Issue
Math. Model. Nat. Phenom.
Volume 15, 2020
Mathematical immunology
Article Number 16
Number of page(s) 20
DOI https://doi.org/10.1051/mmnp/2019038
Published online 12 March 2020
  1. E. Avila-Vales, N. Chan-Chi, G.E. Garcia-Almeida and C. Vargas-De-Leon, Stability and Hopf bifurcation in a delayed viral infection model with mitosis transmission. Appl. Math. Comput. 259 (2015) 293–312. [Google Scholar]
  2. E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J. Math. Anal. 33 (2002) 1144–1165. [CrossRef] [MathSciNet] [Google Scholar]
  3. A.A. Canabarro, I.M. Gl’eria and M.L. Lyra, Periodic solutions and chaos in a non-linear model for the delayed cellular immune response. Physica A 342 (2004) 234–241. [Google Scholar]
  4. M.S. Ciupe, B.L. Bivort, D.M. Bortz and P.W. Nelson, Estimating kinetic paraneters from HIV primary infection data through the eyes of three different mathematical models. Math. Biosci. 200 (2006) 1–27. [Google Scholar]
  5. R.V. Culshaw, S Ruan and G. Webb, A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay. J. Math. Biol. 46 (2003) 425–444. [CrossRef] [PubMed] [Google Scholar]
  6. R.J. De Boer and A.S. Perelson, Target cell limited and immune control models of HIV infection: a comparison. J. Theoret. Biol. 190 (1998) 201–214. [CrossRef] [Google Scholar]
  7. Y. Dong, G. Huang, R. Miyazaki and Y. Takeuchi, Dynamics in a tumor immune system with time delays. Appl. Math. Comput. 252 (2015) 99–113. [Google Scholar]
  8. A.M. Elaiw and N.H. AlShamrani, Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal. Nonlinear Anal. Real World Appl. 26 (2015) 161–190. [Google Scholar]
  9. J.K. Hale and S.M.V. Lunel, Introduction to Functional Differential Equations. Springer Verlag, New York (1993). [CrossRef] [Google Scholar]
  10. B.D. Hassard, N.D. Kazarionoff and Y.H. Wan, Vol. 41 of Theory and Applications of Hopf Bifurcation. CUP Archive (1981). [Google Scholar]
  11. Z. Hu, J. Liu, H. Wang and W. Ma, Analysis of the dynamics of a delayed HIV pathogenesis model. J. Math. Anal. Appl. 234 (2010) 461–476. [Google Scholar]
  12. Z. Hu, J. Zhang, H. Wang, W. Ma and F Liao, Dynamics of a delayed viral infection model with logistic growth and immune impairment. Appl. Math. Model. 38 (2014) 524–534. [Google Scholar]
  13. X. Lai and X. Zou, Modeling HIV-1 virus dynamics with both virus-to-cell infection and cell-to-cell transmission. SIAM J. Appl. Math. 74 (2014) 898–917. [Google Scholar]
  14. 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. [Google Scholar]
  15. F. Li and J. Wang, Analysis of an HIV infection model with logistic target-cell growth and cell-to-cell transmission. Chaos Soliton Fract. 81 (2015) 136–145. [CrossRef] [Google Scholar]
  16. X. Li and J. Wei, On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays. Chaos Solitons Fract. 26 (2005) 519–526. [CrossRef] [MathSciNet] [Google Scholar]
  17. J.Z. Lin, R. Xu and X.H. 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. [Google Scholar]
  18. A. Murase, T. Sasaki and T. Kajiwara, Stability analysis of pathogen-immune interaction dynamics. J. Math. Biol. 51 (2005) 247–267. [CrossRef] [PubMed] [Google Scholar]
  19. Y. Muroya, Y. Enastu and H. Li, Global stability of a delayed HTLV-1 infection model with a class of non-linear incidence rates andCTL simmune response. Appl. Math. Comput. 219 (2013) 59–73. [Google Scholar]
  20. K. 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. Math. Biosci. 235 (2012) 98–109. [Google Scholar]
  21. X.Y. Song, S.L. Wang and J. Dong, Stability properties and Hopf bifurcation of a delayed viral infection model with lytic immune response. J. Math. Anal. Appl. 373 (2011) 345–355. [Google Scholar]
  22. S. Tipsri and W. Chinviriyasit, The effect of time delay on the dynamics of an SEIR model with nonlinear incidence. Chaos Solitons Fract. 75 (2015) 153–172. [CrossRef] [Google Scholar]
  23. C. vargas-de-leon, Stability analysis of a model for HBV infection with cure of infected cells and intracellula delay. Appl. Math. Comput. 219 (2012) 389–398. [Google Scholar]
  24. 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. [CrossRef] [Google Scholar]
  25. T.L. Wang, Z.X. Hu and F.C. Liao, Stability and Hopf bifurcation for a virus infection model with delayed humoral immunity response. J. Math. Anal. Appl. 411 (2014) 63–74. [Google Scholar]
  26. J. Wang, J. Lang and X. Zou, Analysis of an age structured HIV infection model with virus-to-cell infection and cell-to-cell transmission. Nonlinear Anal. Real World Appl. 34 (2017) 75–96. [Google Scholar]
  27. K.F. Wang, W.D. Wang, H.Y. Pang and X.N. Liu, Complex dynamic behavior in a viral model with delaye dimmune response. Physica D 226 (2007) 197–208. [Google Scholar]
  28. K.F. Wang, W.D. Wang and X.N. Liu, Global stability in a viral infection model with lytic and nonlytic immune responses. Comput. Math. Appl. 51 (2006) 1593–1610. [Google Scholar]
  29. 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. [Google Scholar]

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