Global dynamics of a delayed within-host viral infection model with both virus-to-cell and cell-to-cell transmissions

Mathematical Biosciences

Volumn 270, Issue , 2015, Pages 183-191

  Yang, Yu ^a   Zou, Lan ^b   Ruan, Shigui ^c  

^a ZHEJIANG INTERNATIONAL STUDIES UNIVERSITY   (China)

^b SICHUAN UNIVERSITY   (China)

^c University of Miami   (United States)

Author keywords

Distributed delay; Global stability; Hopf bifurcation; Lyapunov functional; Within host dynamics

Indexed keywords

CELLS; DISEASES; DYNAMICS; HOPF BIFURCATION; LYAPUNOV FUNCTIONS; VIRUSES;

34K20; 34K25; 92C50; 92D25; DISTRIBUTED DELAYS; GLOBAL STABILITY; LYAPUNOV FUNCTIONALS;

CYTOLOGY;

BIFURCATION; DISEASE TRANSMISSION; NUMERICAL MODEL; VIRAL DISEASE;

ARTICLE; CELL TO CELL TRANSMISSION; DISTRIBUTED DELAY; DYNAMICS; HEPATITIS B; HUMAN IMMUNODEFICIENCY VIRUS INFECTION; HUMAN T CELL LEUKEMIA VIRUS INFECTION; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; SIMULATION; VIRUS CELL INTERACTION; VIRUS ENTRY; VIRUS INFECTION; VIRUS LATENCY; VIRUS TO CELL TRANSMISSION; VIRUS TRANSMISSION; HOST PATHOGEN INTERACTION; HTLV-1 INFECTION; HUMAN; THEORETICAL MODEL; TRANSMISSION;

HEPATITIS B VIRUS; HUMAN T-LYMPHOTROPIC VIRUS 1;

HEPATITIS B; HIV INFECTIONS; HOST-PATHOGEN INTERACTIONS; HTLV-I INFECTIONS; HUMANS; MODELS, THEORETICAL;

EID: 84949536142     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2015.05.001     Document Type: Article

References (50)

1. Atkinson F.V., Haddock J.R. On determining phase spaces for functional differential equations. Funkcial. Ekvac. 1988, 31:331-347.
2. Bangham C.R.M. The immune control and cell-to-cell spread of human T-lymphotropic virus type 1. J. Gen. Virol. 2003, 84:3177-3189.
3. Banks H.T., Bortz D.M., Holte S.E. Incorporation of variability into the modeling of viral delays in HIV infection dynamics. Math. Biosci. 2003, 183:63-91.
4. Beretta E., Kuang Y. Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J. Math. Anal. 2002, 33:1144-1165.
5. Bonhoeffer S., May R.M., Shaw G.M., Nowak M.A. Virus dynamics and drug therapy. Proc. Natl. Acad. Sci. USA 1997, 94:6971-6976.
6. + T-cells. Math. Biosci. 2000, 165:27-39.
7. Culshaw R.V., Ruan S., Webb G. A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay. J. Math. Biol. 2003, 46:425-444.
8. Dahari H., Loa A., Ribeiroa R.M., Perelson A.S. Modeling hepatitis C virus dynamics: liver regeneration and critical drug efficacy. J. Theor. Biol. 2007, 247:371-381.
9. Debroy S., Bolker B.M., Martcheva M. Bistability and long-term cure in a within-host model of hepatitis C. J. Biol. Syst. 2011, 19:533-550.
10. De Leenheer P., Smith H.L. Virus dynamics: a global analysis. SIAM J. Appl. Math. 2003, 63:1313-1327.
11. Dimitrov D.S., Willey R.L., Sato H., Chang L.-J., Blumenthal R., Martin M.A. Quantitation of human immunodeficiency virus type 1 infection kinetics. J. Virol. 1993, 67:2182-2190.
12. Dixit N.M., Layden-Almer J.E., Layden T.J., Perelson A.S. Modelling how ribavirin improves interferon response rates in hepatitis C virus infection. Nature 2004, 432:922-924.
13. Dixit N.M., Markowitz M., Ho D.D., Perelson A.S. Estimates of intracellular delay and average drug efficacy from viral load data of HIV-infected individuals under antiretroviral therapy. Antivir. Ther. 2004, 9:237-246.
14. Eikenberry S., Hews S., Nagy J.D., Kuang Y. The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth. Math. Biosci. Eng. 2009, 6:283-299.
15. Grossman Z., Feinberg M., Kuznetsov V., Dimitrov D., Paul W. HIV infection: how effective is drug combination treatment?. Immunol. Today 1998, 19:528-532.
16. Grossman Z., Feinberg M., Paul W.E. Multiple modes of cellular activation and virus transmission in HIV infection: a role for chronically and latently infected cells in sustaining viral replication. Proc. Natl. Acad. Sci. USA 1998, 95:6314-6319.
17. Grossman Z., Polis M., Feinberg M.B. et al., Ongoing HIV dissemination during HAART. Nat. Med. 1999, 5:1099-1104.
18. Gummuluru S., Kinsey C.M., Emerman M. An in vitro rapid-turnover assay for human immunodeficiency virus type 1 replication selects for cell-to-cell spread of virua. J. Virol. 2000, 74:10882-10891.
19. Hale J.K., Kato J. Phase space for retarded equations with infinite delay. Funkcial. Ekvac. 1978, 21:11-41.
20. Hale J.K., Lunel S.M.V. Introduction to Functional Differential Equations, Appl. Math. Sci. 1993, Springer-Verlag, New York.
21. Herz A.V.M., Bonhoeffer S., Anderson R.M., May R.M., Nowak M.A. Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay. Proc. Natl. Acad. Sci. USA 1996, 93:7247-7251.
22. Katri P., Ruan S. Dynamics of human T-cell lymphotropic virus i (HTLV-I) infection of CD4+T-cells. Comptes Rendus Biol. 2004, 327(No. 11):1009-1016.
23. Kirschner D.E., Webb G. A model for treatment strategy in the chemotherapy of AIDs. Bull. Math. Biol. 1996, 58:167-190.
24. Kuang Y. Delay Differential Equations with Applications in Population Biology 1993, Academic Press, San Diego.
25. Lai X., Zou X. Modelling HIV-1 virus dynamics with both virus-to-cell infection and cell-to-cell transmission. SIAM J. Appl. Math. 2014, 74:898-917.
26. Li M.Y., Shu H. Impact of intracellular delays and target-cell dynamics on in vivo viral infections. SIAM J. Appl. Math. 2010, 70:2434-2448.
27. Liu S., Wang S., Wang L. Global dynamics of delay epidemic models with nonlinear incidence rate and relapse. Nonlinear Anal. RWA 2011, 11:119-127.
28. Lloyd A.L. The dependence of viral parameter estimates on the assumed viral life cycle: limitations of studies of viral load data. Proc. R. Soc. Lond. B 2001, 268:847-854.
29. Mittler J., Sulzer B., Neumann A., Perelson A. Influence of delayed virus production on viral dynamics in HIV-1 infected patients. Math. Biosci. 1998, 152:143-163.
30. Müller V., Marée A.F.M., De Boer R.J. Small variations in multiple parameters account for wide variations in HIV-1 set-points: a novel modelling approach. Proc. R. Soc. Lond. B 2001, 268:235-242.
31. Nelson P.W., Murray J.D., Perelson A.S. A model of HIV-1 pathogenesis that includes an intracellular delay. Math. Biosci. 2000, 163:201-215.
32. Nelson P.W., Perelson A.S. Mathematical analysis of delay differential equation models of HIV-1 infection. Math. Biosci. 2002, 179:73-94.
33. Neumann A.U., Lam N.P., Dahari H., Gretch D.R., Wiley T.E., Layden T.J., Perelson A.S. Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science 1998, 282:103-107.
34. Nowak M.A., Bangham C.R.M. Population dynamics of immune responses to persistent viruses. Science 1996, 272:74-79.
35. Nowak M.A., May R.M. Virus Dynamics: Mathematical Principles of Immunology and Virology 2000, Oxford University Press, Oxford.
36. Pawelek K.A., Liu S., Pahlevani F., Rong L. A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data. Math. Biosci. 2012, 235:98-109.
37. Perelson A.S., Kirschner D.E., De Boer R. Dynamics of HIV infection of CD4+ T cells. Math. Biosci. 1993, 114:81-125.
38. Perelson A.S., Nelson P.W. Mathematical analysis of HIV-I: dynamics in vivo. SIAM Review 1999, 41:3-44.
39. Pourbashash H., Pilyugin S.S., McCluskey C.C., De Leenheer P. Global analysis of within host virus models with cell-to-cell viral transmission. Discrete Contin. Dyn. Syst. B 2014, 19:3341-3357.
40. Röst G., Wu J. SEIR epidemiological model with varying infectivity and infinite delay. Math. Biosci. Eng. 2008, 5:389-402.
41. Sattentau Q. Avoiding the void: cell-to-cell spread of human viruses. Nat. Rev. Microbiol. 2008, 6:815-826.
42. Shu H., Wang L., Watmough J. Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL immune responses. SIAM J. Appl. Math. 2013, 73:1280-1302.
43. Sigal A., Kim J.T., Balazs A.B., Dekel E., Mayo A., Milo R., Baltimore D. Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy. Nature 2011, 477:95-98.
44. Spouge J.L., Shrager R.I., Dimitrov D.S. HIV-1 infection kinetics in tissue cultures. Math. Biosci. 1996, 138:1-22.
45. Stilianakis N.I., Seydel J. Modeling the T-cell dynamics and pathogenesis of HTLV-I infection. Bull. Math. Biol. 1999, 61:935-947.
46. Wang Y., Zhou Y., Wu J., Hefferman J. Oscillatory viral dynamics in a delayed HIV pathogenesis model. Math. Biosci. 2009, 219:104-112.
47. Sturdevant C.B., Joseph S.B., Schnell G., Price R.W., Swanstrom R. et al., Compartmentalized replication of R5 T cell-tropic HIV-1 in the central nervous system early in the course of infection. PLoS Pathog. 2015, 11(3). 10.1371/journal.ppat.1004720.
48. Wodarz D., Lloyd A.L., Jansen V.A.A., Nowak M.A. Dynamics of macrophage and T cell infection by HIV. J. Theor. Biol. 1999, 196:101-113.
49. Wodarz D., Nowak M.A., Bangham C.R.M. The dynamics of HTLV-I response and the CTL response. Immunol. Today 1999, 20:220-227.
50. Zhu H., Zou X. Impact of delays in cell infection and virus production on HIV-1 dynamics. Math. Med. Biol. 2008, 25:99-112.