 (2014), 63–74. |
[31] | R. Xu, Global stability of an HIV-1 infection model with saturation infection and intracellular delay, J. Math. Anal. Appl., 375 (2011), 75–81. |
[32] | J. Xu, Y. Geng and Y. Zhou, Global dynamics for an age-structured HIV virus infection model with cellular infection and antiretroviral therapy, Appl. Math. Comput., 305 (2017), 62–83. |
[33] | Y. Yan and W. Wang, Global stability of a five-dimensional model with immune responses and delay, Discrete and Continuous Dynamical Systems - Series B, 17 (2012), 401–416. |
[34] | H. Zhu and X. Zou, Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay, Discrete and Continuous Dynamical Systems - Series B, 12 (2009), 511– 524. |